Re: Coherent states of a superposition

2019-02-11 Thread Bruno Marchal

> On 11 Feb 2019, at 13:00, agrayson2...@gmail.com wrote:
> 
> 
> 
> On Monday, February 11, 2019 at 2:20:25 AM UTC, agrays...@gmail.com wrote:
> 
> 
> On Tuesday, February 5, 2019 at 8:43:59 PM UTC, agrays...@gmail.com <> wrote:
> 
> 
> On Monday, February 4, 2019 at 8:56:57 AM UTC-7, Bruno Marchal wrote:
> 
>> On 3 Feb 2019, at 00:03, agrays...@gmail.com <> wrote:
>> 
>> 
>> 
>> On Saturday, February 2, 2019 at 2:59:30 PM UTC-7, agrays...@gmail.com 
>>  wrote:
>> 
>> 
>> On Saturday, February 2, 2019 at 1:40:29 AM UTC-7, Bruno Marchal wrote:
>> 
>>> On 1 Feb 2019, at 21:29, agrays...@gmail.com <> wrote:
>>> 
>>> 
>>> 
>>> On Friday, February 1, 2019 at 5:55:30 AM UTC-7, Bruno Marchal wrote:
>>> 
 On 31 Jan 2019, at 21:10, agrays...@gmail.com <> wrote:
 
 
 
 On Thursday, January 31, 2019 at 6:47:12 AM UTC-7, Bruno Marchal wrote:
 
> On 31 Jan 2019, at 01:28, agrays...@gmail.com <> wrote:
> 
> 
> 
> On Wednesday, January 30, 2019 at 2:38:58 PM UTC-7, agrays...@gmail.com 
>  wrote:
> 
> 
> On Wednesday, January 30, 2019 at 5:16:05 AM UTC-7, Bruno Marchal wrote:
> 
>> On 30 Jan 2019, at 02:59, agrays...@gmail.com <> wrote:
>> 
>> 
>> 
>> On Tuesday, January 29, 2019 at 4:37:34 AM UTC-7, Bruno Marchal wrote:
>> 
>>> On 28 Jan 2019, at 22:50, agrays...@gmail.com <> wrote:
>>> 
>>> 
>>> 
>>> On Friday, January 25, 2019 at 7:33:05 AM UTC-7, Bruno Marchal wrote:
>>> 
 On 24 Jan 2019, at 09:29, agrays...@gmail.com <> wrote:
 
 
 
 On Sunday, January 20, 2019 at 11:54:43 AM UTC, agrays...@gmail.com 
  wrote:
 
 
 On Sunday, January 20, 2019 at 9:56:17 AM UTC, Bruno Marchal wrote:
 
> On 18 Jan 2019, at 18:50, agrays...@gmail.com <> wrote:
> 
> 
> 
> On Friday, January 18, 2019 at 12:09:58 PM UTC, Bruno Marchal wrote:
> 
>> On 17 Jan 2019, at 14:48, agrays...@gmail.com <> wrote:
>> 
>> 
>> 
>> On Thursday, January 17, 2019 at 12:36:07 PM UTC, Bruno Marchal 
>> wrote:
>> 
>>> On 17 Jan 2019, at 09:33, agrays...@gmail.com <> wrote:
>>> 
>>> 
>>> 
>>> On Thursday, January 17, 2019 at 3:58:48 AM UTC, Brent wrote:
>>> 
>>> 
>>> On 1/16/2019 7:25 PM, agrays...@gmail.com <> wrote:
 
 
 On Monday, January 14, 2019 at 6:12:43 AM UTC, Brent wrote:
 
 
 On 1/13/2019 9:51 PM, agrays...@gmail.com <> wrote:
> This means, to me, that the arbitrary phase angles have 
> absolutely no effect on the resultant interference pattern which 
> is observed. But isn't this what the phase angles are supposed to 
> effect? AG
 
 The screen pattern is determined by relative phase angles for the 
 different paths that reach the same point on the screen.  The 
 relative angles only depend on different path lengths, so the 
 overall phase angle is irrelevant.
 
 Brent
 
 Sure, except there areTWO forms of phase interference in Wave 
 Mechanics; the one you refer to above, and another discussed in 
 the Stackexchange links I previously posted. In the latter case, 
 the wf is expressed as a superposition, say of two states, where 
 we consider two cases; a multiplicative complex phase shift is 
 included prior to the sum, and different complex phase shifts 
 multiplying each component, all of the form e^i (theta). Easy to 
 show that interference exists in the latter case, but not the 
 former. Now suppose we take the inner product of the wf with the 
 ith eigenstate of the superposition, in order to calculate the 
 probability of measuring the eigenvalue of the ith eigenstate, 
 applying one of the postulates of QM, keeping in mind that each 
 eigenstate is multiplied by a DIFFERENT complex phase shift.  If 
 we further assume the eigenstates are mutually orthogonal, the 
 probability of measuring each eigenvalue does NOT depend on the 
 different phase shifts. What happened to the interference 
 demonstrated by the Stackexchange links? TIA, AG 
 
>>> Your measurement projected it out. It's like measuring which slit 
>>> the photon goes through...it eliminates the interference.
>>> 
>>> Brent
>>> 
>>> That's what I suspected; that going to an orthogonal basis, I 
>>> departed from the examples in Stackexchange where an arbitrary 
>>> superposition is 

Re: Coherent states of a superposition

2019-02-11 Thread agrayson2000


On Monday, February 11, 2019 at 2:20:25 AM UTC, agrays...@gmail.com wrote:
>
>
>
> On Tuesday, February 5, 2019 at 8:43:59 PM UTC, agrays...@gmail.com wrote:
>>
>>
>>
>> On Monday, February 4, 2019 at 8:56:57 AM UTC-7, Bruno Marchal wrote:
>>>
>>>
>>> On 3 Feb 2019, at 00:03, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Saturday, February 2, 2019 at 2:59:30 PM UTC-7, agrays...@gmail.com 
>>> wrote:



 On Saturday, February 2, 2019 at 1:40:29 AM UTC-7, Bruno Marchal wrote:
>
>
> On 1 Feb 2019, at 21:29, agrays...@gmail.com wrote:
>
>
>
> On Friday, February 1, 2019 at 5:55:30 AM UTC-7, Bruno Marchal wrote:
>>
>>
>> On 31 Jan 2019, at 21:10, agrays...@gmail.com wrote:
>>
>>
>>
>> On Thursday, January 31, 2019 at 6:47:12 AM UTC-7, Bruno Marchal 
>> wrote:
>>>
>>>
>>> On 31 Jan 2019, at 01:28, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Wednesday, January 30, 2019 at 2:38:58 PM UTC-7, agrays...@
>>> gmail.com wrote:



 On Wednesday, January 30, 2019 at 5:16:05 AM UTC-7, Bruno Marchal 
 wrote:
>
>
> On 30 Jan 2019, at 02:59, agrays...@gmail.com wrote:
>
>
>
> On Tuesday, January 29, 2019 at 4:37:34 AM UTC-7, Bruno Marchal 
> wrote:
>>
>>
>> On 28 Jan 2019, at 22:50, agrays...@gmail.com wrote:
>>
>>
>>
>> On Friday, January 25, 2019 at 7:33:05 AM UTC-7, Bruno Marchal 
>> wrote:
>>>
>>>
>>> On 24 Jan 2019, at 09:29, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Sunday, January 20, 2019 at 11:54:43 AM UTC, agrays...@
>>> gmail.com wrote:



 On Sunday, January 20, 2019 at 9:56:17 AM UTC, Bruno Marchal 
 wrote:
>
>
> On 18 Jan 2019, at 18:50, agrays...@gmail.com wrote:
>
>
>
> On Friday, January 18, 2019 at 12:09:58 PM UTC, Bruno Marchal 
> wrote:
>>
>>
>> On 17 Jan 2019, at 14:48, agrays...@gmail.com wrote:
>>
>>
>>
>> On Thursday, January 17, 2019 at 12:36:07 PM UTC, Bruno 
>> Marchal wrote:
>>>
>>>
>>> On 17 Jan 2019, at 09:33, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Thursday, January 17, 2019 at 3:58:48 AM UTC, Brent wrote:



 On 1/16/2019 7:25 PM, agrays...@gmail.com wrote:



 On Monday, January 14, 2019 at 6:12:43 AM UTC, Brent wrote:
>
>
>
> On 1/13/2019 9:51 PM, agrays...@gmail.com wrote:
>
> This means, to me, that the arbitrary phase angles have 
> absolutely no effect on the resultant interference pattern 
> which is 
> observed. But isn't this what the phase angles are supposed 
> to effect? AG
>
>
> The screen pattern is determined by *relative phase 
> angles for the different paths that reach the same point on 
> the screen*.  
> The relative angles only depend on different path lengths, so 
> the overall 
> phase angle is irrelevant.
>
> Brent
>


 *Sure, except there areTWO forms of phase interference in 
 Wave Mechanics; the one you refer to above, and another 
 discussed in the 
 Stackexchange links I previously posted. In the latter case, 
 the wf is 
 expressed as a superposition, say of two states, where we 
 consider two 
 cases; a multiplicative complex phase shift is included prior 
 to the sum, 
 and different complex phase shifts multiplying each component, 
 all of the 
 form e^i (theta). Easy to show that interference exists in the 
 latter case, 
 but not the former. Now suppose we take the inner product of 
 the wf with 
 the ith eigenstate of the superposition, in order to calculate 
 the 
 probability of measuring the eigenvalue of the ith eigenstate, 
 applying one 
 of the postulates of QM, keeping in mind that each eigenstate 
 is multiplied 
 by a DIFFERENT complex 

Re: Coherent states of a superposition

2019-02-10 Thread agrayson2000


On Tuesday, February 5, 2019 at 8:43:59 PM UTC, agrays...@gmail.com wrote:
>
>
>
> On Monday, February 4, 2019 at 8:56:57 AM UTC-7, Bruno Marchal wrote:
>>
>>
>> On 3 Feb 2019, at 00:03, agrays...@gmail.com wrote:
>>
>>
>>
>> On Saturday, February 2, 2019 at 2:59:30 PM UTC-7, agrays...@gmail.com 
>> wrote:
>>>
>>>
>>>
>>> On Saturday, February 2, 2019 at 1:40:29 AM UTC-7, Bruno Marchal wrote:


 On 1 Feb 2019, at 21:29, agrays...@gmail.com wrote:



 On Friday, February 1, 2019 at 5:55:30 AM UTC-7, Bruno Marchal wrote:
>
>
> On 31 Jan 2019, at 21:10, agrays...@gmail.com wrote:
>
>
>
> On Thursday, January 31, 2019 at 6:47:12 AM UTC-7, Bruno Marchal wrote:
>>
>>
>> On 31 Jan 2019, at 01:28, agrays...@gmail.com wrote:
>>
>>
>>
>> On Wednesday, January 30, 2019 at 2:38:58 PM UTC-7, agrays...@
>> gmail.com wrote:
>>>
>>>
>>>
>>> On Wednesday, January 30, 2019 at 5:16:05 AM UTC-7, Bruno Marchal 
>>> wrote:


 On 30 Jan 2019, at 02:59, agrays...@gmail.com wrote:



 On Tuesday, January 29, 2019 at 4:37:34 AM UTC-7, Bruno Marchal 
 wrote:
>
>
> On 28 Jan 2019, at 22:50, agrays...@gmail.com wrote:
>
>
>
> On Friday, January 25, 2019 at 7:33:05 AM UTC-7, Bruno Marchal 
> wrote:
>>
>>
>> On 24 Jan 2019, at 09:29, agrays...@gmail.com wrote:
>>
>>
>>
>> On Sunday, January 20, 2019 at 11:54:43 AM UTC, agrays...@
>> gmail.com wrote:
>>>
>>>
>>>
>>> On Sunday, January 20, 2019 at 9:56:17 AM UTC, Bruno Marchal 
>>> wrote:


 On 18 Jan 2019, at 18:50, agrays...@gmail.com wrote:



 On Friday, January 18, 2019 at 12:09:58 PM UTC, Bruno Marchal 
 wrote:
>
>
> On 17 Jan 2019, at 14:48, agrays...@gmail.com wrote:
>
>
>
> On Thursday, January 17, 2019 at 12:36:07 PM UTC, Bruno 
> Marchal wrote:
>>
>>
>> On 17 Jan 2019, at 09:33, agrays...@gmail.com wrote:
>>
>>
>>
>> On Thursday, January 17, 2019 at 3:58:48 AM UTC, Brent wrote:
>>>
>>>
>>>
>>> On 1/16/2019 7:25 PM, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Monday, January 14, 2019 at 6:12:43 AM UTC, Brent wrote:



 On 1/13/2019 9:51 PM, agrays...@gmail.com wrote:

 This means, to me, that the arbitrary phase angles have 
 absolutely no effect on the resultant interference pattern 
 which is 
 observed. But isn't this what the phase angles are supposed to 
 effect? AG


 The screen pattern is determined by *relative phase angles 
 for the different paths that reach the same point on the 
 screen*.  
 The relative angles only depend on different path lengths, so 
 the overall 
 phase angle is irrelevant.

 Brent

>>>
>>>
>>> *Sure, except there areTWO forms of phase interference in 
>>> Wave Mechanics; the one you refer to above, and another 
>>> discussed in the 
>>> Stackexchange links I previously posted. In the latter case, 
>>> the wf is 
>>> expressed as a superposition, say of two states, where we 
>>> consider two 
>>> cases; a multiplicative complex phase shift is included prior 
>>> to the sum, 
>>> and different complex phase shifts multiplying each component, 
>>> all of the 
>>> form e^i (theta). Easy to show that interference exists in the 
>>> latter case, 
>>> but not the former. Now suppose we take the inner product of 
>>> the wf with 
>>> the ith eigenstate of the superposition, in order to calculate 
>>> the 
>>> probability of measuring the eigenvalue of the ith eigenstate, 
>>> applying one 
>>> of the postulates of QM, keeping in mind that each eigenstate 
>>> is multiplied 
>>> by a DIFFERENT complex phase shift.  If we further assume the 
>>> eigenstates 
>>> are mutually orthogonal, the probability of measuring each 
>>> eigenvalue does 
>>> NOT depend on the different phase shifts. What 

Re: Coherent states of a superposition

2019-02-05 Thread agrayson2000


On Monday, February 4, 2019 at 8:56:57 AM UTC-7, Bruno Marchal wrote:
>
>
> On 3 Feb 2019, at 00:03, agrays...@gmail.com  wrote:
>
>
>
> On Saturday, February 2, 2019 at 2:59:30 PM UTC-7, agrays...@gmail.com 
> wrote:
>>
>>
>>
>> On Saturday, February 2, 2019 at 1:40:29 AM UTC-7, Bruno Marchal wrote:
>>>
>>>
>>> On 1 Feb 2019, at 21:29, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Friday, February 1, 2019 at 5:55:30 AM UTC-7, Bruno Marchal wrote:


 On 31 Jan 2019, at 21:10, agrays...@gmail.com wrote:



 On Thursday, January 31, 2019 at 6:47:12 AM UTC-7, Bruno Marchal wrote:
>
>
> On 31 Jan 2019, at 01:28, agrays...@gmail.com wrote:
>
>
>
> On Wednesday, January 30, 2019 at 2:38:58 PM UTC-7, agrays...@
> gmail.com wrote:
>>
>>
>>
>> On Wednesday, January 30, 2019 at 5:16:05 AM UTC-7, Bruno Marchal 
>> wrote:
>>>
>>>
>>> On 30 Jan 2019, at 02:59, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Tuesday, January 29, 2019 at 4:37:34 AM UTC-7, Bruno Marchal 
>>> wrote:


 On 28 Jan 2019, at 22:50, agrays...@gmail.com wrote:



 On Friday, January 25, 2019 at 7:33:05 AM UTC-7, Bruno Marchal 
 wrote:
>
>
> On 24 Jan 2019, at 09:29, agrays...@gmail.com wrote:
>
>
>
> On Sunday, January 20, 2019 at 11:54:43 AM UTC, agrays...@
> gmail.com wrote:
>>
>>
>>
>> On Sunday, January 20, 2019 at 9:56:17 AM UTC, Bruno Marchal 
>> wrote:
>>>
>>>
>>> On 18 Jan 2019, at 18:50, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Friday, January 18, 2019 at 12:09:58 PM UTC, Bruno Marchal 
>>> wrote:


 On 17 Jan 2019, at 14:48, agrays...@gmail.com wrote:



 On Thursday, January 17, 2019 at 12:36:07 PM UTC, Bruno Marchal 
 wrote:
>
>
> On 17 Jan 2019, at 09:33, agrays...@gmail.com wrote:
>
>
>
> On Thursday, January 17, 2019 at 3:58:48 AM UTC, Brent wrote:
>>
>>
>>
>> On 1/16/2019 7:25 PM, agrays...@gmail.com wrote:
>>
>>
>>
>> On Monday, January 14, 2019 at 6:12:43 AM UTC, Brent wrote:
>>>
>>>
>>>
>>> On 1/13/2019 9:51 PM, agrays...@gmail.com wrote:
>>>
>>> This means, to me, that the arbitrary phase angles have 
>>> absolutely no effect on the resultant interference pattern 
>>> which is 
>>> observed. But isn't this what the phase angles are supposed to 
>>> effect? AG
>>>
>>>
>>> The screen pattern is determined by *relative phase angles 
>>> for the different paths that reach the same point on the 
>>> screen*.  
>>> The relative angles only depend on different path lengths, so 
>>> the overall 
>>> phase angle is irrelevant.
>>>
>>> Brent
>>>
>>
>>
>> *Sure, except there areTWO forms of phase interference in 
>> Wave Mechanics; the one you refer to above, and another 
>> discussed in the 
>> Stackexchange links I previously posted. In the latter case, the 
>> wf is 
>> expressed as a superposition, say of two states, where we 
>> consider two 
>> cases; a multiplicative complex phase shift is included prior to 
>> the sum, 
>> and different complex phase shifts multiplying each component, 
>> all of the 
>> form e^i (theta). Easy to show that interference exists in the 
>> latter case, 
>> but not the former. Now suppose we take the inner product of the 
>> wf with 
>> the ith eigenstate of the superposition, in order to calculate 
>> the 
>> probability of measuring the eigenvalue of the ith eigenstate, 
>> applying one 
>> of the postulates of QM, keeping in mind that each eigenstate is 
>> multiplied 
>> by a DIFFERENT complex phase shift.  If we further assume the 
>> eigenstates 
>> are mutually orthogonal, the probability of measuring each 
>> eigenvalue does 
>> NOT depend on the different phase shifts. What happened to the 
>> interference 
>> demonstrated by the Stackexchange links? TIA, AG *
>>
>> Your measurement projected it out. It's like measuring which 
>> slit the 

Re: Coherent states of a superposition

2019-02-04 Thread Bruno Marchal

> On 3 Feb 2019, at 00:03, agrayson2...@gmail.com wrote:
> 
> 
> 
> On Saturday, February 2, 2019 at 2:59:30 PM UTC-7, agrays...@gmail.com wrote:
> 
> 
> On Saturday, February 2, 2019 at 1:40:29 AM UTC-7, Bruno Marchal wrote:
> 
>> On 1 Feb 2019, at 21:29, agrays...@gmail.com <> wrote:
>> 
>> 
>> 
>> On Friday, February 1, 2019 at 5:55:30 AM UTC-7, Bruno Marchal wrote:
>> 
>>> On 31 Jan 2019, at 21:10, agrays...@gmail.com <> wrote:
>>> 
>>> 
>>> 
>>> On Thursday, January 31, 2019 at 6:47:12 AM UTC-7, Bruno Marchal wrote:
>>> 
 On 31 Jan 2019, at 01:28, agrays...@gmail.com <> wrote:
 
 
 
 On Wednesday, January 30, 2019 at 2:38:58 PM UTC-7, agrays...@gmail.com 
  wrote:
 
 
 On Wednesday, January 30, 2019 at 5:16:05 AM UTC-7, Bruno Marchal wrote:
 
> On 30 Jan 2019, at 02:59, agrays...@gmail.com <> wrote:
> 
> 
> 
> On Tuesday, January 29, 2019 at 4:37:34 AM UTC-7, Bruno Marchal wrote:
> 
>> On 28 Jan 2019, at 22:50, agrays...@gmail.com <> wrote:
>> 
>> 
>> 
>> On Friday, January 25, 2019 at 7:33:05 AM UTC-7, Bruno Marchal wrote:
>> 
>>> On 24 Jan 2019, at 09:29, agrays...@gmail.com <> wrote:
>>> 
>>> 
>>> 
>>> On Sunday, January 20, 2019 at 11:54:43 AM UTC, agrays...@gmail.com 
>>>  wrote:
>>> 
>>> 
>>> On Sunday, January 20, 2019 at 9:56:17 AM UTC, Bruno Marchal wrote:
>>> 
 On 18 Jan 2019, at 18:50, agrays...@gmail.com <> wrote:
 
 
 
 On Friday, January 18, 2019 at 12:09:58 PM UTC, Bruno Marchal wrote:
 
> On 17 Jan 2019, at 14:48, agrays...@gmail.com <> wrote:
> 
> 
> 
> On Thursday, January 17, 2019 at 12:36:07 PM UTC, Bruno Marchal wrote:
> 
>> On 17 Jan 2019, at 09:33, agrays...@gmail.com <> wrote:
>> 
>> 
>> 
>> On Thursday, January 17, 2019 at 3:58:48 AM UTC, Brent wrote:
>> 
>> 
>> On 1/16/2019 7:25 PM, agrays...@gmail.com <> wrote:
>>> 
>>> 
>>> On Monday, January 14, 2019 at 6:12:43 AM UTC, Brent wrote:
>>> 
>>> 
>>> On 1/13/2019 9:51 PM, agrays...@gmail.com <> wrote:
 This means, to me, that the arbitrary phase angles have absolutely 
 no effect on the resultant interference pattern which is observed. 
 But isn't this what the phase angles are supposed to effect? AG
>>> 
>>> The screen pattern is determined by relative phase angles for the 
>>> different paths that reach the same point on the screen.  The 
>>> relative angles only depend on different path lengths, so the 
>>> overall phase angle is irrelevant.
>>> 
>>> Brent
>>> 
>>> Sure, except there areTWO forms of phase interference in Wave 
>>> Mechanics; the one you refer to above, and another discussed in the 
>>> Stackexchange links I previously posted. In the latter case, the wf 
>>> is expressed as a superposition, say of two states, where we 
>>> consider two cases; a multiplicative complex phase shift is 
>>> included prior to the sum, and different complex phase shifts 
>>> multiplying each component, all of the form e^i (theta). Easy to 
>>> show that interference exists in the latter case, but not the 
>>> former. Now suppose we take the inner product of the wf with the 
>>> ith eigenstate of the superposition, in order to calculate the 
>>> probability of measuring the eigenvalue of the ith eigenstate, 
>>> applying one of the postulates of QM, keeping in mind that each 
>>> eigenstate is multiplied by a DIFFERENT complex phase shift.  If we 
>>> further assume the eigenstates are mutually orthogonal, the 
>>> probability of measuring each eigenvalue does NOT depend on the 
>>> different phase shifts. What happened to the interference 
>>> demonstrated by the Stackexchange links? TIA, AG 
>>> 
>> Your measurement projected it out. It's like measuring which slit 
>> the photon goes through...it eliminates the interference.
>> 
>> Brent
>> 
>> That's what I suspected; that going to an orthogonal basis, I 
>> departed from the examples in Stackexchange where an arbitrary 
>> superposition is used in the analysis of interference. Nevertheless, 
>> isn't it possible to transform from an arbitrary superposition to 
>> one using an orthogonal basis? And aren't all bases equivalent from 
>> a linear algebra pov? If all bases are equivalent, why would 
>> transforming to an orthogonal basis lose interference, whereas a 
>> general superposition does not? TIA, AG
> 
> I don’t understand this. All the bases we 

Re: Coherent states of a superposition

2019-02-02 Thread agrayson2000


On Saturday, February 2, 2019 at 2:59:30 PM UTC-7, agrays...@gmail.com 
wrote:
>
>
>
> On Saturday, February 2, 2019 at 1:40:29 AM UTC-7, Bruno Marchal wrote:
>>
>>
>> On 1 Feb 2019, at 21:29, agrays...@gmail.com wrote:
>>
>>
>>
>> On Friday, February 1, 2019 at 5:55:30 AM UTC-7, Bruno Marchal wrote:
>>>
>>>
>>> On 31 Jan 2019, at 21:10, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Thursday, January 31, 2019 at 6:47:12 AM UTC-7, Bruno Marchal wrote:


 On 31 Jan 2019, at 01:28, agrays...@gmail.com wrote:



 On Wednesday, January 30, 2019 at 2:38:58 PM UTC-7, agrays...@gmail.com 
 wrote:
>
>
>
> On Wednesday, January 30, 2019 at 5:16:05 AM UTC-7, Bruno Marchal 
> wrote:
>>
>>
>> On 30 Jan 2019, at 02:59, agrays...@gmail.com wrote:
>>
>>
>>
>> On Tuesday, January 29, 2019 at 4:37:34 AM UTC-7, Bruno Marchal wrote:
>>>
>>>
>>> On 28 Jan 2019, at 22:50, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Friday, January 25, 2019 at 7:33:05 AM UTC-7, Bruno Marchal wrote:


 On 24 Jan 2019, at 09:29, agrays...@gmail.com wrote:



 On Sunday, January 20, 2019 at 11:54:43 AM UTC, agrays...@gmail.com
  wrote:
>
>
>
> On Sunday, January 20, 2019 at 9:56:17 AM UTC, Bruno Marchal wrote:
>>
>>
>> On 18 Jan 2019, at 18:50, agrays...@gmail.com wrote:
>>
>>
>>
>> On Friday, January 18, 2019 at 12:09:58 PM UTC, Bruno Marchal 
>> wrote:
>>>
>>>
>>> On 17 Jan 2019, at 14:48, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Thursday, January 17, 2019 at 12:36:07 PM UTC, Bruno Marchal 
>>> wrote:


 On 17 Jan 2019, at 09:33, agrays...@gmail.com wrote:



 On Thursday, January 17, 2019 at 3:58:48 AM UTC, Brent wrote:
>
>
>
> On 1/16/2019 7:25 PM, agrays...@gmail.com wrote:
>
>
>
> On Monday, January 14, 2019 at 6:12:43 AM UTC, Brent wrote:
>>
>>
>>
>> On 1/13/2019 9:51 PM, agrays...@gmail.com wrote:
>>
>> This means, to me, that the arbitrary phase angles have 
>> absolutely no effect on the resultant interference pattern which 
>> is 
>> observed. But isn't this what the phase angles are supposed to 
>> effect? AG
>>
>>
>> The screen pattern is determined by *relative phase angles 
>> for the different paths that reach the same point on the 
>> screen*.  
>> The relative angles only depend on different path lengths, so 
>> the overall 
>> phase angle is irrelevant.
>>
>> Brent
>>
>
>
> *Sure, except there areTWO forms of phase interference in Wave 
> Mechanics; the one you refer to above, and another discussed in 
> the 
> Stackexchange links I previously posted. In the latter case, the 
> wf is 
> expressed as a superposition, say of two states, where we 
> consider two 
> cases; a multiplicative complex phase shift is included prior to 
> the sum, 
> and different complex phase shifts multiplying each component, 
> all of the 
> form e^i (theta). Easy to show that interference exists in the 
> latter case, 
> but not the former. Now suppose we take the inner product of the 
> wf with 
> the ith eigenstate of the superposition, in order to calculate 
> the 
> probability of measuring the eigenvalue of the ith eigenstate, 
> applying one 
> of the postulates of QM, keeping in mind that each eigenstate is 
> multiplied 
> by a DIFFERENT complex phase shift.  If we further assume the 
> eigenstates 
> are mutually orthogonal, the probability of measuring each 
> eigenvalue does 
> NOT depend on the different phase shifts. What happened to the 
> interference 
> demonstrated by the Stackexchange links? TIA, AG *
>
> Your measurement projected it out. It's like measuring which 
> slit the photon goes through...it eliminates the interference.
>
> Brent
>

 *That's what I suspected; that going to an orthogonal basis, I 
 departed from the examples in Stackexchange where an arbitrary 
 superposition is used in the 

Re: Coherent states of a superposition

2019-02-02 Thread agrayson2000


On Saturday, February 2, 2019 at 1:40:29 AM UTC-7, Bruno Marchal wrote:
>
>
> On 1 Feb 2019, at 21:29, agrays...@gmail.com  wrote:
>
>
>
> On Friday, February 1, 2019 at 5:55:30 AM UTC-7, Bruno Marchal wrote:
>>
>>
>> On 31 Jan 2019, at 21:10, agrays...@gmail.com wrote:
>>
>>
>>
>> On Thursday, January 31, 2019 at 6:47:12 AM UTC-7, Bruno Marchal wrote:
>>>
>>>
>>> On 31 Jan 2019, at 01:28, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Wednesday, January 30, 2019 at 2:38:58 PM UTC-7, agrays...@gmail.com 
>>> wrote:



 On Wednesday, January 30, 2019 at 5:16:05 AM UTC-7, Bruno Marchal wrote:
>
>
> On 30 Jan 2019, at 02:59, agrays...@gmail.com wrote:
>
>
>
> On Tuesday, January 29, 2019 at 4:37:34 AM UTC-7, Bruno Marchal wrote:
>>
>>
>> On 28 Jan 2019, at 22:50, agrays...@gmail.com wrote:
>>
>>
>>
>> On Friday, January 25, 2019 at 7:33:05 AM UTC-7, Bruno Marchal wrote:
>>>
>>>
>>> On 24 Jan 2019, at 09:29, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Sunday, January 20, 2019 at 11:54:43 AM UTC, agrays...@gmail.com 
>>> wrote:



 On Sunday, January 20, 2019 at 9:56:17 AM UTC, Bruno Marchal wrote:
>
>
> On 18 Jan 2019, at 18:50, agrays...@gmail.com wrote:
>
>
>
> On Friday, January 18, 2019 at 12:09:58 PM UTC, Bruno Marchal 
> wrote:
>>
>>
>> On 17 Jan 2019, at 14:48, agrays...@gmail.com wrote:
>>
>>
>>
>> On Thursday, January 17, 2019 at 12:36:07 PM UTC, Bruno Marchal 
>> wrote:
>>>
>>>
>>> On 17 Jan 2019, at 09:33, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Thursday, January 17, 2019 at 3:58:48 AM UTC, Brent wrote:



 On 1/16/2019 7:25 PM, agrays...@gmail.com wrote:



 On Monday, January 14, 2019 at 6:12:43 AM UTC, Brent wrote:
>
>
>
> On 1/13/2019 9:51 PM, agrays...@gmail.com wrote:
>
> This means, to me, that the arbitrary phase angles have 
> absolutely no effect on the resultant interference pattern which 
> is 
> observed. But isn't this what the phase angles are supposed to 
> effect? AG
>
>
> The screen pattern is determined by *relative phase angles 
> for the different paths that reach the same point on the screen*. 
>  
> The relative angles only depend on different path lengths, so the 
> overall 
> phase angle is irrelevant.
>
> Brent
>


 *Sure, except there areTWO forms of phase interference in Wave 
 Mechanics; the one you refer to above, and another discussed in 
 the 
 Stackexchange links I previously posted. In the latter case, the 
 wf is 
 expressed as a superposition, say of two states, where we consider 
 two 
 cases; a multiplicative complex phase shift is included prior to 
 the sum, 
 and different complex phase shifts multiplying each component, all 
 of the 
 form e^i (theta). Easy to show that interference exists in the 
 latter case, 
 but not the former. Now suppose we take the inner product of the 
 wf with 
 the ith eigenstate of the superposition, in order to calculate the 
 probability of measuring the eigenvalue of the ith eigenstate, 
 applying one 
 of the postulates of QM, keeping in mind that each eigenstate is 
 multiplied 
 by a DIFFERENT complex phase shift.  If we further assume the 
 eigenstates 
 are mutually orthogonal, the probability of measuring each 
 eigenvalue does 
 NOT depend on the different phase shifts. What happened to the 
 interference 
 demonstrated by the Stackexchange links? TIA, AG *

 Your measurement projected it out. It's like measuring which 
 slit the photon goes through...it eliminates the interference.

 Brent

>>>
>>> *That's what I suspected; that going to an orthogonal basis, I 
>>> departed from the examples in Stackexchange where an arbitrary 
>>> superposition is used in the analysis of interference. 
>>> Nevertheless, isn't 
>>> it possible to transform from an arbitrary superposition to one 
>>> using an 
>>> orthogonal basis? And aren't all bases equivalent from a linear 
>>> algebra 

Re: Coherent states of a superposition

2019-02-02 Thread Bruno Marchal

> On 1 Feb 2019, at 21:29, agrayson2...@gmail.com wrote:
> 
> 
> 
> On Friday, February 1, 2019 at 5:55:30 AM UTC-7, Bruno Marchal wrote:
> 
>> On 31 Jan 2019, at 21:10, agrays...@gmail.com  wrote:
>> 
>> 
>> 
>> On Thursday, January 31, 2019 at 6:47:12 AM UTC-7, Bruno Marchal wrote:
>> 
>>> On 31 Jan 2019, at 01:28, agrays...@gmail.com <> wrote:
>>> 
>>> 
>>> 
>>> On Wednesday, January 30, 2019 at 2:38:58 PM UTC-7, agrays...@gmail.com 
>>>  wrote:
>>> 
>>> 
>>> On Wednesday, January 30, 2019 at 5:16:05 AM UTC-7, Bruno Marchal wrote:
>>> 
 On 30 Jan 2019, at 02:59, agrays...@gmail.com <> wrote:
 
 
 
 On Tuesday, January 29, 2019 at 4:37:34 AM UTC-7, Bruno Marchal wrote:
 
> On 28 Jan 2019, at 22:50, agrays...@gmail.com <> wrote:
> 
> 
> 
> On Friday, January 25, 2019 at 7:33:05 AM UTC-7, Bruno Marchal wrote:
> 
>> On 24 Jan 2019, at 09:29, agrays...@gmail.com <> wrote:
>> 
>> 
>> 
>> On Sunday, January 20, 2019 at 11:54:43 AM UTC, agrays...@gmail.com 
>>  wrote:
>> 
>> 
>> On Sunday, January 20, 2019 at 9:56:17 AM UTC, Bruno Marchal wrote:
>> 
>>> On 18 Jan 2019, at 18:50, agrays...@gmail.com <> wrote:
>>> 
>>> 
>>> 
>>> On Friday, January 18, 2019 at 12:09:58 PM UTC, Bruno Marchal wrote:
>>> 
 On 17 Jan 2019, at 14:48, agrays...@gmail.com <> wrote:
 
 
 
 On Thursday, January 17, 2019 at 12:36:07 PM UTC, Bruno Marchal wrote:
 
> On 17 Jan 2019, at 09:33, agrays...@gmail.com <> wrote:
> 
> 
> 
> On Thursday, January 17, 2019 at 3:58:48 AM UTC, Brent wrote:
> 
> 
> On 1/16/2019 7:25 PM, agrays...@gmail.com <> wrote:
>> 
>> 
>> On Monday, January 14, 2019 at 6:12:43 AM UTC, Brent wrote:
>> 
>> 
>> On 1/13/2019 9:51 PM, agrays...@gmail.com <> wrote:
>>> This means, to me, that the arbitrary phase angles have absolutely 
>>> no effect on the resultant interference pattern which is observed. 
>>> But isn't this what the phase angles are supposed to effect? AG
>> 
>> The screen pattern is determined by relative phase angles for the 
>> different paths that reach the same point on the screen.  The 
>> relative angles only depend on different path lengths, so the 
>> overall phase angle is irrelevant.
>> 
>> Brent
>> 
>> Sure, except there areTWO forms of phase interference in Wave 
>> Mechanics; the one you refer to above, and another discussed in the 
>> Stackexchange links I previously posted. In the latter case, the wf 
>> is expressed as a superposition, say of two states, where we 
>> consider two cases; a multiplicative complex phase shift is included 
>> prior to the sum, and different complex phase shifts multiplying 
>> each component, all of the form e^i (theta). Easy to show that 
>> interference exists in the latter case, but not the former. Now 
>> suppose we take the inner product of the wf with the ith eigenstate 
>> of the superposition, in order to calculate the probability of 
>> measuring the eigenvalue of the ith eigenstate, applying one of the 
>> postulates of QM, keeping in mind that each eigenstate is multiplied 
>> by a DIFFERENT complex phase shift.  If we further assume the 
>> eigenstates are mutually orthogonal, the probability of measuring 
>> each eigenvalue does NOT depend on the different phase shifts. What 
>> happened to the interference demonstrated by the Stackexchange 
>> links? TIA, AG 
>> 
> Your measurement projected it out. It's like measuring which slit the 
> photon goes through...it eliminates the interference.
> 
> Brent
> 
> That's what I suspected; that going to an orthogonal basis, I 
> departed from the examples in Stackexchange where an arbitrary 
> superposition is used in the analysis of interference. Nevertheless, 
> isn't it possible to transform from an arbitrary superposition to one 
> using an orthogonal basis? And aren't all bases equivalent from a 
> linear algebra pov? If all bases are equivalent, why would 
> transforming to an orthogonal basis lose interference, whereas a 
> general superposition does not? TIA, AG
 
 I don’t understand this. All the bases we have used all the time are 
 supposed to be orthonormal bases. We suppose that the scalar product 
 (e_i e_j) = delta_i_j, when presenting the Born rule, and the quantum 
 formalism.
 
 Bruno
 
 Generally, bases in a vector space are NOT orthonormal. 
>>> 
>>> Right. But we can 

Re: Coherent states of a superposition

2019-02-01 Thread agrayson2000


On Friday, February 1, 2019 at 1:29:49 PM UTC-7, agrays...@gmail.com wrote:
>
>
>
> On Friday, February 1, 2019 at 5:55:30 AM UTC-7, Bruno Marchal wrote:
>>
>>
>> On 31 Jan 2019, at 21:10, agrays...@gmail.com wrote:
>>
>>
>>
>> On Thursday, January 31, 2019 at 6:47:12 AM UTC-7, Bruno Marchal wrote:
>>>
>>>
>>> On 31 Jan 2019, at 01:28, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Wednesday, January 30, 2019 at 2:38:58 PM UTC-7, agrays...@gmail.com 
>>> wrote:



 On Wednesday, January 30, 2019 at 5:16:05 AM UTC-7, Bruno Marchal wrote:
>
>
> On 30 Jan 2019, at 02:59, agrays...@gmail.com wrote:
>
>
>
> On Tuesday, January 29, 2019 at 4:37:34 AM UTC-7, Bruno Marchal wrote:
>>
>>
>> On 28 Jan 2019, at 22:50, agrays...@gmail.com wrote:
>>
>>
>>
>> On Friday, January 25, 2019 at 7:33:05 AM UTC-7, Bruno Marchal wrote:
>>>
>>>
>>> On 24 Jan 2019, at 09:29, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Sunday, January 20, 2019 at 11:54:43 AM UTC, agrays...@gmail.com 
>>> wrote:



 On Sunday, January 20, 2019 at 9:56:17 AM UTC, Bruno Marchal wrote:
>
>
> On 18 Jan 2019, at 18:50, agrays...@gmail.com wrote:
>
>
>
> On Friday, January 18, 2019 at 12:09:58 PM UTC, Bruno Marchal 
> wrote:
>>
>>
>> On 17 Jan 2019, at 14:48, agrays...@gmail.com wrote:
>>
>>
>>
>> On Thursday, January 17, 2019 at 12:36:07 PM UTC, Bruno Marchal 
>> wrote:
>>>
>>>
>>> On 17 Jan 2019, at 09:33, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Thursday, January 17, 2019 at 3:58:48 AM UTC, Brent wrote:



 On 1/16/2019 7:25 PM, agrays...@gmail.com wrote:



 On Monday, January 14, 2019 at 6:12:43 AM UTC, Brent wrote:
>
>
>
> On 1/13/2019 9:51 PM, agrays...@gmail.com wrote:
>
> This means, to me, that the arbitrary phase angles have 
> absolutely no effect on the resultant interference pattern which 
> is 
> observed. But isn't this what the phase angles are supposed to 
> effect? AG
>
>
> The screen pattern is determined by *relative phase angles 
> for the different paths that reach the same point on the screen*. 
>  
> The relative angles only depend on different path lengths, so the 
> overall 
> phase angle is irrelevant.
>
> Brent
>


 *Sure, except there areTWO forms of phase interference in Wave 
 Mechanics; the one you refer to above, and another discussed in 
 the 
 Stackexchange links I previously posted. In the latter case, the 
 wf is 
 expressed as a superposition, say of two states, where we consider 
 two 
 cases; a multiplicative complex phase shift is included prior to 
 the sum, 
 and different complex phase shifts multiplying each component, all 
 of the 
 form e^i (theta). Easy to show that interference exists in the 
 latter case, 
 but not the former. Now suppose we take the inner product of the 
 wf with 
 the ith eigenstate of the superposition, in order to calculate the 
 probability of measuring the eigenvalue of the ith eigenstate, 
 applying one 
 of the postulates of QM, keeping in mind that each eigenstate is 
 multiplied 
 by a DIFFERENT complex phase shift.  If we further assume the 
 eigenstates 
 are mutually orthogonal, the probability of measuring each 
 eigenvalue does 
 NOT depend on the different phase shifts. What happened to the 
 interference 
 demonstrated by the Stackexchange links? TIA, AG *

 Your measurement projected it out. It's like measuring which 
 slit the photon goes through...it eliminates the interference.

 Brent

>>>
>>> *That's what I suspected; that going to an orthogonal basis, I 
>>> departed from the examples in Stackexchange where an arbitrary 
>>> superposition is used in the analysis of interference. 
>>> Nevertheless, isn't 
>>> it possible to transform from an arbitrary superposition to one 
>>> using an 
>>> orthogonal basis? And aren't all bases equivalent from a linear 
>>> algebra 
>>> pov? If all bases are equivalent, why 

Re: Coherent states of a superposition

2019-02-01 Thread agrayson2000


On Thursday, January 31, 2019 at 5:07:55 PM UTC-7, Philip Thrift wrote:
>
>
>
> On Thursday, January 31, 2019 at 2:10:06 PM UTC-6, agrays...@gmail.com 
> wrote:
>
> ... the phase angles are responsible for interference. I doubt that 
> result. Am I mistaken? AG
>
>
>
> Whatever approach you take, it's still like each possibility has a little 
> spin wheel marking its phase:
>
>   https://www.online-stopwatch.com/images/wheel-dice.png 
>
> When combined, phases in the same general direction reinforce. Phases that 
> don't, interfere.
>
> - pt
>


*I think you're right. Although the cross terms are zeroed out when using 
orthonormal eigenstates in the superposition, there is interference due to 
the interactions of the waves remaining. AG *

-- 
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Re: Coherent states of a superposition

2019-02-01 Thread agrayson2000


On Friday, February 1, 2019 at 5:55:30 AM UTC-7, Bruno Marchal wrote:
>
>
> On 31 Jan 2019, at 21:10, agrays...@gmail.com  wrote:
>
>
>
> On Thursday, January 31, 2019 at 6:47:12 AM UTC-7, Bruno Marchal wrote:
>>
>>
>> On 31 Jan 2019, at 01:28, agrays...@gmail.com wrote:
>>
>>
>>
>> On Wednesday, January 30, 2019 at 2:38:58 PM UTC-7, agrays...@gmail.com 
>> wrote:
>>>
>>>
>>>
>>> On Wednesday, January 30, 2019 at 5:16:05 AM UTC-7, Bruno Marchal wrote:


 On 30 Jan 2019, at 02:59, agrays...@gmail.com wrote:



 On Tuesday, January 29, 2019 at 4:37:34 AM UTC-7, Bruno Marchal wrote:
>
>
> On 28 Jan 2019, at 22:50, agrays...@gmail.com wrote:
>
>
>
> On Friday, January 25, 2019 at 7:33:05 AM UTC-7, Bruno Marchal wrote:
>>
>>
>> On 24 Jan 2019, at 09:29, agrays...@gmail.com wrote:
>>
>>
>>
>> On Sunday, January 20, 2019 at 11:54:43 AM UTC, agrays...@gmail.com 
>> wrote:
>>>
>>>
>>>
>>> On Sunday, January 20, 2019 at 9:56:17 AM UTC, Bruno Marchal wrote:


 On 18 Jan 2019, at 18:50, agrays...@gmail.com wrote:



 On Friday, January 18, 2019 at 12:09:58 PM UTC, Bruno Marchal wrote:
>
>
> On 17 Jan 2019, at 14:48, agrays...@gmail.com wrote:
>
>
>
> On Thursday, January 17, 2019 at 12:36:07 PM UTC, Bruno Marchal 
> wrote:
>>
>>
>> On 17 Jan 2019, at 09:33, agrays...@gmail.com wrote:
>>
>>
>>
>> On Thursday, January 17, 2019 at 3:58:48 AM UTC, Brent wrote:
>>>
>>>
>>>
>>> On 1/16/2019 7:25 PM, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Monday, January 14, 2019 at 6:12:43 AM UTC, Brent wrote:



 On 1/13/2019 9:51 PM, agrays...@gmail.com wrote:

 This means, to me, that the arbitrary phase angles have 
 absolutely no effect on the resultant interference pattern which 
 is 
 observed. But isn't this what the phase angles are supposed to 
 effect? AG


 The screen pattern is determined by *relative phase angles for 
 the different paths that reach the same point on the screen*.  
 The relative angles only depend on different path lengths, so the 
 overall 
 phase angle is irrelevant.

 Brent

>>>
>>>
>>> *Sure, except there areTWO forms of phase interference in Wave 
>>> Mechanics; the one you refer to above, and another discussed in the 
>>> Stackexchange links I previously posted. In the latter case, the wf 
>>> is 
>>> expressed as a superposition, say of two states, where we consider 
>>> two 
>>> cases; a multiplicative complex phase shift is included prior to 
>>> the sum, 
>>> and different complex phase shifts multiplying each component, all 
>>> of the 
>>> form e^i (theta). Easy to show that interference exists in the 
>>> latter case, 
>>> but not the former. Now suppose we take the inner product of the wf 
>>> with 
>>> the ith eigenstate of the superposition, in order to calculate the 
>>> probability of measuring the eigenvalue of the ith eigenstate, 
>>> applying one 
>>> of the postulates of QM, keeping in mind that each eigenstate is 
>>> multiplied 
>>> by a DIFFERENT complex phase shift.  If we further assume the 
>>> eigenstates 
>>> are mutually orthogonal, the probability of measuring each 
>>> eigenvalue does 
>>> NOT depend on the different phase shifts. What happened to the 
>>> interference 
>>> demonstrated by the Stackexchange links? TIA, AG *
>>>
>>> Your measurement projected it out. It's like measuring which 
>>> slit the photon goes through...it eliminates the interference.
>>>
>>> Brent
>>>
>>
>> *That's what I suspected; that going to an orthogonal basis, I 
>> departed from the examples in Stackexchange where an arbitrary 
>> superposition is used in the analysis of interference. Nevertheless, 
>> isn't 
>> it possible to transform from an arbitrary superposition to one 
>> using an 
>> orthogonal basis? And aren't all bases equivalent from a linear 
>> algebra 
>> pov? If all bases are equivalent, why would transforming to an 
>> orthogonal 
>> basis lose interference, whereas a general superposition does not? 
>> TIA, AG*
>>
>>
>> I don’t understand this. All the bases we have used all the time 
>> are 

Re: Coherent states of a superposition

2019-02-01 Thread Bruno Marchal

> On 31 Jan 2019, at 21:10, agrayson2...@gmail.com wrote:
> 
> 
> 
> On Thursday, January 31, 2019 at 6:47:12 AM UTC-7, Bruno Marchal wrote:
> 
>> On 31 Jan 2019, at 01:28, agrays...@gmail.com  wrote:
>> 
>> 
>> 
>> On Wednesday, January 30, 2019 at 2:38:58 PM UTC-7, agrays...@gmail.com 
>>  wrote:
>> 
>> 
>> On Wednesday, January 30, 2019 at 5:16:05 AM UTC-7, Bruno Marchal wrote:
>> 
>>> On 30 Jan 2019, at 02:59, agrays...@gmail.com <> wrote:
>>> 
>>> 
>>> 
>>> On Tuesday, January 29, 2019 at 4:37:34 AM UTC-7, Bruno Marchal wrote:
>>> 
 On 28 Jan 2019, at 22:50, agrays...@gmail.com <> wrote:
 
 
 
 On Friday, January 25, 2019 at 7:33:05 AM UTC-7, Bruno Marchal wrote:
 
> On 24 Jan 2019, at 09:29, agrays...@gmail.com <> wrote:
> 
> 
> 
> On Sunday, January 20, 2019 at 11:54:43 AM UTC, agrays...@gmail.com 
>  wrote:
> 
> 
> On Sunday, January 20, 2019 at 9:56:17 AM UTC, Bruno Marchal wrote:
> 
>> On 18 Jan 2019, at 18:50, agrays...@gmail.com <> wrote:
>> 
>> 
>> 
>> On Friday, January 18, 2019 at 12:09:58 PM UTC, Bruno Marchal wrote:
>> 
>>> On 17 Jan 2019, at 14:48, agrays...@gmail.com <> wrote:
>>> 
>>> 
>>> 
>>> On Thursday, January 17, 2019 at 12:36:07 PM UTC, Bruno Marchal wrote:
>>> 
 On 17 Jan 2019, at 09:33, agrays...@gmail.com <> wrote:
 
 
 
 On Thursday, January 17, 2019 at 3:58:48 AM UTC, Brent wrote:
 
 
 On 1/16/2019 7:25 PM, agrays...@gmail.com <> wrote:
> 
> 
> On Monday, January 14, 2019 at 6:12:43 AM UTC, Brent wrote:
> 
> 
> On 1/13/2019 9:51 PM, agrays...@gmail.com <> wrote:
>> This means, to me, that the arbitrary phase angles have absolutely 
>> no effect on the resultant interference pattern which is observed. 
>> But isn't this what the phase angles are supposed to effect? AG
> 
> The screen pattern is determined by relative phase angles for the 
> different paths that reach the same point on the screen.  The 
> relative angles only depend on different path lengths, so the overall 
> phase angle is irrelevant.
> 
> Brent
> 
> Sure, except there areTWO forms of phase interference in Wave 
> Mechanics; the one you refer to above, and another discussed in the 
> Stackexchange links I previously posted. In the latter case, the wf 
> is expressed as a superposition, say of two states, where we consider 
> two cases; a multiplicative complex phase shift is included prior to 
> the sum, and different complex phase shifts multiplying each 
> component, all of the form e^i (theta). Easy to show that 
> interference exists in the latter case, but not the former. Now 
> suppose we take the inner product of the wf with the ith eigenstate 
> of the superposition, in order to calculate the probability of 
> measuring the eigenvalue of the ith eigenstate, applying one of the 
> postulates of QM, keeping in mind that each eigenstate is multiplied 
> by a DIFFERENT complex phase shift.  If we further assume the 
> eigenstates are mutually orthogonal, the probability of measuring 
> each eigenvalue does NOT depend on the different phase shifts. What 
> happened to the interference demonstrated by the Stackexchange links? 
> TIA, AG 
> 
 Your measurement projected it out. It's like measuring which slit the 
 photon goes through...it eliminates the interference.
 
 Brent
 
 That's what I suspected; that going to an orthogonal basis, I departed 
 from the examples in Stackexchange where an arbitrary superposition is 
 used in the analysis of interference. Nevertheless, isn't it possible 
 to transform from an arbitrary superposition to one using an 
 orthogonal basis? And aren't all bases equivalent from a linear 
 algebra pov? If all bases are equivalent, why would transforming to an 
 orthogonal basis lose interference, whereas a general superposition 
 does not? TIA, AG
>>> 
>>> I don’t understand this. All the bases we have used all the time are 
>>> supposed to be orthonormal bases. We suppose that the scalar product 
>>> (e_i e_j) = delta_i_j, when presenting the Born rule, and the quantum 
>>> formalism.
>>> 
>>> Bruno
>>> 
>>> Generally, bases in a vector space are NOT orthonormal. 
>> 
>> Right. But we can always build an orthonormal base with a decent scalar 
>> product, like in Hilbert space, 
>> 
>> 
>> 
>>> For example, in the vector space of vectors in the plane, any pair of 
>>> non-parallel vectors form a basis. Same for any general 

Re: Coherent states of a superposition

2019-01-31 Thread Philip Thrift


On Thursday, January 31, 2019 at 2:10:06 PM UTC-6, agrays...@gmail.com 
wrote:

... the phase angles are responsible for interference. I doubt that result. 
Am I mistaken? AG



Whatever approach you take, it's still like each possibility has a little 
spin wheel marking its phase:

  https://www.online-stopwatch.com/images/wheel-dice.png 

When combined, phases in the same general direction reinforce. Phases that 
don't, interfere.

- pt

-- 
You received this message because you are subscribed to the Google Groups 
"Everything List" group.
To unsubscribe from this group and stop receiving emails from it, send an email 
to everything-list+unsubscr...@googlegroups.com.
To post to this group, send email to everything-list@googlegroups.com.
Visit this group at https://groups.google.com/group/everything-list.
For more options, visit https://groups.google.com/d/optout.


Re: Coherent states of a superposition

2019-01-31 Thread agrayson2000


On Thursday, January 31, 2019 at 6:47:12 AM UTC-7, Bruno Marchal wrote:
>
>
> On 31 Jan 2019, at 01:28, agrays...@gmail.com  wrote:
>
>
>
> On Wednesday, January 30, 2019 at 2:38:58 PM UTC-7, agrays...@gmail.com 
> wrote:
>>
>>
>>
>> On Wednesday, January 30, 2019 at 5:16:05 AM UTC-7, Bruno Marchal wrote:
>>>
>>>
>>> On 30 Jan 2019, at 02:59, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Tuesday, January 29, 2019 at 4:37:34 AM UTC-7, Bruno Marchal wrote:


 On 28 Jan 2019, at 22:50, agrays...@gmail.com wrote:



 On Friday, January 25, 2019 at 7:33:05 AM UTC-7, Bruno Marchal wrote:
>
>
> On 24 Jan 2019, at 09:29, agrays...@gmail.com wrote:
>
>
>
> On Sunday, January 20, 2019 at 11:54:43 AM UTC, agrays...@gmail.com 
> wrote:
>>
>>
>>
>> On Sunday, January 20, 2019 at 9:56:17 AM UTC, Bruno Marchal wrote:
>>>
>>>
>>> On 18 Jan 2019, at 18:50, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Friday, January 18, 2019 at 12:09:58 PM UTC, Bruno Marchal wrote:


 On 17 Jan 2019, at 14:48, agrays...@gmail.com wrote:



 On Thursday, January 17, 2019 at 12:36:07 PM UTC, Bruno Marchal 
 wrote:
>
>
> On 17 Jan 2019, at 09:33, agrays...@gmail.com wrote:
>
>
>
> On Thursday, January 17, 2019 at 3:58:48 AM UTC, Brent wrote:
>>
>>
>>
>> On 1/16/2019 7:25 PM, agrays...@gmail.com wrote:
>>
>>
>>
>> On Monday, January 14, 2019 at 6:12:43 AM UTC, Brent wrote:
>>>
>>>
>>>
>>> On 1/13/2019 9:51 PM, agrays...@gmail.com wrote:
>>>
>>> This means, to me, that the arbitrary phase angles have 
>>> absolutely no effect on the resultant interference pattern which is 
>>> observed. But isn't this what the phase angles are supposed to 
>>> effect? AG
>>>
>>>
>>> The screen pattern is determined by *relative phase angles for 
>>> the different paths that reach the same point on the screen*.  
>>> The relative angles only depend on different path lengths, so the 
>>> overall 
>>> phase angle is irrelevant.
>>>
>>> Brent
>>>
>>
>>
>> *Sure, except there areTWO forms of phase interference in Wave 
>> Mechanics; the one you refer to above, and another discussed in the 
>> Stackexchange links I previously posted. In the latter case, the wf 
>> is 
>> expressed as a superposition, say of two states, where we consider 
>> two 
>> cases; a multiplicative complex phase shift is included prior to the 
>> sum, 
>> and different complex phase shifts multiplying each component, all 
>> of the 
>> form e^i (theta). Easy to show that interference exists in the 
>> latter case, 
>> but not the former. Now suppose we take the inner product of the wf 
>> with 
>> the ith eigenstate of the superposition, in order to calculate the 
>> probability of measuring the eigenvalue of the ith eigenstate, 
>> applying one 
>> of the postulates of QM, keeping in mind that each eigenstate is 
>> multiplied 
>> by a DIFFERENT complex phase shift.  If we further assume the 
>> eigenstates 
>> are mutually orthogonal, the probability of measuring each 
>> eigenvalue does 
>> NOT depend on the different phase shifts. What happened to the 
>> interference 
>> demonstrated by the Stackexchange links? TIA, AG *
>>
>> Your measurement projected it out. It's like measuring which slit 
>> the photon goes through...it eliminates the interference.
>>
>> Brent
>>
>
> *That's what I suspected; that going to an orthogonal basis, I 
> departed from the examples in Stackexchange where an arbitrary 
> superposition is used in the analysis of interference. Nevertheless, 
> isn't 
> it possible to transform from an arbitrary superposition to one using 
> an 
> orthogonal basis? And aren't all bases equivalent from a linear 
> algebra 
> pov? If all bases are equivalent, why would transforming to an 
> orthogonal 
> basis lose interference, whereas a general superposition does not? 
> TIA, AG*
>
>
> I don’t understand this. All the bases we have used all the time 
> are supposed to be orthonormal bases. We suppose that the scalar 
> product 
> (e_i e_j) = delta_i_j, when presenting the Born rule, and the quantum 
> formalism.
>
> Bruno
>

 *Generally, bases in a vector space are NOT 

Re: Coherent states of a superposition

2019-01-31 Thread Bruno Marchal

> On 31 Jan 2019, at 01:28, agrayson2...@gmail.com wrote:
> 
> 
> 
> On Wednesday, January 30, 2019 at 2:38:58 PM UTC-7, agrays...@gmail.com wrote:
> 
> 
> On Wednesday, January 30, 2019 at 5:16:05 AM UTC-7, Bruno Marchal wrote:
> 
>> On 30 Jan 2019, at 02:59, agrays...@gmail.com <> wrote:
>> 
>> 
>> 
>> On Tuesday, January 29, 2019 at 4:37:34 AM UTC-7, Bruno Marchal wrote:
>> 
>>> On 28 Jan 2019, at 22:50, agrays...@gmail.com <> wrote:
>>> 
>>> 
>>> 
>>> On Friday, January 25, 2019 at 7:33:05 AM UTC-7, Bruno Marchal wrote:
>>> 
 On 24 Jan 2019, at 09:29, agrays...@gmail.com <> wrote:
 
 
 
 On Sunday, January 20, 2019 at 11:54:43 AM UTC, agrays...@gmail.com 
  wrote:
 
 
 On Sunday, January 20, 2019 at 9:56:17 AM UTC, Bruno Marchal wrote:
 
> On 18 Jan 2019, at 18:50, agrays...@gmail.com <> wrote:
> 
> 
> 
> On Friday, January 18, 2019 at 12:09:58 PM UTC, Bruno Marchal wrote:
> 
>> On 17 Jan 2019, at 14:48, agrays...@gmail.com <> wrote:
>> 
>> 
>> 
>> On Thursday, January 17, 2019 at 12:36:07 PM UTC, Bruno Marchal wrote:
>> 
>>> On 17 Jan 2019, at 09:33, agrays...@gmail.com <> wrote:
>>> 
>>> 
>>> 
>>> On Thursday, January 17, 2019 at 3:58:48 AM UTC, Brent wrote:
>>> 
>>> 
>>> On 1/16/2019 7:25 PM, agrays...@gmail.com <> wrote:
 
 
 On Monday, January 14, 2019 at 6:12:43 AM UTC, Brent wrote:
 
 
 On 1/13/2019 9:51 PM, agrays...@gmail.com <> wrote:
> This means, to me, that the arbitrary phase angles have absolutely no 
> effect on the resultant interference pattern which is observed. But 
> isn't this what the phase angles are supposed to effect? AG
 
 The screen pattern is determined by relative phase angles for the 
 different paths that reach the same point on the screen.  The relative 
 angles only depend on different path lengths, so the overall phase 
 angle is irrelevant.
 
 Brent
 
 Sure, except there areTWO forms of phase interference in Wave 
 Mechanics; the one you refer to above, and another discussed in the 
 Stackexchange links I previously posted. In the latter case, the wf is 
 expressed as a superposition, say of two states, where we consider two 
 cases; a multiplicative complex phase shift is included prior to the 
 sum, and different complex phase shifts multiplying each component, 
 all of the form e^i (theta). Easy to show that interference exists in 
 the latter case, but not the former. Now suppose we take the inner 
 product of the wf with the ith eigenstate of the superposition, in 
 order to calculate the probability of measuring the eigenvalue of the 
 ith eigenstate, applying one of the postulates of QM, keeping in mind 
 that each eigenstate is multiplied by a DIFFERENT complex phase shift. 
  If we further assume the eigenstates are mutually orthogonal, the 
 probability of measuring each eigenvalue does NOT depend on the 
 different phase shifts. What happened to the interference demonstrated 
 by the Stackexchange links? TIA, AG 
 
>>> Your measurement projected it out. It's like measuring which slit the 
>>> photon goes through...it eliminates the interference.
>>> 
>>> Brent
>>> 
>>> That's what I suspected; that going to an orthogonal basis, I departed 
>>> from the examples in Stackexchange where an arbitrary superposition is 
>>> used in the analysis of interference. Nevertheless, isn't it possible 
>>> to transform from an arbitrary superposition to one using an orthogonal 
>>> basis? And aren't all bases equivalent from a linear algebra pov? If 
>>> all bases are equivalent, why would transforming to an orthogonal basis 
>>> lose interference, whereas a general superposition does not? TIA, AG
>> 
>> I don’t understand this. All the bases we have used all the time are 
>> supposed to be orthonormal bases. We suppose that the scalar product 
>> (e_i e_j) = delta_i_j, when presenting the Born rule, and the quantum 
>> formalism.
>> 
>> Bruno
>> 
>> Generally, bases in a vector space are NOT orthonormal. 
> 
> Right. But we can always build an orthonormal base with a decent scalar 
> product, like in Hilbert space, 
> 
> 
> 
>> For example, in the vector space of vectors in the plane, any pair of 
>> non-parallel vectors form a basis. Same for any general superposition of 
>> states in QM. HOWEVER, eigenfunctions with distinct eigenvalues ARE 
>> orthogonal.
> 
> Absolutely. And when choosing a non degenerate 
> observable/measuring-device, we work in the base of its eigenvectors. A 
> superposition is better seen as a sum of 

Re: Coherent states of a superposition

2019-01-30 Thread agrayson2000


On Wednesday, January 30, 2019 at 2:38:58 PM UTC-7, agrays...@gmail.com 
wrote:
>
>
>
> On Wednesday, January 30, 2019 at 5:16:05 AM UTC-7, Bruno Marchal wrote:
>>
>>
>> On 30 Jan 2019, at 02:59, agrays...@gmail.com wrote:
>>
>>
>>
>> On Tuesday, January 29, 2019 at 4:37:34 AM UTC-7, Bruno Marchal wrote:
>>>
>>>
>>> On 28 Jan 2019, at 22:50, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Friday, January 25, 2019 at 7:33:05 AM UTC-7, Bruno Marchal wrote:


 On 24 Jan 2019, at 09:29, agrays...@gmail.com wrote:



 On Sunday, January 20, 2019 at 11:54:43 AM UTC, agrays...@gmail.com 
 wrote:
>
>
>
> On Sunday, January 20, 2019 at 9:56:17 AM UTC, Bruno Marchal wrote:
>>
>>
>> On 18 Jan 2019, at 18:50, agrays...@gmail.com wrote:
>>
>>
>>
>> On Friday, January 18, 2019 at 12:09:58 PM UTC, Bruno Marchal wrote:
>>>
>>>
>>> On 17 Jan 2019, at 14:48, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Thursday, January 17, 2019 at 12:36:07 PM UTC, Bruno Marchal 
>>> wrote:


 On 17 Jan 2019, at 09:33, agrays...@gmail.com wrote:



 On Thursday, January 17, 2019 at 3:58:48 AM UTC, Brent wrote:
>
>
>
> On 1/16/2019 7:25 PM, agrays...@gmail.com wrote:
>
>
>
> On Monday, January 14, 2019 at 6:12:43 AM UTC, Brent wrote:
>>
>>
>>
>> On 1/13/2019 9:51 PM, agrays...@gmail.com wrote:
>>
>> This means, to me, that the arbitrary phase angles have 
>> absolutely no effect on the resultant interference pattern which is 
>> observed. But isn't this what the phase angles are supposed to 
>> effect? AG
>>
>>
>> The screen pattern is determined by *relative phase angles for 
>> the different paths that reach the same point on the screen*.  
>> The relative angles only depend on different path lengths, so the 
>> overall 
>> phase angle is irrelevant.
>>
>> Brent
>>
>
>
> *Sure, except there areTWO forms of phase interference in Wave 
> Mechanics; the one you refer to above, and another discussed in the 
> Stackexchange links I previously posted. In the latter case, the wf 
> is 
> expressed as a superposition, say of two states, where we consider 
> two 
> cases; a multiplicative complex phase shift is included prior to the 
> sum, 
> and different complex phase shifts multiplying each component, all of 
> the 
> form e^i (theta). Easy to show that interference exists in the latter 
> case, 
> but not the former. Now suppose we take the inner product of the wf 
> with 
> the ith eigenstate of the superposition, in order to calculate the 
> probability of measuring the eigenvalue of the ith eigenstate, 
> applying one 
> of the postulates of QM, keeping in mind that each eigenstate is 
> multiplied 
> by a DIFFERENT complex phase shift.  If we further assume the 
> eigenstates 
> are mutually orthogonal, the probability of measuring each eigenvalue 
> does 
> NOT depend on the different phase shifts. What happened to the 
> interference 
> demonstrated by the Stackexchange links? TIA, AG *
>
> Your measurement projected it out. It's like measuring which slit 
> the photon goes through...it eliminates the interference.
>
> Brent
>

 *That's what I suspected; that going to an orthogonal basis, I 
 departed from the examples in Stackexchange where an arbitrary 
 superposition is used in the analysis of interference. Nevertheless, 
 isn't 
 it possible to transform from an arbitrary superposition to one using 
 an 
 orthogonal basis? And aren't all bases equivalent from a linear 
 algebra 
 pov? If all bases are equivalent, why would transforming to an 
 orthogonal 
 basis lose interference, whereas a general superposition does not? 
 TIA, AG*


 I don’t understand this. All the bases we have used all the time 
 are supposed to be orthonormal bases. We suppose that the scalar 
 product 
 (e_i e_j) = delta_i_j, when presenting the Born rule, and the quantum 
 formalism.

 Bruno

>>>
>>> *Generally, bases in a vector space are NOT orthonormal. *
>>>
>>>
>>> Right. But we can always build an orthonormal base with a decent 
>>> scalar product, like in Hilbert space, 
>>>
>>>
>>>
>>> *For example, in the vector space of vectors in the plane, any pair 
>>> of non-parallel vectors form 

Re: Coherent states of a superposition

2019-01-30 Thread agrayson2000


On Wednesday, January 30, 2019 at 5:16:05 AM UTC-7, Bruno Marchal wrote:
>
>
> On 30 Jan 2019, at 02:59, agrays...@gmail.com  wrote:
>
>
>
> On Tuesday, January 29, 2019 at 4:37:34 AM UTC-7, Bruno Marchal wrote:
>>
>>
>> On 28 Jan 2019, at 22:50, agrays...@gmail.com wrote:
>>
>>
>>
>> On Friday, January 25, 2019 at 7:33:05 AM UTC-7, Bruno Marchal wrote:
>>>
>>>
>>> On 24 Jan 2019, at 09:29, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Sunday, January 20, 2019 at 11:54:43 AM UTC, agrays...@gmail.com 
>>> wrote:



 On Sunday, January 20, 2019 at 9:56:17 AM UTC, Bruno Marchal wrote:
>
>
> On 18 Jan 2019, at 18:50, agrays...@gmail.com wrote:
>
>
>
> On Friday, January 18, 2019 at 12:09:58 PM UTC, Bruno Marchal wrote:
>>
>>
>> On 17 Jan 2019, at 14:48, agrays...@gmail.com wrote:
>>
>>
>>
>> On Thursday, January 17, 2019 at 12:36:07 PM UTC, Bruno Marchal wrote:
>>>
>>>
>>> On 17 Jan 2019, at 09:33, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Thursday, January 17, 2019 at 3:58:48 AM UTC, Brent wrote:



 On 1/16/2019 7:25 PM, agrays...@gmail.com wrote:



 On Monday, January 14, 2019 at 6:12:43 AM UTC, Brent wrote:
>
>
>
> On 1/13/2019 9:51 PM, agrays...@gmail.com wrote:
>
> This means, to me, that the arbitrary phase angles have absolutely 
> no effect on the resultant interference pattern which is observed. 
> But 
> isn't this what the phase angles are supposed to effect? AG
>
>
> The screen pattern is determined by *relative phase angles for 
> the different paths that reach the same point on the screen*.  
> The relative angles only depend on different path lengths, so the 
> overall 
> phase angle is irrelevant.
>
> Brent
>


 *Sure, except there areTWO forms of phase interference in Wave 
 Mechanics; the one you refer to above, and another discussed in the 
 Stackexchange links I previously posted. In the latter case, the wf is 
 expressed as a superposition, say of two states, where we consider two 
 cases; a multiplicative complex phase shift is included prior to the 
 sum, 
 and different complex phase shifts multiplying each component, all of 
 the 
 form e^i (theta). Easy to show that interference exists in the latter 
 case, 
 but not the former. Now suppose we take the inner product of the wf 
 with 
 the ith eigenstate of the superposition, in order to calculate the 
 probability of measuring the eigenvalue of the ith eigenstate, 
 applying one 
 of the postulates of QM, keeping in mind that each eigenstate is 
 multiplied 
 by a DIFFERENT complex phase shift.  If we further assume the 
 eigenstates 
 are mutually orthogonal, the probability of measuring each eigenvalue 
 does 
 NOT depend on the different phase shifts. What happened to the 
 interference 
 demonstrated by the Stackexchange links? TIA, AG *

 Your measurement projected it out. It's like measuring which slit 
 the photon goes through...it eliminates the interference.

 Brent

>>>
>>> *That's what I suspected; that going to an orthogonal basis, I 
>>> departed from the examples in Stackexchange where an arbitrary 
>>> superposition is used in the analysis of interference. Nevertheless, 
>>> isn't 
>>> it possible to transform from an arbitrary superposition to one using 
>>> an 
>>> orthogonal basis? And aren't all bases equivalent from a linear algebra 
>>> pov? If all bases are equivalent, why would transforming to an 
>>> orthogonal 
>>> basis lose interference, whereas a general superposition does not? TIA, 
>>> AG*
>>>
>>>
>>> I don’t understand this. All the bases we have used all the time are 
>>> supposed to be orthonormal bases. We suppose that the scalar product 
>>> (e_i 
>>> e_j) = delta_i_j, when presenting the Born rule, and the quantum 
>>> formalism.
>>>
>>> Bruno
>>>
>>
>> *Generally, bases in a vector space are NOT orthonormal. *
>>
>>
>> Right. But we can always build an orthonormal base with a decent 
>> scalar product, like in Hilbert space, 
>>
>>
>>
>> *For example, in the vector space of vectors in the plane, any pair 
>> of non-parallel vectors form a basis. Same for any general superposition 
>> of 
>> states in QM. HOWEVER, eigenfunctions with distinct eigenvalues ARE 
>> orthogonal.*
>>
>>
>> Absolutely. And when choosing a non degenerate 
>> observable/measuring-device, we work in 

Re: Coherent states of a superposition

2019-01-30 Thread Bruno Marchal

> On 30 Jan 2019, at 02:59, agrayson2...@gmail.com wrote:
> 
> 
> 
> On Tuesday, January 29, 2019 at 4:37:34 AM UTC-7, Bruno Marchal wrote:
> 
>> On 28 Jan 2019, at 22:50, agrays...@gmail.com  wrote:
>> 
>> 
>> 
>> On Friday, January 25, 2019 at 7:33:05 AM UTC-7, Bruno Marchal wrote:
>> 
>>> On 24 Jan 2019, at 09:29, agrays...@gmail.com <> wrote:
>>> 
>>> 
>>> 
>>> On Sunday, January 20, 2019 at 11:54:43 AM UTC, agrays...@gmail.com 
>>>  wrote:
>>> 
>>> 
>>> On Sunday, January 20, 2019 at 9:56:17 AM UTC, Bruno Marchal wrote:
>>> 
 On 18 Jan 2019, at 18:50, agrays...@gmail.com <> wrote:
 
 
 
 On Friday, January 18, 2019 at 12:09:58 PM UTC, Bruno Marchal wrote:
 
> On 17 Jan 2019, at 14:48, agrays...@gmail.com <> wrote:
> 
> 
> 
> On Thursday, January 17, 2019 at 12:36:07 PM UTC, Bruno Marchal wrote:
> 
>> On 17 Jan 2019, at 09:33, agrays...@gmail.com <> wrote:
>> 
>> 
>> 
>> On Thursday, January 17, 2019 at 3:58:48 AM UTC, Brent wrote:
>> 
>> 
>> On 1/16/2019 7:25 PM, agrays...@gmail.com <> wrote:
>>> 
>>> 
>>> On Monday, January 14, 2019 at 6:12:43 AM UTC, Brent wrote:
>>> 
>>> 
>>> On 1/13/2019 9:51 PM, agrays...@gmail.com <> wrote:
 This means, to me, that the arbitrary phase angles have absolutely no 
 effect on the resultant interference pattern which is observed. But 
 isn't this what the phase angles are supposed to effect? AG
>>> 
>>> The screen pattern is determined by relative phase angles for the 
>>> different paths that reach the same point on the screen.  The relative 
>>> angles only depend on different path lengths, so the overall phase 
>>> angle is irrelevant.
>>> 
>>> Brent
>>> 
>>> Sure, except there areTWO forms of phase interference in Wave 
>>> Mechanics; the one you refer to above, and another discussed in the 
>>> Stackexchange links I previously posted. In the latter case, the wf is 
>>> expressed as a superposition, say of two states, where we consider two 
>>> cases; a multiplicative complex phase shift is included prior to the 
>>> sum, and different complex phase shifts multiplying each component, all 
>>> of the form e^i (theta). Easy to show that interference exists in the 
>>> latter case, but not the former. Now suppose we take the inner product 
>>> of the wf with the ith eigenstate of the superposition, in order to 
>>> calculate the probability of measuring the eigenvalue of the ith 
>>> eigenstate, applying one of the postulates of QM, keeping in mind that 
>>> each eigenstate is multiplied by a DIFFERENT complex phase shift.  If 
>>> we further assume the eigenstates are mutually orthogonal, the 
>>> probability of measuring each eigenvalue does NOT depend on the 
>>> different phase shifts. What happened to the interference demonstrated 
>>> by the Stackexchange links? TIA, AG 
>>> 
>> Your measurement projected it out. It's like measuring which slit the 
>> photon goes through...it eliminates the interference.
>> 
>> Brent
>> 
>> That's what I suspected; that going to an orthogonal basis, I departed 
>> from the examples in Stackexchange where an arbitrary superposition is 
>> used in the analysis of interference. Nevertheless, isn't it possible to 
>> transform from an arbitrary superposition to one using an orthogonal 
>> basis? And aren't all bases equivalent from a linear algebra pov? If all 
>> bases are equivalent, why would transforming to an orthogonal basis lose 
>> interference, whereas a general superposition does not? TIA, AG
> 
> I don’t understand this. All the bases we have used all the time are 
> supposed to be orthonormal bases. We suppose that the scalar product (e_i 
> e_j) = delta_i_j, when presenting the Born rule, and the quantum 
> formalism.
> 
> Bruno
> 
> Generally, bases in a vector space are NOT orthonormal. 
 
 Right. But we can always build an orthonormal base with a decent scalar 
 product, like in Hilbert space, 
 
 
 
> For example, in the vector space of vectors in the plane, any pair of 
> non-parallel vectors form a basis. Same for any general superposition of 
> states in QM. HOWEVER, eigenfunctions with distinct eigenvalues ARE 
> orthogonal.
 
 Absolutely. And when choosing a non degenerate 
 observable/measuring-device, we work in the base of its eigenvectors. A 
 superposition is better seen as a sum of some eigenvectors of some 
 observable. That is the crazy thing in QM. The same particle can be 
 superposed in the state of being here and there. Two different positions 
 of one particle can be superposed.
 
 This is a common misinterpretation. Just because a wf can be expressed in 
 different ways (as a vector in the 

Re: Coherent states of a superposition

2019-01-29 Thread agrayson2000


On Tuesday, January 29, 2019 at 4:37:34 AM UTC-7, Bruno Marchal wrote:
>
>
> On 28 Jan 2019, at 22:50, agrays...@gmail.com  wrote:
>
>
>
> On Friday, January 25, 2019 at 7:33:05 AM UTC-7, Bruno Marchal wrote:
>>
>>
>> On 24 Jan 2019, at 09:29, agrays...@gmail.com wrote:
>>
>>
>>
>> On Sunday, January 20, 2019 at 11:54:43 AM UTC, agrays...@gmail.com 
>> wrote:
>>>
>>>
>>>
>>> On Sunday, January 20, 2019 at 9:56:17 AM UTC, Bruno Marchal wrote:


 On 18 Jan 2019, at 18:50, agrays...@gmail.com wrote:



 On Friday, January 18, 2019 at 12:09:58 PM UTC, Bruno Marchal wrote:
>
>
> On 17 Jan 2019, at 14:48, agrays...@gmail.com wrote:
>
>
>
> On Thursday, January 17, 2019 at 12:36:07 PM UTC, Bruno Marchal wrote:
>>
>>
>> On 17 Jan 2019, at 09:33, agrays...@gmail.com wrote:
>>
>>
>>
>> On Thursday, January 17, 2019 at 3:58:48 AM UTC, Brent wrote:
>>>
>>>
>>>
>>> On 1/16/2019 7:25 PM, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Monday, January 14, 2019 at 6:12:43 AM UTC, Brent wrote:



 On 1/13/2019 9:51 PM, agrays...@gmail.com wrote:

 This means, to me, that the arbitrary phase angles have absolutely 
 no effect on the resultant interference pattern which is observed. But 
 isn't this what the phase angles are supposed to effect? AG


 The screen pattern is determined by *relative phase angles for the 
 different paths that reach the same point on the screen*.  The 
 relative angles only depend on different path lengths, so the overall 
 phase 
 angle is irrelevant.

 Brent

>>>
>>>
>>> *Sure, except there areTWO forms of phase interference in Wave 
>>> Mechanics; the one you refer to above, and another discussed in the 
>>> Stackexchange links I previously posted. In the latter case, the wf is 
>>> expressed as a superposition, say of two states, where we consider two 
>>> cases; a multiplicative complex phase shift is included prior to the 
>>> sum, 
>>> and different complex phase shifts multiplying each component, all of 
>>> the 
>>> form e^i (theta). Easy to show that interference exists in the latter 
>>> case, 
>>> but not the former. Now suppose we take the inner product of the wf 
>>> with 
>>> the ith eigenstate of the superposition, in order to calculate the 
>>> probability of measuring the eigenvalue of the ith eigenstate, applying 
>>> one 
>>> of the postulates of QM, keeping in mind that each eigenstate is 
>>> multiplied 
>>> by a DIFFERENT complex phase shift.  If we further assume the 
>>> eigenstates 
>>> are mutually orthogonal, the probability of measuring each eigenvalue 
>>> does 
>>> NOT depend on the different phase shifts. What happened to the 
>>> interference 
>>> demonstrated by the Stackexchange links? TIA, AG *
>>>
>>> Your measurement projected it out. It's like measuring which slit 
>>> the photon goes through...it eliminates the interference.
>>>
>>> Brent
>>>
>>
>> *That's what I suspected; that going to an orthogonal basis, I 
>> departed from the examples in Stackexchange where an arbitrary 
>> superposition is used in the analysis of interference. Nevertheless, 
>> isn't 
>> it possible to transform from an arbitrary superposition to one using an 
>> orthogonal basis? And aren't all bases equivalent from a linear algebra 
>> pov? If all bases are equivalent, why would transforming to an 
>> orthogonal 
>> basis lose interference, whereas a general superposition does not? TIA, 
>> AG*
>>
>>
>> I don’t understand this. All the bases we have used all the time are 
>> supposed to be orthonormal bases. We suppose that the scalar product 
>> (e_i 
>> e_j) = delta_i_j, when presenting the Born rule, and the quantum 
>> formalism.
>>
>> Bruno
>>
>
> *Generally, bases in a vector space are NOT orthonormal. *
>
>
> Right. But we can always build an orthonormal base with a decent 
> scalar product, like in Hilbert space, 
>
>
>
> *For example, in the vector space of vectors in the plane, any pair of 
> non-parallel vectors form a basis. Same for any general superposition of 
> states in QM. HOWEVER, eigenfunctions with distinct eigenvalues ARE 
> orthogonal.*
>
>
> Absolutely. And when choosing a non degenerate 
> observable/measuring-device, we work in the base of its eigenvectors. A 
> superposition is better seen as a sum of some eigenvectors of some 
> observable. That is the crazy thing in QM. The same particle can be 
> superposed in the state of being here and there. Two different positions 
> of 
> one particle can be 

Re: Coherent states of a superposition

2019-01-29 Thread Bruno Marchal

> On 28 Jan 2019, at 22:50, agrayson2...@gmail.com wrote:
> 
> 
> 
> On Friday, January 25, 2019 at 7:33:05 AM UTC-7, Bruno Marchal wrote:
> 
>> On 24 Jan 2019, at 09:29, agrays...@gmail.com  wrote:
>> 
>> 
>> 
>> On Sunday, January 20, 2019 at 11:54:43 AM UTC, agrays...@gmail.com 
>>  wrote:
>> 
>> 
>> On Sunday, January 20, 2019 at 9:56:17 AM UTC, Bruno Marchal wrote:
>> 
>>> On 18 Jan 2019, at 18:50, agrays...@gmail.com <> wrote:
>>> 
>>> 
>>> 
>>> On Friday, January 18, 2019 at 12:09:58 PM UTC, Bruno Marchal wrote:
>>> 
 On 17 Jan 2019, at 14:48, agrays...@gmail.com <> wrote:
 
 
 
 On Thursday, January 17, 2019 at 12:36:07 PM UTC, Bruno Marchal wrote:
 
> On 17 Jan 2019, at 09:33, agrays...@gmail.com <> wrote:
> 
> 
> 
> On Thursday, January 17, 2019 at 3:58:48 AM UTC, Brent wrote:
> 
> 
> On 1/16/2019 7:25 PM, agrays...@gmail.com <> wrote:
>> 
>> 
>> On Monday, January 14, 2019 at 6:12:43 AM UTC, Brent wrote:
>> 
>> 
>> On 1/13/2019 9:51 PM, agrays...@gmail.com <> wrote:
>>> This means, to me, that the arbitrary phase angles have absolutely no 
>>> effect on the resultant interference pattern which is observed. But 
>>> isn't this what the phase angles are supposed to effect? AG
>> 
>> The screen pattern is determined by relative phase angles for the 
>> different paths that reach the same point on the screen.  The relative 
>> angles only depend on different path lengths, so the overall phase angle 
>> is irrelevant.
>> 
>> Brent
>> 
>> Sure, except there areTWO forms of phase interference in Wave Mechanics; 
>> the one you refer to above, and another discussed in the Stackexchange 
>> links I previously posted. In the latter case, the wf is expressed as a 
>> superposition, say of two states, where we consider two cases; a 
>> multiplicative complex phase shift is included prior to the sum, and 
>> different complex phase shifts multiplying each component, all of the 
>> form e^i (theta). Easy to show that interference exists in the latter 
>> case, but not the former. Now suppose we take the inner product of the 
>> wf with the ith eigenstate of the superposition, in order to calculate 
>> the probability of measuring the eigenvalue of the ith eigenstate, 
>> applying one of the postulates of QM, keeping in mind that each 
>> eigenstate is multiplied by a DIFFERENT complex phase shift.  If we 
>> further assume the eigenstates are mutually orthogonal, the probability 
>> of measuring each eigenvalue does NOT depend on the different phase 
>> shifts. What happened to the interference demonstrated by the 
>> Stackexchange links? TIA, AG 
>> 
> Your measurement projected it out. It's like measuring which slit the 
> photon goes through...it eliminates the interference.
> 
> Brent
> 
> That's what I suspected; that going to an orthogonal basis, I departed 
> from the examples in Stackexchange where an arbitrary superposition is 
> used in the analysis of interference. Nevertheless, isn't it possible to 
> transform from an arbitrary superposition to one using an orthogonal 
> basis? And aren't all bases equivalent from a linear algebra pov? If all 
> bases are equivalent, why would transforming to an orthogonal basis lose 
> interference, whereas a general superposition does not? TIA, AG
 
 I don’t understand this. All the bases we have used all the time are 
 supposed to be orthonormal bases. We suppose that the scalar product (e_i 
 e_j) = delta_i_j, when presenting the Born rule, and the quantum formalism.
 
 Bruno
 
 Generally, bases in a vector space are NOT orthonormal. 
>>> 
>>> Right. But we can always build an orthonormal base with a decent scalar 
>>> product, like in Hilbert space, 
>>> 
>>> 
>>> 
 For example, in the vector space of vectors in the plane, any pair of 
 non-parallel vectors form a basis. Same for any general superposition of 
 states in QM. HOWEVER, eigenfunctions with distinct eigenvalues ARE 
 orthogonal.
>>> 
>>> Absolutely. And when choosing a non degenerate observable/measuring-device, 
>>> we work in the base of its eigenvectors. A superposition is better seen as 
>>> a sum of some eigenvectors of some observable. That is the crazy thing in 
>>> QM. The same particle can be superposed in the state of being here and 
>>> there. Two different positions of one particle can be superposed.
>>> 
>>> This is a common misinterpretation. Just because a wf can be expressed in 
>>> different ways (as a vector in the plane can be expressed in uncountably 
>>> many different bases), doesn't mean a particle can exist in different 
>>> positions in space at the same time. AG
>> 
>> It has a non null amplitude of probability of being here and there at the 
>> same time, like having 

Re: Coherent states of a superposition

2019-01-28 Thread agrayson2000


On Friday, January 25, 2019 at 7:33:05 AM UTC-7, Bruno Marchal wrote:
>
>
> On 24 Jan 2019, at 09:29, agrays...@gmail.com  wrote:
>
>
>
> On Sunday, January 20, 2019 at 11:54:43 AM UTC, agrays...@gmail.com wrote:
>>
>>
>>
>> On Sunday, January 20, 2019 at 9:56:17 AM UTC, Bruno Marchal wrote:
>>>
>>>
>>> On 18 Jan 2019, at 18:50, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Friday, January 18, 2019 at 12:09:58 PM UTC, Bruno Marchal wrote:


 On 17 Jan 2019, at 14:48, agrays...@gmail.com wrote:



 On Thursday, January 17, 2019 at 12:36:07 PM UTC, Bruno Marchal wrote:
>
>
> On 17 Jan 2019, at 09:33, agrays...@gmail.com wrote:
>
>
>
> On Thursday, January 17, 2019 at 3:58:48 AM UTC, Brent wrote:
>>
>>
>>
>> On 1/16/2019 7:25 PM, agrays...@gmail.com wrote:
>>
>>
>>
>> On Monday, January 14, 2019 at 6:12:43 AM UTC, Brent wrote:
>>>
>>>
>>>
>>> On 1/13/2019 9:51 PM, agrays...@gmail.com wrote:
>>>
>>> This means, to me, that the arbitrary phase angles have absolutely 
>>> no effect on the resultant interference pattern which is observed. But 
>>> isn't this what the phase angles are supposed to effect? AG
>>>
>>>
>>> The screen pattern is determined by *relative phase angles for the 
>>> different paths that reach the same point on the screen*.  The 
>>> relative angles only depend on different path lengths, so the overall 
>>> phase 
>>> angle is irrelevant.
>>>
>>> Brent
>>>
>>
>>
>> *Sure, except there areTWO forms of phase interference in Wave 
>> Mechanics; the one you refer to above, and another discussed in the 
>> Stackexchange links I previously posted. In the latter case, the wf is 
>> expressed as a superposition, say of two states, where we consider two 
>> cases; a multiplicative complex phase shift is included prior to the 
>> sum, 
>> and different complex phase shifts multiplying each component, all of 
>> the 
>> form e^i (theta). Easy to show that interference exists in the latter 
>> case, 
>> but not the former. Now suppose we take the inner product of the wf with 
>> the ith eigenstate of the superposition, in order to calculate the 
>> probability of measuring the eigenvalue of the ith eigenstate, applying 
>> one 
>> of the postulates of QM, keeping in mind that each eigenstate is 
>> multiplied 
>> by a DIFFERENT complex phase shift.  If we further assume the 
>> eigenstates 
>> are mutually orthogonal, the probability of measuring each eigenvalue 
>> does 
>> NOT depend on the different phase shifts. What happened to the 
>> interference 
>> demonstrated by the Stackexchange links? TIA, AG *
>>
>> Your measurement projected it out. It's like measuring which slit the 
>> photon goes through...it eliminates the interference.
>>
>> Brent
>>
>
> *That's what I suspected; that going to an orthogonal basis, I 
> departed from the examples in Stackexchange where an arbitrary 
> superposition is used in the analysis of interference. Nevertheless, 
> isn't 
> it possible to transform from an arbitrary superposition to one using an 
> orthogonal basis? And aren't all bases equivalent from a linear algebra 
> pov? If all bases are equivalent, why would transforming to an orthogonal 
> basis lose interference, whereas a general superposition does not? TIA, 
> AG*
>
>
> I don’t understand this. All the bases we have used all the time are 
> supposed to be orthonormal bases. We suppose that the scalar product (e_i 
> e_j) = delta_i_j, when presenting the Born rule, and the quantum 
> formalism.
>
> Bruno
>

 *Generally, bases in a vector space are NOT orthonormal. *


 Right. But we can always build an orthonormal base with a decent scalar 
 product, like in Hilbert space, 



 *For example, in the vector space of vectors in the plane, any pair of 
 non-parallel vectors form a basis. Same for any general superposition of 
 states in QM. HOWEVER, eigenfunctions with distinct eigenvalues ARE 
 orthogonal.*


 Absolutely. And when choosing a non degenerate 
 observable/measuring-device, we work in the base of its eigenvectors. A 
 superposition is better seen as a sum of some eigenvectors of some 
 observable. That is the crazy thing in QM. The same particle can be 
 superposed in the state of being here and there. Two different positions 
 of 
 one particle can be superposed.

>>>
>>> *This is a common misinterpretation. Just because a wf can be expressed 
>>> in different ways (as a vector in the plane can be expressed in uncountably 
>>> many different bases), doesn't mean a particle can exist in different 
>>> positions in space at the same time. AG*
>>>

Re: Coherent states of a superposition

2019-01-25 Thread Bruno Marchal

> On 24 Jan 2019, at 09:29, agrayson2...@gmail.com wrote:
> 
> 
> 
> On Sunday, January 20, 2019 at 11:54:43 AM UTC, agrays...@gmail.com 
>  wrote:
> 
> 
> On Sunday, January 20, 2019 at 9:56:17 AM UTC, Bruno Marchal wrote:
> 
>> On 18 Jan 2019, at 18:50, agrays...@gmail.com <> wrote:
>> 
>> 
>> 
>> On Friday, January 18, 2019 at 12:09:58 PM UTC, Bruno Marchal wrote:
>> 
>>> On 17 Jan 2019, at 14:48, agrays...@gmail.com <> wrote:
>>> 
>>> 
>>> 
>>> On Thursday, January 17, 2019 at 12:36:07 PM UTC, Bruno Marchal wrote:
>>> 
 On 17 Jan 2019, at 09:33, agrays...@gmail.com <> wrote:
 
 
 
 On Thursday, January 17, 2019 at 3:58:48 AM UTC, Brent wrote:
 
 
 On 1/16/2019 7:25 PM, agrays...@gmail.com <> wrote:
> 
> 
> On Monday, January 14, 2019 at 6:12:43 AM UTC, Brent wrote:
> 
> 
> On 1/13/2019 9:51 PM, agrays...@gmail.com <> wrote:
>> This means, to me, that the arbitrary phase angles have absolutely no 
>> effect on the resultant interference pattern which is observed. But 
>> isn't this what the phase angles are supposed to effect? AG
> 
> The screen pattern is determined by relative phase angles for the 
> different paths that reach the same point on the screen.  The relative 
> angles only depend on different path lengths, so the overall phase angle 
> is irrelevant.
> 
> Brent
> 
> Sure, except there areTWO forms of phase interference in Wave Mechanics; 
> the one you refer to above, and another discussed in the Stackexchange 
> links I previously posted. In the latter case, the wf is expressed as a 
> superposition, say of two states, where we consider two cases; a 
> multiplicative complex phase shift is included prior to the sum, and 
> different complex phase shifts multiplying each component, all of the 
> form e^i (theta). Easy to show that interference exists in the latter 
> case, but not the former. Now suppose we take the inner product of the wf 
> with the ith eigenstate of the superposition, in order to calculate the 
> probability of measuring the eigenvalue of the ith eigenstate, applying 
> one of the postulates of QM, keeping in mind that each eigenstate is 
> multiplied by a DIFFERENT complex phase shift.  If we further assume the 
> eigenstates are mutually orthogonal, the probability of measuring each 
> eigenvalue does NOT depend on the different phase shifts. What happened 
> to the interference demonstrated by the Stackexchange links? TIA, AG 
> 
 Your measurement projected it out. It's like measuring which slit the 
 photon goes through...it eliminates the interference.
 
 Brent
 
 That's what I suspected; that going to an orthogonal basis, I departed 
 from the examples in Stackexchange where an arbitrary superposition is 
 used in the analysis of interference. Nevertheless, isn't it possible to 
 transform from an arbitrary superposition to one using an orthogonal 
 basis? And aren't all bases equivalent from a linear algebra pov? If all 
 bases are equivalent, why would transforming to an orthogonal basis lose 
 interference, whereas a general superposition does not? TIA, AG
>>> 
>>> I don’t understand this. All the bases we have used all the time are 
>>> supposed to be orthonormal bases. We suppose that the scalar product (e_i 
>>> e_j) = delta_i_j, when presenting the Born rule, and the quantum formalism.
>>> 
>>> Bruno
>>> 
>>> Generally, bases in a vector space are NOT orthonormal. 
>> 
>> Right. But we can always build an orthonormal base with a decent scalar 
>> product, like in Hilbert space, 
>> 
>> 
>> 
>>> For example, in the vector space of vectors in the plane, any pair of 
>>> non-parallel vectors form a basis. Same for any general superposition of 
>>> states in QM. HOWEVER, eigenfunctions with distinct eigenvalues ARE 
>>> orthogonal.
>> 
>> Absolutely. And when choosing a non degenerate observable/measuring-device, 
>> we work in the base of its eigenvectors. A superposition is better seen as a 
>> sum of some eigenvectors of some observable. That is the crazy thing in QM. 
>> The same particle can be superposed in the state of being here and there. 
>> Two different positions of one particle can be superposed.
>> 
>> This is a common misinterpretation. Just because a wf can be expressed in 
>> different ways (as a vector in the plane can be expressed in uncountably 
>> many different bases), doesn't mean a particle can exist in different 
>> positions in space at the same time. AG
> 
> It has a non null amplitude of probability of being here and there at the 
> same time, like having a non null amplitude of probability of going through 
> each slit in the two slits experience.
> 
> If not, you can’t explain the inference patterns, especially in the photon 
> self-interference.
> 
> 
> 
> 
>> 
>> Using a non orthonormal base makes 

Re: Coherent states of a superposition

2019-01-24 Thread agrayson2000


On Sunday, January 20, 2019 at 11:54:43 AM UTC, agrays...@gmail.com wrote:
>
>
>
> On Sunday, January 20, 2019 at 9:56:17 AM UTC, Bruno Marchal wrote:
>>
>>
>> On 18 Jan 2019, at 18:50, agrays...@gmail.com wrote:
>>
>>
>>
>> On Friday, January 18, 2019 at 12:09:58 PM UTC, Bruno Marchal wrote:
>>>
>>>
>>> On 17 Jan 2019, at 14:48, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Thursday, January 17, 2019 at 12:36:07 PM UTC, Bruno Marchal wrote:


 On 17 Jan 2019, at 09:33, agrays...@gmail.com wrote:



 On Thursday, January 17, 2019 at 3:58:48 AM UTC, Brent wrote:
>
>
>
> On 1/16/2019 7:25 PM, agrays...@gmail.com wrote:
>
>
>
> On Monday, January 14, 2019 at 6:12:43 AM UTC, Brent wrote: 
>>
>>
>>
>> On 1/13/2019 9:51 PM, agrays...@gmail.com wrote:
>>
>> This means, to me, that the arbitrary phase angles have absolutely no 
>> effect on the resultant interference pattern which is observed. But 
>> isn't 
>> this what the phase angles are supposed to effect? AG
>>
>>
>> The screen pattern is determined by *relative phase angles for the 
>> different paths that reach the same point on the screen*.  The 
>> relative angles only depend on different path lengths, so the overall 
>> phase 
>> angle is irrelevant.
>>
>> Brent
>>
>
>
> *Sure, except there areTWO forms of phase interference in Wave 
> Mechanics; the one you refer to above, and another discussed in the 
> Stackexchange links I previously posted. In the latter case, the wf is 
> expressed as a superposition, say of two states, where we consider two 
> cases; a multiplicative complex phase shift is included prior to the sum, 
> and different complex phase shifts multiplying each component, all of the 
> form e^i (theta). Easy to show that interference exists in the latter 
> case, 
> but not the former. Now suppose we take the inner product of the wf with 
> the ith eigenstate of the superposition, in order to calculate the 
> probability of measuring the eigenvalue of the ith eigenstate, applying 
> one 
> of the postulates of QM, keeping in mind that each eigenstate is 
> multiplied 
> by a DIFFERENT complex phase shift.  If we further assume the eigenstates 
> are mutually orthogonal, the probability of measuring each eigenvalue 
> does 
> NOT depend on the different phase shifts. What happened to the 
> interference 
> demonstrated by the Stackexchange links? TIA, AG *
>
> Your measurement projected it out. It's like measuring which slit the 
> photon goes through...it eliminates the interference.
>
> Brent
>

 *That's what I suspected; that going to an orthogonal basis, I departed 
 from the examples in Stackexchange where an arbitrary superposition is 
 used 
 in the analysis of interference. Nevertheless, isn't it possible to 
 transform from an arbitrary superposition to one using an orthogonal 
 basis? 
 And aren't all bases equivalent from a linear algebra pov? If all bases 
 are 
 equivalent, why would transforming to an orthogonal basis lose 
 interference, whereas a general superposition does not? TIA, AG*


 I don’t understand this. All the bases we have used all the time are 
 supposed to be orthonormal bases. We suppose that the scalar product (e_i 
 e_j) = delta_i_j, when presenting the Born rule, and the quantum formalism.

 Bruno

>>>
>>> *Generally, bases in a vector space are NOT orthonormal. *
>>>
>>>
>>> Right. But we can always build an orthonormal base with a decent scalar 
>>> product, like in Hilbert space, 
>>>
>>>
>>>
>>> *For example, in the vector space of vectors in the plane, any pair of 
>>> non-parallel vectors form a basis. Same for any general superposition of 
>>> states in QM. HOWEVER, eigenfunctions with distinct eigenvalues ARE 
>>> orthogonal.*
>>>
>>>
>>> Absolutely. And when choosing a non degenerate 
>>> observable/measuring-device, we work in the base of its eigenvectors. A 
>>> superposition is better seen as a sum of some eigenvectors of some 
>>> observable. That is the crazy thing in QM. The same particle can be 
>>> superposed in the state of being here and there. Two different positions of 
>>> one particle can be superposed.
>>>
>>
>> *This is a common misinterpretation. Just because a wf can be expressed 
>> in different ways (as a vector in the plane can be expressed in uncountably 
>> many different bases), doesn't mean a particle can exist in different 
>> positions in space at the same time. AG*
>>
>>
>> It has a non null amplitude of probability of being here and there at the 
>> same time, like having a non null amplitude of probability of going through 
>> each slit in the two slits experience.
>>
>> If not, you can’t explain the inference patterns, especially in the 
>> 

Re: Coherent states of a superposition

2019-01-20 Thread 'scerir' via Everything List

> Il 20 gennaio 2019 alle 13.25 agrayson2...@gmail.com ha scritto:
> 
> 
> 
> On Sunday, January 20, 2019 at 12:10:25 PM UTC, scerir wrote:
> 
> > > 
> > 
> > > > > Il 20 gennaio 2019 alle 12.56 agrays...@gmail.com ha 
> > scritto:
> > > 
> > > 
> > > 
> > > On Sunday, January 20, 2019 at 10:46:01 AM UTC, scerir wrote:
> > > 
> > > > > > > 
> > > > 
> > > > [BRUNO writes] It has a non null amplitude of 
> > > > probability of being here and there at the same time, like having a non 
> > > > null amplitude of probability of going through each slit in the two 
> > > > slits experience. If not, you can’t explain the inference patterns, 
> > > > especially in the photon self-interference.
> > > > 
> > > > 
> > > > Interesting to point out that, in the two-slit, it is 
> > > > possible to have interference even when there is just one slit open 
> > > > (and the other slit shut, and viceversa, with some appropriate 
> > > > frequence). In this case it seems that the two amplitudes cannot 
> > > > interfere.
> > > > 
> > > > - Leonard Mandel : "On the Possibility of Observing 
> > > > Interference Effects with Light Beams Divided by a Shutter", 
> > > > J.Opt.Soc.Amer.,
> > > > 49, (1959), 931.
> > > > - R.M. Sillitto, Catherine Wykes: "An Interference 
> > > > Experiment With Light Beams Modulated In Anti-Phase By An Electro-Optic 
> > > > Shutter",
> > > > Physics Letters, 39-A-4, (1972), 333-334.
> > > > 
> > > > > > > 
> > > Isn't this called diffraction? AG
> > > 
> > > > > 
> > No, they show it is interference
> > 
> > > 
> ??? CMIIAW, but I'm pretty sure that single slit interference is called 
> DIFFRACTION. There is interference for a single slit. Apply Huygen's 
> principle where each point in the slit acts as source of waves which mutually 
> interference. AG
> 

Interference is interference. Diffraction is diffraction.

After useful considerations by Leonard Mandel [J. Opt. Soc. Amer., 49, (1959), 
931] at last R.M. Sillitto and Catherine Wykes [Physics Letters, 39-A-4, 
(1972), 333] performed the experiment suggested by Janossy and Nagy (1956) and 
found a beautiful INTERFERENCE when just one photon was present in their 
interferometer, at a time, and when their electro-optic shutter (closing one or 
the other slit, alternatively) was switched several times during the 
time-travel of each photon.

In terms of photons (that is to say: particles) the condition for INTERFERENCE 
is that the two in principle *possible* paths lead to the same cell of phase 
space, so that the path of each photon is intrinsically indeterminate (the 
usual 'welcher weg', or 'which path', issue).

Of course the shutter must be switched in a time which is less than the 
uncertainty in the time arrival of the photon.

In other words. Here the INTERFERENCE seems to be due to the 
indistinguishability of the two possible paths (only one of these paths is 
actual, because there is that shutter). It is very difficult to see here an 
interference between two amplitudes.

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Re: Coherent states of a superposition

2019-01-20 Thread agrayson2000


On Sunday, January 20, 2019 at 12:10:25 PM UTC, scerir wrote:
>
>
> Il 20 gennaio 2019 alle 12.56 agrays...@gmail.com  ha 
> scritto: 
>
>
>
> On Sunday, January 20, 2019 at 10:46:01 AM UTC, scerir wrote:
>
>
> [BRUNO writes] It has a non null amplitude of probability of being here 
> and there at the same time, like having a non null amplitude of probability 
> of going through each slit in the two slits experience. If not, you can’t 
> explain the inference patterns, especially in the photon self-interference.
>
>
> Interesting to point out that, in the two-slit, it is possible to have 
> interference even when there is just one slit open (and the other slit 
> shut, and viceversa, with some appropriate frequence). In this case it 
> seems that the two amplitudes cannot interfere. 
>
> - Leonard Mandel : "On the Possibility of Observing Interference Effects 
> with Light Beams Divided by a Shutter", J.Opt.Soc.Amer., 
> 49, (1959), 931. 
> - R.M. Sillitto, Catherine Wykes: "An Interference Experiment With Light 
> Beams Modulated In Anti-Phase By An Electro-Optic Shutter", 
> Physics Letters, 39-A-4, (1972), 333-334.
>
>
> *Isn't this called diffraction? AG *
>
> No, they show it is interference
>


*??? CMIIAW, but I'm pretty sure that single slit interference is called 
DIFFRACTION. There is interference for a single slit. Apply Huygen's 
principle where each point in the slit acts as source of waves which 
mutually interference. AG *

>  
> -- 
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> . 
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> For more options, visit https://groups.google.com/d/optout. 
>
>

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Re: Coherent states of a superposition

2019-01-20 Thread 'scerir' via Everything List

> Il 20 gennaio 2019 alle 12.56 agrayson2...@gmail.com ha scritto:
> 
> 
> 
> On Sunday, January 20, 2019 at 10:46:01 AM UTC, scerir wrote:
> 
> > > 
> > 
> > [BRUNO writes] It has a non null amplitude of probability of being 
> > here and there at the same time, like having a non null amplitude of 
> > probability of going through each slit in the two slits experience. If not, 
> > you can’t explain the inference patterns, especially in the photon 
> > self-interference.
> > 
> > 
> > Interesting to point out that, in the two-slit, it is possible to 
> > have interference even when there is just one slit open (and the other slit 
> > shut, and viceversa, with some appropriate frequence). In this case it 
> > seems that the two amplitudes cannot interfere.
> > 
> > - Leonard Mandel : "On the Possibility of Observing Interference 
> > Effects with Light Beams Divided by a Shutter", J.Opt.Soc.Amer.,
> > 49, (1959), 931.
> > - R.M. Sillitto, Catherine Wykes: "An Interference Experiment With 
> > Light Beams Modulated In Anti-Phase By An Electro-Optic Shutter",
> > Physics Letters, 39-A-4, (1972), 333-334.
> > 
> > > 
> Isn't this called diffraction? AG
> 

No, they show it is interference

> 
>  
> 
> --
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Re: Coherent states of a superposition

2019-01-20 Thread agrayson2000


On Sunday, January 20, 2019 at 11:54:43 AM UTC, agrays...@gmail.com wrote:
>
>
>
> On Sunday, January 20, 2019 at 9:56:17 AM UTC, Bruno Marchal wrote:
>>
>>
>> On 18 Jan 2019, at 18:50, agrays...@gmail.com wrote:
>>
>>
>>
>> On Friday, January 18, 2019 at 12:09:58 PM UTC, Bruno Marchal wrote:
>>>
>>>
>>> On 17 Jan 2019, at 14:48, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Thursday, January 17, 2019 at 12:36:07 PM UTC, Bruno Marchal wrote:


 On 17 Jan 2019, at 09:33, agrays...@gmail.com wrote:



 On Thursday, January 17, 2019 at 3:58:48 AM UTC, Brent wrote:
>
>
>
> On 1/16/2019 7:25 PM, agrays...@gmail.com wrote:
>
>
>
> On Monday, January 14, 2019 at 6:12:43 AM UTC, Brent wrote: 
>>
>>
>>
>> On 1/13/2019 9:51 PM, agrays...@gmail.com wrote:
>>
>> This means, to me, that the arbitrary phase angles have absolutely no 
>> effect on the resultant interference pattern which is observed. But 
>> isn't 
>> this what the phase angles are supposed to effect? AG
>>
>>
>> The screen pattern is determined by *relative phase angles for the 
>> different paths that reach the same point on the screen*.  The 
>> relative angles only depend on different path lengths, so the overall 
>> phase 
>> angle is irrelevant.
>>
>> Brent
>>
>
>
> *Sure, except there areTWO forms of phase interference in Wave 
> Mechanics; the one you refer to above, and another discussed in the 
> Stackexchange links I previously posted. In the latter case, the wf is 
> expressed as a superposition, say of two states, where we consider two 
> cases; a multiplicative complex phase shift is included prior to the sum, 
> and different complex phase shifts multiplying each component, all of the 
> form e^i (theta). Easy to show that interference exists in the latter 
> case, 
> but not the former. Now suppose we take the inner product of the wf with 
> the ith eigenstate of the superposition, in order to calculate the 
> probability of measuring the eigenvalue of the ith eigenstate, applying 
> one 
> of the postulates of QM, keeping in mind that each eigenstate is 
> multiplied 
> by a DIFFERENT complex phase shift.  If we further assume the eigenstates 
> are mutually orthogonal, the probability of measuring each eigenvalue 
> does 
> NOT depend on the different phase shifts. What happened to the 
> interference 
> demonstrated by the Stackexchange links? TIA, AG *
>
> Your measurement projected it out. It's like measuring which slit the 
> photon goes through...it eliminates the interference.
>
> Brent
>

 *That's what I suspected; that going to an orthogonal basis, I departed 
 from the examples in Stackexchange where an arbitrary superposition is 
 used 
 in the analysis of interference. Nevertheless, isn't it possible to 
 transform from an arbitrary superposition to one using an orthogonal 
 basis? 
 And aren't all bases equivalent from a linear algebra pov? If all bases 
 are 
 equivalent, why would transforming to an orthogonal basis lose 
 interference, whereas a general superposition does not? TIA, AG*


 I don’t understand this. All the bases we have used all the time are 
 supposed to be orthonormal bases. We suppose that the scalar product (e_i 
 e_j) = delta_i_j, when presenting the Born rule, and the quantum formalism.

 Bruno

>>>
>>> *Generally, bases in a vector space are NOT orthonormal. *
>>>
>>>
>>> Right. But we can always build an orthonormal base with a decent scalar 
>>> product, like in Hilbert space, 
>>>
>>>
>>>
>>> *For example, in the vector space of vectors in the plane, any pair of 
>>> non-parallel vectors form a basis. Same for any general superposition of 
>>> states in QM. HOWEVER, eigenfunctions with distinct eigenvalues ARE 
>>> orthogonal.*
>>>
>>>
>>> Absolutely. And when choosing a non degenerate 
>>> observable/measuring-device, we work in the base of its eigenvectors. A 
>>> superposition is better seen as a sum of some eigenvectors of some 
>>> observable. That is the crazy thing in QM. The same particle can be 
>>> superposed in the state of being here and there. Two different positions of 
>>> one particle can be superposed.
>>>
>>
>> *This is a common misinterpretation. Just because a wf can be expressed 
>> in different ways (as a vector in the plane can be expressed in uncountably 
>> many different bases), doesn't mean a particle can exist in different 
>> positions in space at the same time. AG*
>>
>>
>> It has a non null amplitude of probability of being here and there at the 
>> same time, like having a non null amplitude of probability of going through 
>> each slit in the two slits experience.
>>
>> If not, you can’t explain the inference patterns, especially in the 
>> 

Re: Coherent states of a superposition

2019-01-20 Thread agrayson2000


On Sunday, January 20, 2019 at 10:46:01 AM UTC, scerir wrote:
>
>
> [BRUNO writes] It has a non null amplitude of probability of being here 
> and there at the same time, like having a non null amplitude of probability 
> of going through each slit in the two slits experience. If not, you can’t 
> explain the inference patterns, especially in the photon self-interference.
>
>
> Interesting to point out that, in the two-slit, it is possible to have 
> interference even when there is just one slit open (and the other slit 
> shut, and viceversa, with some appropriate frequence). In this case it 
> seems that the two amplitudes cannot interfere. 
>
> - Leonard Mandel : "On the Possibility of Observing Interference Effects 
> with Light Beams Divided by a Shutter", J.Opt.Soc.Amer., 
> 49, (1959), 931.
> - R.M. Sillitto, Catherine Wykes: "An Interference Experiment With Light 
> Beams Modulated In Anti-Phase By An Electro-Optic Shutter", 
> Physics Letters, 39-A-4, (1972), 333-334.
>


*Isn't this called diffraction? AG *

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Re: Coherent states of a superposition

2019-01-20 Thread agrayson2000


On Sunday, January 20, 2019 at 9:56:17 AM UTC, Bruno Marchal wrote:
>
>
> On 18 Jan 2019, at 18:50, agrays...@gmail.com  wrote:
>
>
>
> On Friday, January 18, 2019 at 12:09:58 PM UTC, Bruno Marchal wrote:
>>
>>
>> On 17 Jan 2019, at 14:48, agrays...@gmail.com wrote:
>>
>>
>>
>> On Thursday, January 17, 2019 at 12:36:07 PM UTC, Bruno Marchal wrote:
>>>
>>>
>>> On 17 Jan 2019, at 09:33, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Thursday, January 17, 2019 at 3:58:48 AM UTC, Brent wrote:



 On 1/16/2019 7:25 PM, agrays...@gmail.com wrote:



 On Monday, January 14, 2019 at 6:12:43 AM UTC, Brent wrote: 
>
>
>
> On 1/13/2019 9:51 PM, agrays...@gmail.com wrote:
>
> This means, to me, that the arbitrary phase angles have absolutely no 
> effect on the resultant interference pattern which is observed. But isn't 
> this what the phase angles are supposed to effect? AG
>
>
> The screen pattern is determined by *relative phase angles for the 
> different paths that reach the same point on the screen*.  The 
> relative angles only depend on different path lengths, so the overall 
> phase 
> angle is irrelevant.
>
> Brent
>


 *Sure, except there areTWO forms of phase interference in Wave 
 Mechanics; the one you refer to above, and another discussed in the 
 Stackexchange links I previously posted. In the latter case, the wf is 
 expressed as a superposition, say of two states, where we consider two 
 cases; a multiplicative complex phase shift is included prior to the sum, 
 and different complex phase shifts multiplying each component, all of the 
 form e^i (theta). Easy to show that interference exists in the latter 
 case, 
 but not the former. Now suppose we take the inner product of the wf with 
 the ith eigenstate of the superposition, in order to calculate the 
 probability of measuring the eigenvalue of the ith eigenstate, applying 
 one 
 of the postulates of QM, keeping in mind that each eigenstate is 
 multiplied 
 by a DIFFERENT complex phase shift.  If we further assume the eigenstates 
 are mutually orthogonal, the probability of measuring each eigenvalue does 
 NOT depend on the different phase shifts. What happened to the 
 interference 
 demonstrated by the Stackexchange links? TIA, AG *

 Your measurement projected it out. It's like measuring which slit the 
 photon goes through...it eliminates the interference.

 Brent

>>>
>>> *That's what I suspected; that going to an orthogonal basis, I departed 
>>> from the examples in Stackexchange where an arbitrary superposition is used 
>>> in the analysis of interference. Nevertheless, isn't it possible to 
>>> transform from an arbitrary superposition to one using an orthogonal basis? 
>>> And aren't all bases equivalent from a linear algebra pov? If all bases are 
>>> equivalent, why would transforming to an orthogonal basis lose 
>>> interference, whereas a general superposition does not? TIA, AG*
>>>
>>>
>>> I don’t understand this. All the bases we have used all the time are 
>>> supposed to be orthonormal bases. We suppose that the scalar product (e_i 
>>> e_j) = delta_i_j, when presenting the Born rule, and the quantum formalism.
>>>
>>> Bruno
>>>
>>
>> *Generally, bases in a vector space are NOT orthonormal. *
>>
>>
>> Right. But we can always build an orthonormal base with a decent scalar 
>> product, like in Hilbert space, 
>>
>>
>>
>> *For example, in the vector space of vectors in the plane, any pair of 
>> non-parallel vectors form a basis. Same for any general superposition of 
>> states in QM. HOWEVER, eigenfunctions with distinct eigenvalues ARE 
>> orthogonal.*
>>
>>
>> Absolutely. And when choosing a non degenerate 
>> observable/measuring-device, we work in the base of its eigenvectors. A 
>> superposition is better seen as a sum of some eigenvectors of some 
>> observable. That is the crazy thing in QM. The same particle can be 
>> superposed in the state of being here and there. Two different positions of 
>> one particle can be superposed.
>>
>
> *This is a common misinterpretation. Just because a wf can be expressed in 
> different ways (as a vector in the plane can be expressed in uncountably 
> many different bases), doesn't mean a particle can exist in different 
> positions in space at the same time. AG*
>
>
> It has a non null amplitude of probability of being here and there at the 
> same time, like having a non null amplitude of probability of going through 
> each slit in the two slits experience.
>
> If not, you can’t explain the inference patterns, especially in the photon 
> self-interference.
>
>
>
>
>
> Using a non orthonormal base makes only things more complex. 
>>
> * I posted a link to this proof a few months ago. IIRC, it was on its 
>> specifically named thread. AG*
>>
>>
>> But all this makes my 

Re: Coherent states of a superposition

2019-01-20 Thread 'scerir' via Everything List

[BRUNO writes] It has a non null amplitude of probability of being here and 
there at the same time, like having a non null amplitude of probability of 
going through each slit in the two slits experience. If not, you can’t explain 
the inference patterns, especially in the photon self-interference.


Interesting to point out that, in the two-slit, it is possible to have 
interference even when there is just one slit open (and the other slit shut, 
and viceversa, with some appropriate frequence). In this case it seems that the 
two amplitudes cannot interfere.

- Leonard Mandel : "On the Possibility of Observing Interference Effects with 
Light Beams Divided by a Shutter", J.Opt.Soc.Amer.,
49, (1959), 931.
- R.M. Sillitto, Catherine Wykes: "An Interference Experiment With Light Beams 
Modulated In Anti-Phase By An Electro-Optic Shutter",
Physics Letters, 39-A-4, (1972), 333-334.

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Re: Coherent states of a superposition

2019-01-20 Thread Bruno Marchal

> On 18 Jan 2019, at 18:50, agrayson2...@gmail.com wrote:
> 
> 
> 
> On Friday, January 18, 2019 at 12:09:58 PM UTC, Bruno Marchal wrote:
> 
>> On 17 Jan 2019, at 14:48, agrays...@gmail.com  wrote:
>> 
>> 
>> 
>> On Thursday, January 17, 2019 at 12:36:07 PM UTC, Bruno Marchal wrote:
>> 
>>> On 17 Jan 2019, at 09:33, agrays...@gmail.com <> wrote:
>>> 
>>> 
>>> 
>>> On Thursday, January 17, 2019 at 3:58:48 AM UTC, Brent wrote:
>>> 
>>> 
>>> On 1/16/2019 7:25 PM, agrays...@gmail.com <> wrote:
 
 
 On Monday, January 14, 2019 at 6:12:43 AM UTC, Brent wrote:
 
 
 On 1/13/2019 9:51 PM, agrays...@gmail.com <> wrote:
> This means, to me, that the arbitrary phase angles have absolutely no 
> effect on the resultant interference pattern which is observed. But isn't 
> this what the phase angles are supposed to effect? AG
 
 The screen pattern is determined by relative phase angles for the 
 different paths that reach the same point on the screen.  The relative 
 angles only depend on different path lengths, so the overall phase angle 
 is irrelevant.
 
 Brent
 
 Sure, except there areTWO forms of phase interference in Wave Mechanics; 
 the one you refer to above, and another discussed in the Stackexchange 
 links I previously posted. In the latter case, the wf is expressed as a 
 superposition, say of two states, where we consider two cases; a 
 multiplicative complex phase shift is included prior to the sum, and 
 different complex phase shifts multiplying each component, all of the form 
 e^i (theta). Easy to show that interference exists in the latter case, but 
 not the former. Now suppose we take the inner product of the wf with the 
 ith eigenstate of the superposition, in order to calculate the probability 
 of measuring the eigenvalue of the ith eigenstate, applying one of the 
 postulates of QM, keeping in mind that each eigenstate is multiplied by a 
 DIFFERENT complex phase shift.  If we further assume the eigenstates are 
 mutually orthogonal, the probability of measuring each eigenvalue does NOT 
 depend on the different phase shifts. What happened to the interference 
 demonstrated by the Stackexchange links? TIA, AG 
 
>>> Your measurement projected it out. It's like measuring which slit the 
>>> photon goes through...it eliminates the interference.
>>> 
>>> Brent
>>> 
>>> That's what I suspected; that going to an orthogonal basis, I departed from 
>>> the examples in Stackexchange where an arbitrary superposition is used in 
>>> the analysis of interference. Nevertheless, isn't it possible to transform 
>>> from an arbitrary superposition to one using an orthogonal basis? And 
>>> aren't all bases equivalent from a linear algebra pov? If all bases are 
>>> equivalent, why would transforming to an orthogonal basis lose 
>>> interference, whereas a general superposition does not? TIA, AG
>> 
>> I don’t understand this. All the bases we have used all the time are 
>> supposed to be orthonormal bases. We suppose that the scalar product (e_i 
>> e_j) = delta_i_j, when presenting the Born rule, and the quantum formalism.
>> 
>> Bruno
>> 
>> Generally, bases in a vector space are NOT orthonormal.
> 
> Right. But we can always build an orthonormal base with a decent scalar 
> product, like in Hilbert space, 
> 
> 
> 
>> For example, in the vector space of vectors in the plane, any pair of 
>> non-parallel vectors form a basis. Same for any general superposition of 
>> states in QM. HOWEVER, eigenfunctions with distinct eigenvalues ARE 
>> orthogonal.
> 
> Absolutely. And when choosing a non degenerate observable/measuring-device, 
> we work in the base of its eigenvectors. A superposition is better seen as a 
> sum of some eigenvectors of some observable. That is the crazy thing in QM. 
> The same particle can be superposed in the state of being here and there. Two 
> different positions of one particle can be superposed.
> 
> This is a common misinterpretation. Just because a wf can be expressed in 
> different ways (as a vector in the plane can be expressed in uncountably many 
> different bases), doesn't mean a particle can exist in different positions in 
> space at the same time. AG

It has a non null amplitude of probability of being here and there at the same 
time, like having a non null amplitude of probability of going through each 
slit in the two slits experience.

If not, you can’t explain the inference patterns, especially in the photon 
self-interference.




> 
> Using a non orthonormal base makes only things more complex. 
>> I posted a link to this proof a few months ago. IIRC, it was on its 
>> specifically named thread. AG
> 
> But all this makes my point. A vector by itself cannot be superposed, but can 
> be seen as the superposition of two other vectors, and if those are 
> orthonormal, that gives by the Born rule the probability to obtain the "Eigen 
> 

Re: Coherent states of a superposition

2019-01-18 Thread agrayson2000


On Friday, January 18, 2019 at 12:09:58 PM UTC, Bruno Marchal wrote:
>
>
> On 17 Jan 2019, at 14:48, agrays...@gmail.com  wrote:
>
>
>
> On Thursday, January 17, 2019 at 12:36:07 PM UTC, Bruno Marchal wrote:
>>
>>
>> On 17 Jan 2019, at 09:33, agrays...@gmail.com wrote:
>>
>>
>>
>> On Thursday, January 17, 2019 at 3:58:48 AM UTC, Brent wrote:
>>>
>>>
>>>
>>> On 1/16/2019 7:25 PM, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Monday, January 14, 2019 at 6:12:43 AM UTC, Brent wrote: 



 On 1/13/2019 9:51 PM, agrays...@gmail.com wrote:

 This means, to me, that the arbitrary phase angles have absolutely no 
 effect on the resultant interference pattern which is observed. But isn't 
 this what the phase angles are supposed to effect? AG


 The screen pattern is determined by *relative phase angles for the 
 different paths that reach the same point on the screen*.  The 
 relative angles only depend on different path lengths, so the overall 
 phase 
 angle is irrelevant.

 Brent

>>>
>>>
>>> *Sure, except there areTWO forms of phase interference in Wave 
>>> Mechanics; the one you refer to above, and another discussed in the 
>>> Stackexchange links I previously posted. In the latter case, the wf is 
>>> expressed as a superposition, say of two states, where we consider two 
>>> cases; a multiplicative complex phase shift is included prior to the sum, 
>>> and different complex phase shifts multiplying each component, all of the 
>>> form e^i (theta). Easy to show that interference exists in the latter case, 
>>> but not the former. Now suppose we take the inner product of the wf with 
>>> the ith eigenstate of the superposition, in order to calculate the 
>>> probability of measuring the eigenvalue of the ith eigenstate, applying one 
>>> of the postulates of QM, keeping in mind that each eigenstate is multiplied 
>>> by a DIFFERENT complex phase shift.  If we further assume the eigenstates 
>>> are mutually orthogonal, the probability of measuring each eigenvalue does 
>>> NOT depend on the different phase shifts. What happened to the interference 
>>> demonstrated by the Stackexchange links? TIA, AG *
>>>
>>> Your measurement projected it out. It's like measuring which slit the 
>>> photon goes through...it eliminates the interference.
>>>
>>> Brent
>>>
>>
>> *That's what I suspected; that going to an orthogonal basis, I departed 
>> from the examples in Stackexchange where an arbitrary superposition is used 
>> in the analysis of interference. Nevertheless, isn't it possible to 
>> transform from an arbitrary superposition to one using an orthogonal basis? 
>> And aren't all bases equivalent from a linear algebra pov? If all bases are 
>> equivalent, why would transforming to an orthogonal basis lose 
>> interference, whereas a general superposition does not? TIA, AG*
>>
>>
>> I don’t understand this. All the bases we have used all the time are 
>> supposed to be orthonormal bases. We suppose that the scalar product (e_i 
>> e_j) = delta_i_j, when presenting the Born rule, and the quantum formalism.
>>
>> Bruno
>>
>
> *Generally, bases in a vector space are NOT orthonormal. *
>
>
> Right. But we can always build an orthonormal base with a decent scalar 
> product, like in Hilbert space, 
>
>
>
> *For example, in the vector space of vectors in the plane, any pair of 
> non-parallel vectors form a basis. Same for any general superposition of 
> states in QM. HOWEVER, eigenfunctions with distinct eigenvalues ARE 
> orthogonal.*
>
>
> Absolutely. And when choosing a non degenerate 
> observable/measuring-device, we work in the base of its eigenvectors. A 
> superposition is better seen as a sum of some eigenvectors of some 
> observable. That is the crazy thing in QM. The same particle can be 
> superposed in the state of being here and there. Two different positions of 
> one particle can be superposed.
>

*This is a common misinterpretation. Just because a wf can be expressed in 
different ways (as a vector in the plane can be expressed in uncountably 
many different bases), doesn't mean a particle can exist in different 
positions in space at the same time. AG*

Using a non orthonormal base makes only things more complex. 
>
* I posted a link to this proof a few months ago. IIRC, it was on its 
> specifically named thread. AG*
>
>
> But all this makes my point. A vector by itself cannot be superposed, but 
> can be seen as the superposition of two other vectors, and if those are 
> orthonormal, that gives by the Born rule the probability to obtain the 
> "Eigen result” corresponding to the measuring apparatus with Eigen vectors 
> given by that orthonormal base.
>
> I’m still not sure about what you would be missing.
>

*You would be missing the interference! Do the math. Calculate the 
probability density of a wf expressed as a superposition of orthonormal 
eigenstates, where each component state has a different phase angle. All 

Re: Coherent states of a superposition

2019-01-18 Thread Bruno Marchal

> On 17 Jan 2019, at 14:48, agrayson2...@gmail.com wrote:
> 
> 
> 
> On Thursday, January 17, 2019 at 12:36:07 PM UTC, Bruno Marchal wrote:
> 
>> On 17 Jan 2019, at 09:33, agrays...@gmail.com  wrote:
>> 
>> 
>> 
>> On Thursday, January 17, 2019 at 3:58:48 AM UTC, Brent wrote:
>> 
>> 
>> On 1/16/2019 7:25 PM, agrays...@gmail.com <> wrote:
>>> 
>>> 
>>> On Monday, January 14, 2019 at 6:12:43 AM UTC, Brent wrote:
>>> 
>>> 
>>> On 1/13/2019 9:51 PM, agrays...@gmail.com <> wrote:
 This means, to me, that the arbitrary phase angles have absolutely no 
 effect on the resultant interference pattern which is observed. But isn't 
 this what the phase angles are supposed to effect? AG
>>> 
>>> The screen pattern is determined by relative phase angles for the different 
>>> paths that reach the same point on the screen.  The relative angles only 
>>> depend on different path lengths, so the overall phase angle is irrelevant.
>>> 
>>> Brent
>>> 
>>> Sure, except there areTWO forms of phase interference in Wave Mechanics; 
>>> the one you refer to above, and another discussed in the Stackexchange 
>>> links I previously posted. In the latter case, the wf is expressed as a 
>>> superposition, say of two states, where we consider two cases; a 
>>> multiplicative complex phase shift is included prior to the sum, and 
>>> different complex phase shifts multiplying each component, all of the form 
>>> e^i (theta). Easy to show that interference exists in the latter case, but 
>>> not the former. Now suppose we take the inner product of the wf with the 
>>> ith eigenstate of the superposition, in order to calculate the probability 
>>> of measuring the eigenvalue of the ith eigenstate, applying one of the 
>>> postulates of QM, keeping in mind that each eigenstate is multiplied by a 
>>> DIFFERENT complex phase shift.  If we further assume the eigenstates are 
>>> mutually orthogonal, the probability of measuring each eigenvalue does NOT 
>>> depend on the different phase shifts. What happened to the interference 
>>> demonstrated by the Stackexchange links? TIA, AG 
>>> 
>> Your measurement projected it out. It's like measuring which slit the photon 
>> goes through...it eliminates the interference.
>> 
>> Brent
>> 
>> That's what I suspected; that going to an orthogonal basis, I departed from 
>> the examples in Stackexchange where an arbitrary superposition is used in 
>> the analysis of interference. Nevertheless, isn't it possible to transform 
>> from an arbitrary superposition to one using an orthogonal basis? And aren't 
>> all bases equivalent from a linear algebra pov? If all bases are equivalent, 
>> why would transforming to an orthogonal basis lose interference, whereas a 
>> general superposition does not? TIA, AG
> 
> I don’t understand this. All the bases we have used all the time are supposed 
> to be orthonormal bases. We suppose that the scalar product (e_i e_j) = 
> delta_i_j, when presenting the Born rule, and the quantum formalism.
> 
> Bruno
> 
> Generally, bases in a vector space are NOT orthonormal.

Right. But we can always build an orthonormal base with a decent scalar 
product, like in Hilbert space, 



> For example, in the vector space of vectors in the plane, any pair of 
> non-parallel vectors form a basis. Same for any general superposition of 
> states in QM. HOWEVER, eigenfunctions with distinct eigenvalues ARE 
> orthogonal.

Absolutely. And when choosing a non degenerate observable/measuring-device, we 
work in the base of its eigenvectors. A superposition is better seen as a sum 
of some eigenvectors of some observable. That is the crazy thing in QM. The 
same particle can be superposed in the state of being here and there. Two 
different positions of one particle can be superposed. Using a non orthonormal 
base makes only things more complex. 





> I posted a link to this proof a few months ago. IIRC, it was on its 
> specifically named thread. AG


But all this makes my point. A vector by itself cannot be superposed, but can 
be seen as the superposition of two other vectors, and if those are 
orthonormal, that gives by the Born rule the probability to obtain the "Eigen 
result” corresponding to the measuring apparatus with Eigen vectors given by 
that orthonormal base.

I’m still not sure about what you would be missing.

Bruno




>> 
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> 
> 
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> You received this message because you are subscribed to the Google Groups 
> "Everything 

Re: Coherent states of a superposition

2019-01-18 Thread agrayson2000


On Thursday, January 17, 2019 at 3:58:48 AM UTC, Brent wrote:
>
>
>
> On 1/16/2019 7:25 PM, agrays...@gmail.com  wrote:
>
>
>
> On Monday, January 14, 2019 at 6:12:43 AM UTC, Brent wrote: 
>>
>>
>>
>> On 1/13/2019 9:51 PM, agrays...@gmail.com wrote:
>>
>> This means, to me, that the arbitrary phase angles have absolutely no 
>> effect on the resultant interference pattern which is observed. But isn't 
>> this what the phase angles are supposed to effect? AG
>>
>>
>> The screen pattern is determined by *relative phase angles for the 
>> different paths that reach the same point on the screen*.  The relative 
>> angles only depend on different path lengths, so the overall phase angle is 
>> irrelevant.
>>
>> Brent
>>
>
>
> *Sure, except there areTWO forms of phase interference in Wave Mechanics; 
> the one you refer to above, and another discussed in the Stackexchange 
> links I previously posted. In the latter case, the wf is expressed as a 
> superposition, say of two states, where we consider two cases; a 
> multiplicative complex phase shift is included prior to the sum, and 
> different complex phase shifts multiplying each component, all of the form 
> e^i (theta). Easy to show that interference exists in the latter case, but 
> not the former. Now suppose we take the inner product of the wf with the 
> ith eigenstate of the superposition, in order to calculate the probability 
> of measuring the eigenvalue of the ith eigenstate, applying one of the 
> postulates of QM, keeping in mind that each eigenstate is multiplied by a 
> DIFFERENT complex phase shift.  If we further assume the eigenstates are 
> mutually orthogonal, the probability of measuring each eigenvalue does NOT 
> depend on the different phase shifts. What happened to the interference 
> demonstrated by the Stackexchange links? TIA, AG *
>
> Your measurement projected it out. It's like measuring which slit the 
> photon goes through...it eliminates the interference.
>
> Brent
>

*But if that's the case, won't the probability density of the eigenvalue 
being measured (by Born's rule) be the value in the absence of 
interference, which I presume is the classical value? AG *

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Re: Coherent states of a superposition

2019-01-17 Thread agrayson2000


On Friday, January 18, 2019 at 4:26:25 AM UTC, agrays...@gmail.com wrote:
>
>
>
> On Friday, January 18, 2019 at 3:49:10 AM UTC, Brent wrote:
>>
>>
>>
>> On 1/17/2019 5:23 PM, agrays...@gmail.com wrote:
>>
>>
>>
>> On Thursday, January 17, 2019 at 8:33:21 AM UTC, agrays...@gmail.com 
>> wrote: 
>>>
>>>
>>>
>>> On Thursday, January 17, 2019 at 3:58:48 AM UTC, Brent wrote: 



 On 1/16/2019 7:25 PM, agrays...@gmail.com wrote:



 On Monday, January 14, 2019 at 6:12:43 AM UTC, Brent wrote: 
>
>
>
> On 1/13/2019 9:51 PM, agrays...@gmail.com wrote:
>
> This means, to me, that the arbitrary phase angles have absolutely no 
> effect on the resultant interference pattern which is observed. But isn't 
> this what the phase angles are supposed to effect? AG
>
>
> The screen pattern is determined by *relative phase angles for the 
> different paths that reach the same point on the screen*.  The 
> relative angles only depend on different path lengths, so the overall 
> phase 
> angle is irrelevant.
>
> Brent
>


 *Sure, except there areTWO forms of phase interference in Wave 
 Mechanics; the one you refer to above, and another discussed in the 
 Stackexchange links I previously posted. In the latter case, the wf is 
 expressed as a superposition, say of two states, where we consider two 
 cases; a multiplicative complex phase shift is included prior to the sum, 
 and different complex phase shifts multiplying each component, all of the 
 form e^i (theta). Easy to show that interference exists in the latter 
 case, 
 but not the former. Now suppose we take the inner product of the wf with 
 the ith eigenstate of the superposition, in order to calculate the 
 probability of measuring the eigenvalue of the ith eigenstate, applying 
 one 
 of the postulates of QM, keeping in mind that each eigenstate is 
 multiplied 
 by a DIFFERENT complex phase shift.  If we further assume the eigenstates 
 are mutually orthogonal, the probability of measuring each eigenvalue does 
 NOT depend on the different phase shifts. What happened to the 
 interference 
 demonstrated by the Stackexchange links? TIA, AG *

 Your measurement projected it out. It's like measuring which slit the 
 photon goes through...it eliminates the interference.

 Brent

>>>
>>> *That's what I suspected; that going to an orthogonal basis, I departed 
>>> from the examples in Stackexchange where an arbitrary superposition is used 
>>> in the analysis of interference. Nevertheless, isn't it possible to 
>>> transform from an arbitrary superposition to one using an orthogonal basis? 
>>> And aren't all bases equivalent from a linear algebra pov? If all bases are 
>>> equivalent, why would transforming to an orthogonal basis lose 
>>> interference, whereas a general superposition does not? TIA, AG*
>>>
>>
>> *I don't get it. If it's easy to show the existence of interference for a 
>> general superposition where the components have different phase shifts, why 
>> would the interference disappear for a special case using orthonormal basis 
>> components? TIA, AG *
>>
>>
>> But taking the inner product with the *ith* eigenstate is not 
>> transforming to a different basis.
>>
>> Brent
>>
>
> *I know. I meant that from a general superposition used in the 
> Stackexchange articles, I wrote that general form as a superposition of 
> eigenstates, and this is where there was an implicit transformation to a 
> different, specific basis. AG *
>

*I suppose you could start with a superposition of eigenstates and get, or 
not get interference depending on the type of mathematical operation is 
performed. So I am unclear what's going on here; why taking the inner 
product is tantamount to looking at which slit the particle is going 
through.  AG *

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Re: Coherent states of a superposition

2019-01-17 Thread agrayson2000


On Friday, January 18, 2019 at 3:49:10 AM UTC, Brent wrote:
>
>
>
> On 1/17/2019 5:23 PM, agrays...@gmail.com  wrote:
>
>
>
> On Thursday, January 17, 2019 at 8:33:21 AM UTC, agrays...@gmail.com 
> wrote: 
>>
>>
>>
>> On Thursday, January 17, 2019 at 3:58:48 AM UTC, Brent wrote: 
>>>
>>>
>>>
>>> On 1/16/2019 7:25 PM, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Monday, January 14, 2019 at 6:12:43 AM UTC, Brent wrote: 



 On 1/13/2019 9:51 PM, agrays...@gmail.com wrote:

 This means, to me, that the arbitrary phase angles have absolutely no 
 effect on the resultant interference pattern which is observed. But isn't 
 this what the phase angles are supposed to effect? AG


 The screen pattern is determined by *relative phase angles for the 
 different paths that reach the same point on the screen*.  The 
 relative angles only depend on different path lengths, so the overall 
 phase 
 angle is irrelevant.

 Brent

>>>
>>>
>>> *Sure, except there areTWO forms of phase interference in Wave 
>>> Mechanics; the one you refer to above, and another discussed in the 
>>> Stackexchange links I previously posted. In the latter case, the wf is 
>>> expressed as a superposition, say of two states, where we consider two 
>>> cases; a multiplicative complex phase shift is included prior to the sum, 
>>> and different complex phase shifts multiplying each component, all of the 
>>> form e^i (theta). Easy to show that interference exists in the latter case, 
>>> but not the former. Now suppose we take the inner product of the wf with 
>>> the ith eigenstate of the superposition, in order to calculate the 
>>> probability of measuring the eigenvalue of the ith eigenstate, applying one 
>>> of the postulates of QM, keeping in mind that each eigenstate is multiplied 
>>> by a DIFFERENT complex phase shift.  If we further assume the eigenstates 
>>> are mutually orthogonal, the probability of measuring each eigenvalue does 
>>> NOT depend on the different phase shifts. What happened to the interference 
>>> demonstrated by the Stackexchange links? TIA, AG *
>>>
>>> Your measurement projected it out. It's like measuring which slit the 
>>> photon goes through...it eliminates the interference.
>>>
>>> Brent
>>>
>>
>> *That's what I suspected; that going to an orthogonal basis, I departed 
>> from the examples in Stackexchange where an arbitrary superposition is used 
>> in the analysis of interference. Nevertheless, isn't it possible to 
>> transform from an arbitrary superposition to one using an orthogonal basis? 
>> And aren't all bases equivalent from a linear algebra pov? If all bases are 
>> equivalent, why would transforming to an orthogonal basis lose 
>> interference, whereas a general superposition does not? TIA, AG*
>>
>
> *I don't get it. If it's easy to show the existence of interference for a 
> general superposition where the components have different phase shifts, why 
> would the interference disappear for a special case using orthonormal basis 
> components? TIA, AG *
>
>
> But taking the inner product with the *ith* eigenstate is not 
> transforming to a different basis.
>
> Brent
>

*I know. I meant that from a general superposition used in the 
Stackexchange articles, I wrote that general form as a superposition of 
eigenstates, and this is where there was an implicit transformation to a 
different, specific basis. AG *

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Re: Coherent states of a superposition

2019-01-17 Thread Brent Meeker



On 1/17/2019 5:23 PM, agrayson2...@gmail.com wrote:



On Thursday, January 17, 2019 at 8:33:21 AM UTC, agrays...@gmail.com 
wrote:




On Thursday, January 17, 2019 at 3:58:48 AM UTC, Brent wrote:



On 1/16/2019 7:25 PM, agrays...@gmail.com wrote:



On Monday, January 14, 2019 at 6:12:43 AM UTC, Brent wrote:



On 1/13/2019 9:51 PM, agrays...@gmail.com wrote:

This means, to me, that the arbitrary phase angles have
absolutely no effect on the resultant interference
pattern which is observed. But isn't this what the phase
angles are supposed to effect? AG


The screen pattern is determined by /*relative* phase
angles for the different paths that reach the same point
on the screen/.  The relative angles only depend on
different path lengths, so the overall phase angle is
irrelevant.

Brent


*Sure, except there areTWO forms of phase interference in
Wave Mechanics; the one you refer to above, and another
discussed in the Stackexchange links I previously posted. In
the latter case, the wf is expressed as a superposition, say
of two states, where we consider two cases; a multiplicative
complex phase shift is included prior to the sum, and
different complex phase shifts multiplying each component,
all of the form e^i (theta). Easy to show that interference
exists in the latter case, but not the former. Now suppose we
take the inner product of the wf with the ith eigenstate of
the superposition, in order to calculate the probability of
measuring the eigenvalue of the ith eigenstate, applying one
of the postulates of QM, keeping in mind that each eigenstate
is multiplied by a DIFFERENT complex phase shift.  If we
further assume the eigenstates are mutually orthogonal, the
probability of measuring each eigenvalue does NOT depend on
the different phase shifts. What happened to the interference
demonstrated by the Stackexchange links? TIA, AG
*


Your measurement projected it out. It's like measuring which
slit the photon goes through...it eliminates the interference.

Brent


*That's what I suspected; that going to an orthogonal basis, I
departed from the examples in Stackexchange where an arbitrary
superposition is used in the analysis of interference.
Nevertheless, isn't it possible to transform from an arbitrary
superposition to one using an orthogonal basis? And aren't all
bases equivalent from a linear algebra pov? If all bases are
equivalent, why would transforming to an orthogonal basis lose
interference, whereas a general superposition does not? TIA, AG*


*I don't get it. If it's easy to show the existence of interference 
for a general superposition where the components have different phase 
shifts, why would the interference disappear for a special case using 
orthonormal basis components? TIA, AG *


But taking the inner product with the /ith/ eigenstate is not 
transforming to a different basis.


Brent

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Re: Coherent states of a superposition

2019-01-17 Thread agrayson2000


On Thursday, January 17, 2019 at 1:48:57 PM UTC, agrays...@gmail.com wrote:
>
>
>
> On Thursday, January 17, 2019 at 12:36:07 PM UTC, Bruno Marchal wrote:
>>
>>
>> On 17 Jan 2019, at 09:33, agrays...@gmail.com wrote:
>>
>>
>>
>> On Thursday, January 17, 2019 at 3:58:48 AM UTC, Brent wrote:
>>>
>>>
>>>
>>> On 1/16/2019 7:25 PM, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Monday, January 14, 2019 at 6:12:43 AM UTC, Brent wrote: 



 On 1/13/2019 9:51 PM, agrays...@gmail.com wrote:

 This means, to me, that the arbitrary phase angles have absolutely no 
 effect on the resultant interference pattern which is observed. But isn't 
 this what the phase angles are supposed to effect? AG


 The screen pattern is determined by *relative phase angles for the 
 different paths that reach the same point on the screen*.  The 
 relative angles only depend on different path lengths, so the overall 
 phase 
 angle is irrelevant.

 Brent

>>>
>>>
>>> *Sure, except there areTWO forms of phase interference in Wave 
>>> Mechanics; the one you refer to above, and another discussed in the 
>>> Stackexchange links I previously posted. In the latter case, the wf is 
>>> expressed as a superposition, say of two states, where we consider two 
>>> cases; a multiplicative complex phase shift is included prior to the sum, 
>>> and different complex phase shifts multiplying each component, all of the 
>>> form e^i (theta). Easy to show that interference exists in the latter case, 
>>> but not the former. Now suppose we take the inner product of the wf with 
>>> the ith eigenstate of the superposition, in order to calculate the 
>>> probability of measuring the eigenvalue of the ith eigenstate, applying one 
>>> of the postulates of QM, keeping in mind that each eigenstate is multiplied 
>>> by a DIFFERENT complex phase shift.  If we further assume the eigenstates 
>>> are mutually orthogonal, the probability of measuring each eigenvalue does 
>>> NOT depend on the different phase shifts. What happened to the interference 
>>> demonstrated by the Stackexchange links? TIA, AG *
>>>
>>> Your measurement projected it out. It's like measuring which slit the 
>>> photon goes through...it eliminates the interference.
>>>
>>> Brent
>>>
>>
>> *That's what I suspected; that going to an orthogonal basis, I departed 
>> from the examples in Stackexchange where an arbitrary superposition is used 
>> in the analysis of interference. Nevertheless, isn't it possible to 
>> transform from an arbitrary superposition to one using an orthogonal basis? 
>> And aren't all bases equivalent from a linear algebra pov? If all bases are 
>> equivalent, why would transforming to an orthogonal basis lose 
>> interference, whereas a general superposition does not? TIA, AG*
>>
>>
>> I don’t understand this. All the bases we have used all the time are 
>> supposed to be orthonormal bases. We suppose that the scalar product (e_i 
>> e_j) = delta_i_j, when presenting the Born rule, and the quantum formalism.
>>
>> Bruno
>>
>
> *Generally, bases in a vector space are NOT orthonormal. For example, in 
> the vector space of vectors in the plane, any pair of non-parallel vectors *
>
 
*(excluding anti parallel vectors) form a basis. AG*

*Same for any general superposition of states in QM. HOWEVER, 
> eigenfunctions with distinct eigenvalues ARE orthogonal. I posted a link to 
> this proof a few months ago. IIRC, it was on its specifically named thread. 
> AG*
>

*Posted on July 25, 2018:*
  
Proof; Eigenfunctions having different eigenvalues are orthogonal

AG

>
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>> "Everything List" group.
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>> email to everything-li...@googlegroups.com.
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>>
>>
>>

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Re: Coherent states of a superposition

2019-01-17 Thread agrayson2000


On Thursday, January 17, 2019 at 8:33:21 AM UTC, agrays...@gmail.com wrote:
>
>
>
> On Thursday, January 17, 2019 at 3:58:48 AM UTC, Brent wrote:
>>
>>
>>
>> On 1/16/2019 7:25 PM, agrays...@gmail.com wrote:
>>
>>
>>
>> On Monday, January 14, 2019 at 6:12:43 AM UTC, Brent wrote: 
>>>
>>>
>>>
>>> On 1/13/2019 9:51 PM, agrays...@gmail.com wrote:
>>>
>>> This means, to me, that the arbitrary phase angles have absolutely no 
>>> effect on the resultant interference pattern which is observed. But isn't 
>>> this what the phase angles are supposed to effect? AG
>>>
>>>
>>> The screen pattern is determined by *relative phase angles for the 
>>> different paths that reach the same point on the screen*.  The relative 
>>> angles only depend on different path lengths, so the overall phase angle is 
>>> irrelevant.
>>>
>>> Brent
>>>
>>
>>
>> *Sure, except there areTWO forms of phase interference in Wave Mechanics; 
>> the one you refer to above, and another discussed in the Stackexchange 
>> links I previously posted. In the latter case, the wf is expressed as a 
>> superposition, say of two states, where we consider two cases; a 
>> multiplicative complex phase shift is included prior to the sum, and 
>> different complex phase shifts multiplying each component, all of the form 
>> e^i (theta). Easy to show that interference exists in the latter case, but 
>> not the former. Now suppose we take the inner product of the wf with the 
>> ith eigenstate of the superposition, in order to calculate the probability 
>> of measuring the eigenvalue of the ith eigenstate, applying one of the 
>> postulates of QM, keeping in mind that each eigenstate is multiplied by a 
>> DIFFERENT complex phase shift.  If we further assume the eigenstates are 
>> mutually orthogonal, the probability of measuring each eigenvalue does NOT 
>> depend on the different phase shifts. What happened to the interference 
>> demonstrated by the Stackexchange links? TIA, AG *
>>
>> Your measurement projected it out. It's like measuring which slit the 
>> photon goes through...it eliminates the interference.
>>
>> Brent
>>
>
> *That's what I suspected; that going to an orthogonal basis, I departed 
> from the examples in Stackexchange where an arbitrary superposition is used 
> in the analysis of interference. Nevertheless, isn't it possible to 
> transform from an arbitrary superposition to one using an orthogonal basis? 
> And aren't all bases equivalent from a linear algebra pov? If all bases are 
> equivalent, why would transforming to an orthogonal basis lose 
> interference, whereas a general superposition does not? TIA, AG*
>

*I don't get it. If it's easy to show the existence of interference for a 
general superposition where the components have different phase shifts, why 
would the interference disappear for a special case using orthonormal basis 
components? TIA, AG *

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Re: Coherent states of a superposition

2019-01-17 Thread agrayson2000


On Thursday, January 17, 2019 at 12:36:07 PM UTC, Bruno Marchal wrote:
>
>
> On 17 Jan 2019, at 09:33, agrays...@gmail.com  wrote:
>
>
>
> On Thursday, January 17, 2019 at 3:58:48 AM UTC, Brent wrote:
>>
>>
>>
>> On 1/16/2019 7:25 PM, agrays...@gmail.com wrote:
>>
>>
>>
>> On Monday, January 14, 2019 at 6:12:43 AM UTC, Brent wrote: 
>>>
>>>
>>>
>>> On 1/13/2019 9:51 PM, agrays...@gmail.com wrote:
>>>
>>> This means, to me, that the arbitrary phase angles have absolutely no 
>>> effect on the resultant interference pattern which is observed. But isn't 
>>> this what the phase angles are supposed to effect? AG
>>>
>>>
>>> The screen pattern is determined by *relative phase angles for the 
>>> different paths that reach the same point on the screen*.  The relative 
>>> angles only depend on different path lengths, so the overall phase angle is 
>>> irrelevant.
>>>
>>> Brent
>>>
>>
>>
>> *Sure, except there areTWO forms of phase interference in Wave Mechanics; 
>> the one you refer to above, and another discussed in the Stackexchange 
>> links I previously posted. In the latter case, the wf is expressed as a 
>> superposition, say of two states, where we consider two cases; a 
>> multiplicative complex phase shift is included prior to the sum, and 
>> different complex phase shifts multiplying each component, all of the form 
>> e^i (theta). Easy to show that interference exists in the latter case, but 
>> not the former. Now suppose we take the inner product of the wf with the 
>> ith eigenstate of the superposition, in order to calculate the probability 
>> of measuring the eigenvalue of the ith eigenstate, applying one of the 
>> postulates of QM, keeping in mind that each eigenstate is multiplied by a 
>> DIFFERENT complex phase shift.  If we further assume the eigenstates are 
>> mutually orthogonal, the probability of measuring each eigenvalue does NOT 
>> depend on the different phase shifts. What happened to the interference 
>> demonstrated by the Stackexchange links? TIA, AG *
>>
>> Your measurement projected it out. It's like measuring which slit the 
>> photon goes through...it eliminates the interference.
>>
>> Brent
>>
>
> *That's what I suspected; that going to an orthogonal basis, I departed 
> from the examples in Stackexchange where an arbitrary superposition is used 
> in the analysis of interference. Nevertheless, isn't it possible to 
> transform from an arbitrary superposition to one using an orthogonal basis? 
> And aren't all bases equivalent from a linear algebra pov? If all bases are 
> equivalent, why would transforming to an orthogonal basis lose 
> interference, whereas a general superposition does not? TIA, AG*
>
>
> I don’t understand this. All the bases we have used all the time are 
> supposed to be orthonormal bases. We suppose that the scalar product (e_i 
> e_j) = delta_i_j, when presenting the Born rule, and the quantum formalism.
>
> Bruno
>

*Generally, bases in a vector space are NOT orthonormal. For example, in 
the vector space of vectors in the plane, any pair of non-parallel vectors 
form a basis. Same for any general superposition of states in QM. HOWEVER, 
eigenfunctions with distinct eigenvalues ARE orthogonal. I posted a link to 
this proof a few months ago. IIRC, it was on its specifically named thread. 
AG*

>
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> "Everything List" group.
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>
>
>

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Re: Coherent states of a superposition

2019-01-17 Thread Bruno Marchal

> On 17 Jan 2019, at 09:33, agrayson2...@gmail.com wrote:
> 
> 
> 
> On Thursday, January 17, 2019 at 3:58:48 AM UTC, Brent wrote:
> 
> 
> On 1/16/2019 7:25 PM, agrays...@gmail.com  wrote:
>> 
>> 
>> On Monday, January 14, 2019 at 6:12:43 AM UTC, Brent wrote:
>> 
>> 
>> On 1/13/2019 9:51 PM, agrays...@gmail.com <> wrote:
>>> This means, to me, that the arbitrary phase angles have absolutely no 
>>> effect on the resultant interference pattern which is observed. But isn't 
>>> this what the phase angles are supposed to effect? AG
>> 
>> The screen pattern is determined by relative phase angles for the different 
>> paths that reach the same point on the screen.  The relative angles only 
>> depend on different path lengths, so the overall phase angle is irrelevant.
>> 
>> Brent
>> 
>> Sure, except there areTWO forms of phase interference in Wave Mechanics; the 
>> one you refer to above, and another discussed in the Stackexchange links I 
>> previously posted. In the latter case, the wf is expressed as a 
>> superposition, say of two states, where we consider two cases; a 
>> multiplicative complex phase shift is included prior to the sum, and 
>> different complex phase shifts multiplying each component, all of the form 
>> e^i (theta). Easy to show that interference exists in the latter case, but 
>> not the former. Now suppose we take the inner product of the wf with the ith 
>> eigenstate of the superposition, in order to calculate the probability of 
>> measuring the eigenvalue of the ith eigenstate, applying one of the 
>> postulates of QM, keeping in mind that each eigenstate is multiplied by a 
>> DIFFERENT complex phase shift.  If we further assume the eigenstates are 
>> mutually orthogonal, the probability of measuring each eigenvalue does NOT 
>> depend on the different phase shifts. What happened to the interference 
>> demonstrated by the Stackexchange links? TIA, AG 
>> 
> Your measurement projected it out. It's like measuring which slit the photon 
> goes through...it eliminates the interference.
> 
> Brent
> 
> That's what I suspected; that going to an orthogonal basis, I departed from 
> the examples in Stackexchange where an arbitrary superposition is used in the 
> analysis of interference. Nevertheless, isn't it possible to transform from 
> an arbitrary superposition to one using an orthogonal basis? And aren't all 
> bases equivalent from a linear algebra pov? If all bases are equivalent, why 
> would transforming to an orthogonal basis lose interference, whereas a 
> general superposition does not? TIA, AG

I don’t understand this. All the bases we have used all the time are supposed 
to be orthonormal bases. We suppose that the scalar product (e_i e_j) = 
delta_i_j, when presenting the Born rule, and the quantum formalism.

Bruno


> 
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Re: Coherent states of a superposition

2019-01-17 Thread agrayson2000


On Thursday, January 17, 2019 at 3:58:48 AM UTC, Brent wrote:
>
>
>
> On 1/16/2019 7:25 PM, agrays...@gmail.com  wrote:
>
>
>
> On Monday, January 14, 2019 at 6:12:43 AM UTC, Brent wrote: 
>>
>>
>>
>> On 1/13/2019 9:51 PM, agrays...@gmail.com wrote:
>>
>> This means, to me, that the arbitrary phase angles have absolutely no 
>> effect on the resultant interference pattern which is observed. But isn't 
>> this what the phase angles are supposed to effect? AG
>>
>>
>> The screen pattern is determined by *relative phase angles for the 
>> different paths that reach the same point on the screen*.  The relative 
>> angles only depend on different path lengths, so the overall phase angle is 
>> irrelevant.
>>
>> Brent
>>
>
>
> *Sure, except there areTWO forms of phase interference in Wave Mechanics; 
> the one you refer to above, and another discussed in the Stackexchange 
> links I previously posted. In the latter case, the wf is expressed as a 
> superposition, say of two states, where we consider two cases; a 
> multiplicative complex phase shift is included prior to the sum, and 
> different complex phase shifts multiplying each component, all of the form 
> e^i (theta). Easy to show that interference exists in the latter case, but 
> not the former. Now suppose we take the inner product of the wf with the 
> ith eigenstate of the superposition, in order to calculate the probability 
> of measuring the eigenvalue of the ith eigenstate, applying one of the 
> postulates of QM, keeping in mind that each eigenstate is multiplied by a 
> DIFFERENT complex phase shift.  If we further assume the eigenstates are 
> mutually orthogonal, the probability of measuring each eigenvalue does NOT 
> depend on the different phase shifts. What happened to the interference 
> demonstrated by the Stackexchange links? TIA, AG *
>
> Your measurement projected it out. It's like measuring which slit the 
> photon goes through...it eliminates the interference.
>
> Brent
>

*That's what I suspected; that going to an orthogonal basis, I departed 
from the examples in Stackexchange where an arbitrary superposition is used 
in the analysis of interference. Nevertheless, isn't it possible to 
transform from an arbitrary superposition to one using an orthogonal basis? 
And aren't all bases equivalent from a linear algebra pov? If all bases are 
equivalent, why would transforming to an orthogonal basis lose 
interference, whereas a general superposition does not? TIA, AG*

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Re: Coherent states of a superposition

2019-01-16 Thread Brent Meeker



On 1/16/2019 7:25 PM, agrayson2...@gmail.com wrote:



On Monday, January 14, 2019 at 6:12:43 AM UTC, Brent wrote:



On 1/13/2019 9:51 PM, agrays...@gmail.com  wrote:

This means, to me, that the arbitrary phase angles have
absolutely no effect on the resultant interference pattern which
is observed. But isn't this what the phase angles are supposed to
effect? AG


The screen pattern is determined by /*relative* phase angles for
the different paths that reach the same point on the screen/.  The
relative angles only depend on different path lengths, so the
overall phase angle is irrelevant.

Brent


*Sure, except there areTWO forms of phase interference in Wave 
Mechanics; the one you refer to above, and another discussed in the 
Stackexchange links I previously posted. In the latter case, the wf is 
expressed as a superposition, say of two states, where we consider two 
cases; a multiplicative complex phase shift is included prior to the 
sum, and different complex phase shifts multiplying each component, 
all of the form e^i (theta). Easy to show that interference exists in 
the latter case, but not the former. Now suppose we take the inner 
product of the wf with the ith eigenstate of the superposition, in 
order to calculate the probability of measuring the eigenvalue of the 
ith eigenstate, applying one of the postulates of QM, keeping in mind 
that each eigenstate is multiplied by a DIFFERENT complex phase 
shift.  If we further assume the eigenstates are mutually orthogonal, 
the probability of measuring each eigenvalue does NOT depend on the 
different phase shifts. What happened to the interference demonstrated 
by the Stackexchange links? TIA, AG

*

Your measurement projected it out. It's like measuring which slit the 
photon goes through...it eliminates the interference.


Brent

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Re: Coherent states of a superposition

2019-01-16 Thread agrayson2000


On Monday, January 14, 2019 at 6:12:43 AM UTC, Brent wrote:
>
>
>
> On 1/13/2019 9:51 PM, agrays...@gmail.com  wrote:
>
> This means, to me, that the arbitrary phase angles have absolutely no 
> effect on the resultant interference pattern which is observed. But isn't 
> this what the phase angles are supposed to effect? AG
>
>
> The screen pattern is determined by *relative phase angles for the 
> different paths that reach the same point on the screen*.  The relative 
> angles only depend on different path lengths, so the overall phase angle is 
> irrelevant.
>
> Brent
>

*Sure, except there areTWO forms of phase interference in Wave Mechanics; 
the one you refer to above, and another discussed in the Stackexchange 
links I previously posted. In the latter case, the wf is expressed as a 
superposition, say of two states, where we consider two cases; a 
multiplicative complex phase shift is included prior to the sum, and 
different complex phase shifts multiplying each component, all of the form 
e^i (theta). Easy to show that interference exists in the latter case, but 
not the former. Now suppose we take the inner product of the wf with the 
ith eigenstate of the superposition, in order to calculate the probability 
of measuring the eigenvalue of the ith eigenstate, applying one of the 
postulates of QM, keeping in mind that each eigenstate is multiplied by a 
DIFFERENT complex phase shift.  If we further assume the eigenstates are 
mutually orthogonal, the probability of measuring each eigenvalue does NOT 
depend on the different phase shifts. What happened to the interference 
demonstrated by the Stackexchange links? TIA, AG *

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Re: Coherent states of a superposition

2019-01-14 Thread agrayson2000


On Tuesday, January 15, 2019 at 12:10:23 AM UTC, Philip Thrift wrote:
>
>
>
> On Monday, January 14, 2019 at 5:52:39 PM UTC-6, agrays...@gmail.com 
> wrote:
>>
>>
>>
>> On Monday, January 14, 2019 at 11:41:15 PM UTC, Philip Thrift wrote:
>>>
>>>
>>>
>>> On Monday, January 14, 2019 at 4:58:52 PM UTC-6, agrays...@gmail.com 
>>> wrote:



 On Monday, January 14, 2019 at 10:27:19 AM UTC, Philip Thrift wrote:
>
>
>
> On Monday, January 14, 2019 at 2:53:53 AM UTC-6, agrays...@gmail.com 
> wrote:
>>
>>
>>
>> On Monday, January 14, 2019 at 6:12:43 AM UTC, Brent wrote:
>>>
>>>
>>>
>>> On 1/13/2019 9:51 PM, agrays...@gmail.com wrote:
>>>
>>> This means, to me, that the arbitrary phase angles have absolutely 
>>> no effect on the resultant interference pattern which is observed. But 
>>> isn't this what the phase angles are supposed to effect? AG
>>>
>>>
>>> The screen pattern is determined by *relative phase angles for the 
>>> different paths that reach the same point on the screen*.  The 
>>> relative angles only depend on different path lengths, so the overall 
>>> phase 
>>> angle is irrelevant.
>>>
>>> Brent
>>>
>>
>> The Stackexchange links affirm the existence of interference for 
>> *relative* phase angles, but say nothing about different path 
>> lengths, which is the way I've previously thought of interference. So I 
>> remain confused on the subject of quantum interference and its relation 
>> to 
>> relative phase angles. AG
>>
>
>
> Each path going to screen has a UCN* (unit complex number). For screen 
> locations that get their paths with UCNs that are in the same general 
> direction (as a vector in the complex plane, angle or phase), the sum of 
> those UCNs will be a complex number with a big length. For other screen 
> locations, the path UCNs when summed will cancel each other out. Hence 
> the 
> light and dark lines on the screen.
>
> * UCN: unit complex numbers [ 
> https://en.wikipedia.org/wiki/Circle_group ]
>
> "In mathematics, the circle group, denoted by T, is the multiplicative 
> group of all complex numbers with absolute value 1, that is, the unit 
> circle in the complex plane or simply the unit complex numbers."
>
> - pt 
>

 Thanks, but I don't think you understand the issue I raised. I 
 discussed two ways to apply relative phases, which results in different 
 probabilities. AG 

>>>
>>> I don't how "relative" helps with anything, but a phase is what it is:
>>>
>>> A physical basis for the phase in Feynman path integration
>>>
>>> https://arxiv.org/abs/quant-ph/0411005
>>>
>>> - pt
>>>
>>
>> The Stackexchange links illustrate global vs relative phases. AG 
>>
>
> I don't have any more to add, but relative phases are covered in an 
> introduction to the PI.
>
> Path Integral Methods and Applications
>
> https://arxiv.org/abs/quant-ph/0004090 
>
> These lectures are intended as an introduction to the technique of path 
> integrals and their applications in physics. 
>
> - pt
>

The inconsistency, if it exists, occurs in Wave Mechanics, not PI 
formulation. AG 

>  
>>>
>>

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Re: Coherent states of a superposition

2019-01-14 Thread Philip Thrift


On Monday, January 14, 2019 at 5:52:39 PM UTC-6, agrays...@gmail.com wrote:
>
>
>
> On Monday, January 14, 2019 at 11:41:15 PM UTC, Philip Thrift wrote:
>>
>>
>>
>> On Monday, January 14, 2019 at 4:58:52 PM UTC-6, agrays...@gmail.com 
>> wrote:
>>>
>>>
>>>
>>> On Monday, January 14, 2019 at 10:27:19 AM UTC, Philip Thrift wrote:



 On Monday, January 14, 2019 at 2:53:53 AM UTC-6, agrays...@gmail.com 
 wrote:
>
>
>
> On Monday, January 14, 2019 at 6:12:43 AM UTC, Brent wrote:
>>
>>
>>
>> On 1/13/2019 9:51 PM, agrays...@gmail.com wrote:
>>
>> This means, to me, that the arbitrary phase angles have absolutely no 
>> effect on the resultant interference pattern which is observed. But 
>> isn't 
>> this what the phase angles are supposed to effect? AG
>>
>>
>> The screen pattern is determined by *relative phase angles for the 
>> different paths that reach the same point on the screen*.  The 
>> relative angles only depend on different path lengths, so the overall 
>> phase 
>> angle is irrelevant.
>>
>> Brent
>>
>
> The Stackexchange links affirm the existence of interference for 
> *relative* phase angles, but say nothing about different path 
> lengths, which is the way I've previously thought of interference. So I 
> remain confused on the subject of quantum interference and its relation 
> to 
> relative phase angles. AG
>


 Each path going to screen has a UCN* (unit complex number). For screen 
 locations that get their paths with UCNs that are in the same general 
 direction (as a vector in the complex plane, angle or phase), the sum of 
 those UCNs will be a complex number with a big length. For other screen 
 locations, the path UCNs when summed will cancel each other out. Hence the 
 light and dark lines on the screen.

 * UCN: unit complex numbers [ 
 https://en.wikipedia.org/wiki/Circle_group ]

 "In mathematics, the circle group, denoted by T, is the multiplicative 
 group of all complex numbers with absolute value 1, that is, the unit 
 circle in the complex plane or simply the unit complex numbers."

 - pt 

>>>
>>> Thanks, but I don't think you understand the issue I raised. I discussed 
>>> two ways to apply relative phases, which results in different 
>>> probabilities. AG 
>>>
>>
>> I don't how "relative" helps with anything, but a phase is what it is:
>>
>> A physical basis for the phase in Feynman path integration
>>
>> https://arxiv.org/abs/quant-ph/0411005
>>
>> - pt
>>
>
> The Stackexchange links illustrate global vs relative phases. AG 
>

I don't have any more to add, but relative phases are covered in an 
introduction to the PI.

Path Integral Methods and Applications

https://arxiv.org/abs/quant-ph/0004090 

These lectures are intended as an introduction to the technique of path 
integrals and their applications in physics. 

- pt

>  
>>
>

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Re: Coherent states of a superposition

2019-01-14 Thread agrayson2000


On Monday, January 14, 2019 at 11:41:15 PM UTC, Philip Thrift wrote:
>
>
>
> On Monday, January 14, 2019 at 4:58:52 PM UTC-6, agrays...@gmail.com 
> wrote:
>>
>>
>>
>> On Monday, January 14, 2019 at 10:27:19 AM UTC, Philip Thrift wrote:
>>>
>>>
>>>
>>> On Monday, January 14, 2019 at 2:53:53 AM UTC-6, agrays...@gmail.com 
>>> wrote:



 On Monday, January 14, 2019 at 6:12:43 AM UTC, Brent wrote:
>
>
>
> On 1/13/2019 9:51 PM, agrays...@gmail.com wrote:
>
> This means, to me, that the arbitrary phase angles have absolutely no 
> effect on the resultant interference pattern which is observed. But isn't 
> this what the phase angles are supposed to effect? AG
>
>
> The screen pattern is determined by *relative phase angles for the 
> different paths that reach the same point on the screen*.  The 
> relative angles only depend on different path lengths, so the overall 
> phase 
> angle is irrelevant.
>
> Brent
>

 The Stackexchange links affirm the existence of interference for 
 *relative* phase angles, but say nothing about different path lengths, 
 which is the way I've previously thought of interference. So I remain 
 confused on the subject of quantum interference and its relation to 
 relative phase angles. AG

>>>
>>>
>>> Each path going to screen has a UCN* (unit complex number). For screen 
>>> locations that get their paths with UCNs that are in the same general 
>>> direction (as a vector in the complex plane, angle or phase), the sum of 
>>> those UCNs will be a complex number with a big length. For other screen 
>>> locations, the path UCNs when summed will cancel each other out. Hence the 
>>> light and dark lines on the screen.
>>>
>>> * UCN: unit complex numbers [ https://en.wikipedia.org/wiki/Circle_group 
>>> ]
>>>
>>> "In mathematics, the circle group, denoted by T, is the multiplicative 
>>> group of all complex numbers with absolute value 1, that is, the unit 
>>> circle in the complex plane or simply the unit complex numbers."
>>>
>>> - pt 
>>>
>>
>> Thanks, but I don't think you understand the issue I raised. I discussed 
>> two ways to apply relative phases, which results in different 
>> probabilities. AG 
>>
>
> I don't how "relative" helps with anything, but a phase is what it is:
>
> A physical basis for the phase in Feynman path integration
>
> https://arxiv.org/abs/quant-ph/0411005
>
> - pt
>

The Stackexchange links illustrate global vs relative phases. AG 

>  
>

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Re: Coherent states of a superposition

2019-01-14 Thread Philip Thrift


On Monday, January 14, 2019 at 4:58:52 PM UTC-6, agrays...@gmail.com wrote:
>
>
>
> On Monday, January 14, 2019 at 10:27:19 AM UTC, Philip Thrift wrote:
>>
>>
>>
>> On Monday, January 14, 2019 at 2:53:53 AM UTC-6, agrays...@gmail.com 
>> wrote:
>>>
>>>
>>>
>>> On Monday, January 14, 2019 at 6:12:43 AM UTC, Brent wrote:



 On 1/13/2019 9:51 PM, agrays...@gmail.com wrote:

 This means, to me, that the arbitrary phase angles have absolutely no 
 effect on the resultant interference pattern which is observed. But isn't 
 this what the phase angles are supposed to effect? AG


 The screen pattern is determined by *relative phase angles for the 
 different paths that reach the same point on the screen*.  The 
 relative angles only depend on different path lengths, so the overall 
 phase 
 angle is irrelevant.

 Brent

>>>
>>> The Stackexchange links affirm the existence of interference for 
>>> *relative* phase angles, but say nothing about different path lengths, 
>>> which is the way I've previously thought of interference. So I remain 
>>> confused on the subject of quantum interference and its relation to 
>>> relative phase angles. AG
>>>
>>
>>
>> Each path going to screen has a UCN* (unit complex number). For screen 
>> locations that get their paths with UCNs that are in the same general 
>> direction (as a vector in the complex plane, angle or phase), the sum of 
>> those UCNs will be a complex number with a big length. For other screen 
>> locations, the path UCNs when summed will cancel each other out. Hence the 
>> light and dark lines on the screen.
>>
>> * UCN: unit complex numbers [ https://en.wikipedia.org/wiki/Circle_group 
>> ]
>>
>> "In mathematics, the circle group, denoted by T, is the multiplicative 
>> group of all complex numbers with absolute value 1, that is, the unit 
>> circle in the complex plane or simply the unit complex numbers."
>>
>> - pt 
>>
>
> Thanks, but I don't think you understand the issue I raised. I discussed 
> two ways to apply relative phases, which results in different 
> probabilities. AG 
>

I don't how "relative" helps with anything, but a phase is what it is:

A physical basis for the phase in Feynman path integration

https://arxiv.org/abs/quant-ph/0411005

- pt
 

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Re: Coherent states of a superposition

2019-01-14 Thread agrayson2000


On Monday, January 14, 2019 at 10:27:19 AM UTC, Philip Thrift wrote:
>
>
>
> On Monday, January 14, 2019 at 2:53:53 AM UTC-6, agrays...@gmail.com 
> wrote:
>>
>>
>>
>> On Monday, January 14, 2019 at 6:12:43 AM UTC, Brent wrote:
>>>
>>>
>>>
>>> On 1/13/2019 9:51 PM, agrays...@gmail.com wrote:
>>>
>>> This means, to me, that the arbitrary phase angles have absolutely no 
>>> effect on the resultant interference pattern which is observed. But isn't 
>>> this what the phase angles are supposed to effect? AG
>>>
>>>
>>> The screen pattern is determined by *relative phase angles for the 
>>> different paths that reach the same point on the screen*.  The relative 
>>> angles only depend on different path lengths, so the overall phase angle is 
>>> irrelevant.
>>>
>>> Brent
>>>
>>
>> The Stackexchange links affirm the existence of interference for 
>> *relative* phase angles, but say nothing about different path lengths, 
>> which is the way I've previously thought of interference. So I remain 
>> confused on the subject of quantum interference and its relation to 
>> relative phase angles. AG
>>
>
>
> Each path going to screen has a UCN* (unit complex number). For screen 
> locations that get their paths with UCNs that are in the same general 
> direction (as a vector in the complex plane, angle or phase), the sum of 
> those UCNs will be a complex number with a big length. For other screen 
> locations, the path UCNs when summed will cancel each other out. Hence the 
> light and dark lines on the screen.
>
> * UCN: unit complex numbers [ https://en.wikipedia.org/wiki/Circle_group ]
>
> "In mathematics, the circle group, denoted by T, is the multiplicative 
> group of all complex numbers with absolute value 1, that is, the unit 
> circle in the complex plane or simply the unit complex numbers."
>
> - pt 
>

Thanks, but I don't think you understand the issue I raised. I discussed 
two ways to apply relative phases, which results in different 
probabilities. AG 

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Re: Coherent states of a superposition

2019-01-14 Thread Philip Thrift


On Monday, January 14, 2019 at 2:53:53 AM UTC-6, agrays...@gmail.com wrote:
>
>
>
> On Monday, January 14, 2019 at 6:12:43 AM UTC, Brent wrote:
>>
>>
>>
>> On 1/13/2019 9:51 PM, agrays...@gmail.com wrote:
>>
>> This means, to me, that the arbitrary phase angles have absolutely no 
>> effect on the resultant interference pattern which is observed. But isn't 
>> this what the phase angles are supposed to effect? AG
>>
>>
>> The screen pattern is determined by *relative phase angles for the 
>> different paths that reach the same point on the screen*.  The relative 
>> angles only depend on different path lengths, so the overall phase angle is 
>> irrelevant.
>>
>> Brent
>>
>
> The Stackexchange links affirm the existence of interference for 
> *relative* phase angles, but say nothing about different path lengths, 
> which is the way I've previously thought of interference. So I remain 
> confused on the subject of quantum interference and its relation to 
> relative phase angles. AG
>


Each path going to screen has a UCN* (unit complex number). For screen 
locations that get their paths with UCNs that are in the same general 
direction (as a vector in the complex plane, angle or phase), the sum of 
those UCNs will be a complex number with a big length. For other screen 
locations, the path UCNs when summed will cancel each other out. Hence the 
light and dark lines on the screen.

* UCN: unit complex numbers [ https://en.wikipedia.org/wiki/Circle_group ]

"In mathematics, the circle group, denoted by T, is the multiplicative 
group of all complex numbers with absolute value 1, that is, the unit 
circle in the complex plane or simply the unit complex numbers."

- pt 

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Re: Coherent states of a superposition

2019-01-14 Thread agrayson2000


On Monday, January 14, 2019 at 6:12:43 AM UTC, Brent wrote:
>
>
>
> On 1/13/2019 9:51 PM, agrays...@gmail.com  wrote:
>
> This means, to me, that the arbitrary phase angles have absolutely no 
> effect on the resultant interference pattern which is observed. But isn't 
> this what the phase angles are supposed to effect? AG
>
>
> The screen pattern is determined by *relative phase angles for the 
> different paths that reach the same point on the screen*.  The relative 
> angles only depend on different path lengths, so the overall phase angle is 
> irrelevant.
>
> Brent
>

The Stackexchange links affirm the existence of interference for *relative* 
phase angles, but say nothing about different path lengths, which is the 
way I've previously thought of interference. So I remain confused on the 
subject of quantum interference and its relation to relative phase angles. 
AG

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Re: Coherent states of a superposition

2019-01-14 Thread agrayson2000


On Monday, January 14, 2019 at 6:12:43 AM UTC, Brent wrote:
>
>
>
> On 1/13/2019 9:51 PM, agrays...@gmail.com  wrote:
>
> This means, to me, that the arbitrary phase angles have absolutely no 
> effect on the resultant interference pattern which is observed. But isn't 
> this what the phase angles are supposed to effect? AG
>
>
> The screen pattern is determined by *relative phase angles for the 
> different paths that reach the same point on the screen*.  The relative 
> angles only depend on different path lengths, so the overall phase angle is 
> irrelevant.
>
> Brent
>


*Here are two links from Stackexchange which show that the global phase 
angle does not effect the interference, but that relative phase angles do, 
which is what you're saying.   *

* 
https://physics.stackexchange.com/questions/177588/the-meaning-of-the-phase-in-the-wave-function*

*https://physics.stackexchange.com/questions/275890/does-overall-phase-matter?noredirect=1=1*

*But I chose to express the wf as a superposition of orthonormal 
eigenfunctions, each multiplied by a probability amplitude and an arbitrary 
relative phase angle. See recent posts. Then I calculated the probability 
of measuring the ith eigenvalue by calculating the norm squared of the 
inner product of the wf with the ith eigenfunction, applying one of the 
postulates of QM. Using this calculation, the probability of measuring the 
ith eigenvalue does NOT depend upon the relative phase angles. AG*

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Re: Coherent states of a superposition

2019-01-13 Thread Brent Meeker



On 1/13/2019 9:51 PM, agrayson2...@gmail.com wrote:
This means, to me, that the arbitrary phase angles have absolutely no 
effect on the resultant interference pattern which is observed. But 
isn't this what the phase angles are supposed to effect? AG


The screen pattern is determined by /*relative* phase angles for the 
different paths that reach the same point on the screen/. The relative 
angles only depend on different path lengths, so the overall phase angle 
is irrelevant.


Brent

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Re: Coherent states of a superposition

2019-01-13 Thread agrayson2000


On Sunday, January 13, 2019 at 7:12:31 PM UTC, agrays...@gmail.com wrote:
>
>
>
> On Sunday, January 13, 2019 at 3:04:10 PM UTC, Bruno Marchal wrote:
>>
>>
>> On 13 Jan 2019, at 07:24, agrays...@gmail.com wrote:
>>
>>
>>
>> On Sunday, January 13, 2019 at 4:13:24 AM UTC, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Saturday, January 12, 2019 at 8:41:23 AM UTC, agrays...@gmail.com 
>>> wrote:



 On Friday, January 11, 2019 at 7:40:13 PM UTC, Brent wrote:
>
>
>
> On 1/11/2019 1:54 AM, agrays...@gmail.com wrote:
>
>
> *How can you prepare a system in any superposition state if you don't 
> know the phase angles beforehand? You fail to distinguish measuring or 
> assuming the phase angles from calculating them. One doesn't need Born's 
> rule to calculate them. Maybe what Bruce meant is that you can never 
> calculate them, but you can prepare a system with any relative phase 
> angles. AG *
>
>
> In practice you prepare a "system" (e.g. a photon) in some particular 
> but unknown phase angle. Then you split the photon, or entangle it with 
> another photon, so that you have two with definite relative phase angles, 
> and with the same frequency,  then those two branches of the photon wave 
> function can interfere, i.e. the photon the interferes with itself as in 
> the Young's slits experiment.  So you only calculate the relative phase 
> shift of the two branches of the wf of the photon, which is enough to 
> define the interference pattern.
>
> Brent
>

 *Can a photon be split without violating conservation of energy? In any 
 event, I see my error on this issue of phase angles, and will describe it, 
 possibly to show I am not a complete idiot when it comes to QM. Stayed 
 tuned. AG*

>>>
>>> *Maybe I spoke too soon. I don't think I've resolved the issue of 
>>> arbitrary phase angles for components of a superposition of states. For 
>>> example, let's say the superposition consists of orthonormal eigenstates, 
>>> each multiplied by a probability amplitude. If each component is multiplied 
>>> by some arbitrary complex number representing a new phase angle, the 
>>> probability of *measuring* the eigenvalue corresponding to each component 
>>> doesn't change due to the orthonormality (taking the inner product of the 
>>> sum or wf, and then its norm squared). But what does apparently change is 
>>> the probability *density* distribution along the screen, say for double 
>>> slit experiment. But the eigenvalue probabilities which don't change with 
>>> an arbitrary change in phase angle, represent positions along the screen 
>>> via the inner product, DO seem to *shift* in value -- that is, the new 
>>> phases have the effect of changing the probability *density* -- and this 
>>> fact. if it is a fact, contradicts my earlier conclusion that changing the 
>>> relative phase angles does NOT change the calculated probability occurrence 
>>> for each eigenvalue. Is it understandable what my issue is here? TIA, AG*
>>>
>>
>> *IOW, if I change the phase angles, the interference changes and 
>> therefore the probability density changes, but this seems to contradict the 
>> fact that changing the phase angles has no effect on the probability of 
>> occurrences of the measured eigenvalues. AG *
>>
>>
>>
>> I have some difficulties to understand what you don’t understand. You 
>> seem to know the Born rule.
>>
>> Imagine some superposition, 1/(sqrt(2)(up + down) say. If you multiply 
>> this by any complex number e^phi, the Born rule will show that the 
>> probabilities does not change. But if, by using Stern Gerlach device, or 
>> David Albert’s nothing-box, which is just a phase shifter, place on the 
>> path of the "down-particle”, to get
>> 1/(sqrt(2)(up + e^phi down), the Born rule shows that this does change 
>> the probability of the outcome, in function of phi.
>>
>> Yes, it is hard to believe that a photon or an election “split” on two 
>> different path, and we can shift the phase of just one path, using that 
>> phase-shifter “nothing box”. Albert called it a “nothing box” because, for 
>> any particle going through it, it does not change any possible measurement 
>> result that you can do on the particles, unless it is put on the term of a 
>> vaster superposition, like in an interferometer.
>>
>> Bruno
>>
>
> Thanks. Here's a thought experiment that might explain my issue/confusion. 
> Suppose we imagine a double slit experiment where the wf is a superposition 
> of states as I've previously described. Now imagine another thought 
> experiment where each component of the superposition is multiplied by an 
> arbitrary phase angle. Will the interference patterns of these two 
> experiment be the same or different? AG 
>

You'll notice that if we cast the experiments as a double slit experiments, 
the eigenvalues being measured are transverse momenta along the 

Re: Coherent states of a superposition

2019-01-13 Thread agrayson2000


On Sunday, January 13, 2019 at 3:04:10 PM UTC, Bruno Marchal wrote:
>
>
> On 13 Jan 2019, at 07:24, agrays...@gmail.com  wrote:
>
>
>
> On Sunday, January 13, 2019 at 4:13:24 AM UTC, agrays...@gmail.com wrote:
>>
>>
>>
>> On Saturday, January 12, 2019 at 8:41:23 AM UTC, agrays...@gmail.com 
>> wrote:
>>>
>>>
>>>
>>> On Friday, January 11, 2019 at 7:40:13 PM UTC, Brent wrote:



 On 1/11/2019 1:54 AM, agrays...@gmail.com wrote:


 *How can you prepare a system in any superposition state if you don't 
 know the phase angles beforehand? You fail to distinguish measuring or 
 assuming the phase angles from calculating them. One doesn't need Born's 
 rule to calculate them. Maybe what Bruce meant is that you can never 
 calculate them, but you can prepare a system with any relative phase 
 angles. AG *


 In practice you prepare a "system" (e.g. a photon) in some particular 
 but unknown phase angle. Then you split the photon, or entangle it with 
 another photon, so that you have two with definite relative phase angles, 
 and with the same frequency,  then those two branches of the photon wave 
 function can interfere, i.e. the photon the interferes with itself as in 
 the Young's slits experiment.  So you only calculate the relative phase 
 shift of the two branches of the wf of the photon, which is enough to 
 define the interference pattern.

 Brent

>>>
>>> *Can a photon be split without violating conservation of energy? In any 
>>> event, I see my error on this issue of phase angles, and will describe it, 
>>> possibly to show I am not a complete idiot when it comes to QM. Stayed 
>>> tuned. AG*
>>>
>>
>> *Maybe I spoke too soon. I don't think I've resolved the issue of 
>> arbitrary phase angles for components of a superposition of states. For 
>> example, let's say the superposition consists of orthonormal eigenstates, 
>> each multiplied by a probability amplitude. If each component is multiplied 
>> by some arbitrary complex number representing a new phase angle, the 
>> probability of *measuring* the eigenvalue corresponding to each component 
>> doesn't change due to the orthonormality (taking the inner product of the 
>> sum or wf, and then its norm squared). But what does apparently change is 
>> the probability *density* distribution along the screen, say for double 
>> slit experiment. But the eigenvalue probabilities which don't change with 
>> an arbitrary change in phase angle, represent positions along the screen 
>> via the inner product, DO seem to *shift* in value -- that is, the new 
>> phases have the effect of changing the probability *density* -- and this 
>> fact. if it is a fact, contradicts my earlier conclusion that changing the 
>> relative phase angles does NOT change the calculated probability occurrence 
>> for each eigenvalue. Is it understandable what my issue is here? TIA, AG*
>>
>
> *IOW, if I change the phase angles, the interference changes and therefore 
> the probability density changes, but this seems to contradict the fact that 
> changing the phase angles has no effect on the probability of occurrences 
> of the measured eigenvalues. AG *
>
>
>
> I have some difficulties to understand what you don’t understand. You seem 
> to know the Born rule.
>
> Imagine some superposition, 1/(sqrt(2)(up + down) say. If you multiply 
> this by any complex number e^phi, the Born rule will show that the 
> probabilities does not change. But if, by using Stern Gerlach device, or 
> David Albert’s nothing-box, which is just a phase shifter, place on the 
> path of the "down-particle”, to get
> 1/(sqrt(2)(up + e^phi down), the Born rule shows that this does change the 
> probability of the outcome, in function of phi.
>
> Yes, it is hard to believe that a photon or an election “split” on two 
> different path, and we can shift the phase of just one path, using that 
> phase-shifter “nothing box”. Albert called it a “nothing box” because, for 
> any particle going through it, it does not change any possible measurement 
> result that you can do on the particles, unless it is put on the term of a 
> vaster superposition, like in an interferometer.
>
> Bruno
>

Thanks. Here's a thought experiment that might explain my issue/confusion. 
Suppose we imagine a double slit experiment where the wf is a superposition 
of states as I've previously described. Now imagine another thought 
experiment where each component of the superposition is multiplied by an 
arbitrary phase angle. Will the interference patterns of these two 
experiment be the same or different? AG  

>
>
>
>
>
>
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Re: Coherent states of a superposition

2019-01-13 Thread Bruno Marchal

> On 13 Jan 2019, at 07:24, agrayson2...@gmail.com wrote:
> 
> 
> 
> On Sunday, January 13, 2019 at 4:13:24 AM UTC, agrays...@gmail.com wrote:
> 
> 
> On Saturday, January 12, 2019 at 8:41:23 AM UTC, agrays...@gmail.com <> wrote:
> 
> 
> On Friday, January 11, 2019 at 7:40:13 PM UTC, Brent wrote:
> 
> 
> On 1/11/2019 1:54 AM, agrays...@gmail.com <> wrote:
>> 
>> How can you prepare a system in any superposition state if you don't know 
>> the phase angles beforehand? You fail to distinguish measuring or assuming 
>> the phase angles from calculating them. One doesn't need Born's rule to 
>> calculate them. Maybe what Bruce meant is that you can never calculate them, 
>> but you can prepare a system with any relative phase angles. AG
> 
> In practice you prepare a "system" (e.g. a photon) in some particular but 
> unknown phase angle. Then you split the photon, or entangle it with another 
> photon, so that you have two with definite relative phase angles, and with 
> the same frequency,  then those two branches of the photon wave function can 
> interfere, i.e. the photon the interferes with itself as in the Young's slits 
> experiment.  So you only calculate the relative phase shift of the two 
> branches of the wf of the photon, which is enough to define the interference 
> pattern.
> 
> Brent
> 
> Can a photon be split without violating conservation of energy? In any event, 
> I see my error on this issue of phase angles, and will describe it, possibly 
> to show I am not a complete idiot when it comes to QM. Stayed tuned. AG
> 
> Maybe I spoke too soon. I don't think I've resolved the issue of arbitrary 
> phase angles for components of a superposition of states. For example, let's 
> say the superposition consists of orthonormal eigenstates, each multiplied by 
> a probability amplitude. If each component is multiplied by some arbitrary 
> complex number representing a new phase angle, the probability of *measuring* 
> the eigenvalue corresponding to each component doesn't change due to the 
> orthonormality (taking the inner product of the sum or wf, and then its norm 
> squared). But what does apparently change is the probability *density* 
> distribution along the screen, say for double slit experiment. But the 
> eigenvalue probabilities which don't change with an arbitrary change in phase 
> angle, represent positions along the screen via the inner product, DO seem to 
> *shift* in value -- that is, the new phases have the effect of changing the 
> probability *density* -- and this fact. if it is a fact, contradicts my 
> earlier conclusion that changing the relative phase angles does NOT change 
> the calculated probability occurrence for each eigenvalue. Is it 
> understandable what my issue is here? TIA, AG
> 
> IOW, if I change the phase angles, the interference changes and therefore the 
> probability density changes, but this seems to contradict the fact that 
> changing the phase angles has no effect on the probability of occurrences of 
> the measured eigenvalues. AG 


I have some difficulties to understand what you don’t understand. You seem to 
know the Born rule.

Imagine some superposition, 1/(sqrt(2)(up + down) say. If you multiply this by 
any complex number e^phi, the Born rule will show that the probabilities does 
not change. But if, by using Stern Gerlach device, or David Albert’s 
nothing-box, which is just a phase shifter, place on the path of the 
"down-particle”, to get
1/(sqrt(2)(up + e^phi down), the Born rule shows that this does change the 
probability of the outcome, in function of phi.

Yes, it is hard to believe that a photon or an election “split” on two 
different path, and we can shift the phase of just one path, using that 
phase-shifter “nothing box”. Albert called it a “nothing box” because, for any 
particle going through it, it does not change any possible measurement result 
that you can do on the particles, unless it is put on the term of a vaster 
superposition, like in an interferometer.

Bruno





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Re: Coherent states of a superposition

2019-01-12 Thread agrayson2000


On Sunday, January 13, 2019 at 4:13:24 AM UTC, agrays...@gmail.com wrote:
>
>
>
> On Saturday, January 12, 2019 at 8:41:23 AM UTC, agrays...@gmail.com 
> wrote:
>>
>>
>>
>> On Friday, January 11, 2019 at 7:40:13 PM UTC, Brent wrote:
>>>
>>>
>>>
>>> On 1/11/2019 1:54 AM, agrays...@gmail.com wrote:
>>>
>>>
>>> *How can you prepare a system in any superposition state if you don't 
>>> know the phase angles beforehand? You fail to distinguish measuring or 
>>> assuming the phase angles from calculating them. One doesn't need Born's 
>>> rule to calculate them. Maybe what Bruce meant is that you can never 
>>> calculate them, but you can prepare a system with any relative phase 
>>> angles. AG *
>>>
>>>
>>> In practice you prepare a "system" (e.g. a photon) in some particular 
>>> but unknown phase angle. Then you split the photon, or entangle it with 
>>> another photon, so that you have two with definite relative phase angles, 
>>> and with the same frequency,  then those two branches of the photon wave 
>>> function can interfere, i.e. the photon the interferes with itself as in 
>>> the Young's slits experiment.  So you only calculate the relative phase 
>>> shift of the two branches of the wf of the photon, which is enough to 
>>> define the interference pattern.
>>>
>>> Brent
>>>
>>
>> *Can a photon be split without violating conservation of energy? In any 
>> event, I see my error on this issue of phase angles, and will describe it, 
>> possibly to show I am not a complete idiot when it comes to QM. Stayed 
>> tuned. AG*
>>
>
> *Maybe I spoke too soon. I don't think I've resolved the issue of 
> arbitrary phase angles for components of a superposition of states. For 
> example, let's say the superposition consists of orthonormal eigenstates, 
> each multiplied by a probability amplitude. If each component is multiplied 
> by some arbitrary complex number representing a new phase angle, the 
> probability of *measuring* the eigenvalue corresponding to each component 
> doesn't change due to the orthonormality (taking the inner product of the 
> sum or wf, and then its norm squared). But what does apparently change is 
> the probability *density* distribution along the screen, say for double 
> slit experiment. But the eigenvalue probabilities which don't change with 
> an arbitrary change in phase angle, represent positions along the screen 
> via the inner product, DO seem to *shift* in value -- that is, the new 
> phases have the effect of changing the probability *density* -- and this 
> fact. if it is a fact, contradicts my earlier conclusion that changing the 
> relative phase angles does NOT change the calculated probability occurrence 
> for each eigenvalue. Is it understandable what my issue is here? TIA, AG*
>

*IOW, if I change the phase angles, the interference changes and therefore 
the probability density changes, but this seems to contradict the fact that 
changing the phase angles has no effect on the probability of occurrences 
of the measured eigenvalues. AG *

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Re: Coherent states of a superposition

2019-01-12 Thread agrayson2000


On Saturday, January 12, 2019 at 8:41:23 AM UTC, agrays...@gmail.com wrote:
>
>
>
> On Friday, January 11, 2019 at 7:40:13 PM UTC, Brent wrote:
>>
>>
>>
>> On 1/11/2019 1:54 AM, agrays...@gmail.com wrote:
>>
>>
>> *How can you prepare a system in any superposition state if you don't 
>> know the phase angles beforehand? You fail to distinguish measuring or 
>> assuming the phase angles from calculating them. One doesn't need Born's 
>> rule to calculate them. Maybe what Bruce meant is that you can never 
>> calculate them, but you can prepare a system with any relative phase 
>> angles. AG *
>>
>>
>> In practice you prepare a "system" (e.g. a photon) in some particular but 
>> unknown phase angle. Then you split the photon, or entangle it with another 
>> photon, so that you have two with definite relative phase angles, and with 
>> the same frequency,  then those two branches of the photon wave function 
>> can interfere, i.e. the photon the interferes with itself as in the Young's 
>> slits experiment.  So you only calculate the relative phase shift of the 
>> two branches of the wf of the photon, which is enough to define the 
>> interference pattern.
>>
>> Brent
>>
>
> *Can a photon be split without violating conservation of energy? In any 
> event, I see my error on this issue of phase angles, and will describe it, 
> possibly to show I am not a complete idiot when it comes to QM. Stayed 
> tuned. AG*
>

*Maybe I spoke too soon. I don't think I've resolved the issue of arbitrary 
phase angles for components of a superposition of states. For example, 
let's say the superposition consists of orthonormal eigenstates, each 
multiplied by a probability amplitude. If each component is multiplied by 
some arbitrary complex number representing a new phase angle, the 
probability of *measuring* the eigenvalue corresponding to each component 
doesn't change due to the orthonormality (taking the inner product of the 
sum or wf, and then its norm squared). But what does apparently change is 
the probability *density* distribution along the screen, say for double 
slit experiment. But the eigenvalue probabilities which don't change with 
an arbitrary change in phase angle, represent positions along the screen 
via the inner product, DO seem to *shift* in value -- that is, the new 
phases have the effect of changing the probability *density* -- and this 
fact. if it is a fact, contradicts my earlier conclusion that changing the 
relative phase angles does NOT change the calculated probability occurrence 
for each eigenvalue. Is it understandable what my issue is here? TIA, AG*

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Re: Coherent states of a superposition

2019-01-12 Thread agrayson2000


On Friday, January 11, 2019 at 7:40:13 PM UTC, Brent wrote:
>
>
>
> On 1/11/2019 1:54 AM, agrays...@gmail.com  wrote:
>
>
> *How can you prepare a system in any superposition state if you don't know 
> the phase angles beforehand? You fail to distinguish measuring or assuming 
> the phase angles from calculating them. One doesn't need Born's rule to 
> calculate them. Maybe what Bruce meant is that you can never calculate 
> them, but you can prepare a system with any relative phase angles. AG *
>
>
> In practice you prepare a "system" (e.g. a photon) in some particular but 
> unknown phase angle. Then you split the photon, or entangle it with another 
> photon, so that you have two with definite relative phase angles, and with 
> the same frequency,  then those two branches of the photon wave function 
> can interfere, i.e. the photon the interferes with itself as in the Young's 
> slits experiment.  So you only calculate the relative phase shift of the 
> two branches of the wf of the photon, which is enough to define the 
> interference pattern.
>
> Brent
>

*Can a photon be split without violating conservation of energy? In any 
event, I see my error on this issue of phase angles, and will describe it, 
possibly to show I am not a complete idiot when it comes to QM. Stayed 
tuned. AG* 

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Re: Coherent states of a superposition

2019-01-11 Thread Philip Thrift


On Wednesday, December 5, 2018 at 5:52:46 AM UTC-6, agrays...@gmail.com 
wrote:
>
>
> Suppose the original wf is expressed in terms of p, and its superposition 
> expansion is also expressed in eigenfunctions with variable p. Does the 
> phase of the original wf carry over into the eigenfunctions as identical 
> for each, or can each component in the superposition have different phases? 
> I ask this because the probability determined by any complex amplitude is 
> independent of its phase. TIA, AG 
>



This may help (or not) on what phases have to do with anything:

  
 http://muonray.blogspot.com/2016/03/the-path-integral-interpretation-of.html

- pt 


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Re: Coherent states of a superposition

2019-01-11 Thread Brent Meeker



On 1/11/2019 1:54 AM, agrayson2...@gmail.com wrote:


*How can you prepare a system in any superposition state if you don't 
know the phase angles beforehand? You fail to distinguish measuring or 
assuming the phase angles from calculating them. One doesn't need 
Born's rule to calculate them. Maybe what Bruce meant is that you can 
never calculate them, but you can prepare a system with any relative 
phase angles. AG *


In practice you prepare a "system" (e.g. a photon) in some particular 
but unknown phase angle. Then you split the photon, or entangle it with 
another photon, so that you have two with definite relative phase 
angles, and with the same frequency,  then those two branches of the 
photon wave function can interfere, i.e. the photon the interferes with 
itself as in the Young's slits experiment.  So you only calculate the 
relative phase shift of the two branches of the wf of the photon, which 
is enough to define the interference pattern.


Brent

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Re: Coherent states of a superposition

2019-01-11 Thread agrayson2000


On Friday, January 11, 2019 at 10:11:10 AM UTC, Bruno Marchal wrote:
>
>
> On 11 Jan 2019, at 10:54, agrays...@gmail.com  wrote:
>
>
>
> On Friday, January 11, 2019 at 9:07:50 AM UTC, Bruno Marchal wrote:
>>
>>
>> On 10 Jan 2019, at 22:08, agrays...@gmail.com wrote:
>>
>>
>>
>> On Thursday, January 10, 2019 at 11:07:51 AM UTC, Bruno Marchal wrote:
>>>
>>>
>>> On 9 Jan 2019, at 07:58, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Monday, January 7, 2019 at 11:37:13 PM UTC, agrays...@gmail.com 
>>> wrote:



 On Monday, January 7, 2019 at 2:52:27 PM UTC, agrays...@gmail.com 
 wrote:
>
>
>
> On Sunday, January 6, 2019 at 10:45:01 PM UTC, Bruce wrote:
>>
>> On Mon, Jan 7, 2019 at 9:42 AM  wrote:
>>
>>> On Saturday, December 8, 2018 at 2:46:41 PM UTC, agrays...@gmail.com 
>>> wrote:

 On Thursday, December 6, 2018 at 5:46:13 PM UTC, 
 agrays...@gmail.com wrote:
>
> On Wednesday, December 5, 2018 at 10:13:57 PM UTC, 
> agrays...@gmail.com wrote:
>>
>> On Wednesday, December 5, 2018 at 9:42:51 PM UTC, Bruce wrote:
>>>
>>> On Wed, Dec 5, 2018 at 10:52 PM  wrote:
>>>
 On Wednesday, December 5, 2018 at 11:42:06 AM UTC, 
 agrays...@gmail.com wrote:
>
> On Tuesday, December 4, 2018 at 9:57:41 PM UTC, Bruce wrote:
>>
>> On Wed, Dec 5, 2018 at 2:36 AM  wrote:
>>
>>>
>>> *Thanks, but I'm looking for a solution within the context 
>>> of interference and coherence, without introducing your theory 
>>> of 
>>> consciousness. Mainstream thinking today is that decoherence 
>>> does occur, 
>>> but this seems to imply preexisting coherence, and therefore 
>>> interference 
>>> among the component states of a superposition. If the 
>>> superposition is 
>>> expressed using eigenfunctions, which are mutually orthogonal 
>>> -- implying 
>>> no mutual interference -- how is decoherence possible, insofar 
>>> as 
>>> coherence, IIUC, doesn't exist using this basis? AG*
>>>
>>
>> I think you misunderstand the meaning of "coherence" when it 
>> is used off an expansion in terms of a set of mutually 
>> orthogonal 
>> eigenvectors. The expansion in some eigenvector basis is written 
>> as
>>
>>|psi> = Sum_i (a_i |v_i>)
>>
>> where |v_i> are the eigenvectors, and i ranges over the 
>> dimension of the Hilbert space. The expansion coefficients are 
>> the complex 
>> numbers a_i. Since these are complex coefficients, they contain 
>> inherent 
>> phases. It is the preservation of these phases of the expansion 
>> coefficients that is meant by "maintaining coherence". So it is 
>> the 
>> coherence of the particular expansion that is implied, and this 
>> has noting 
>> to do with the mutual orthogonality or otherwise of the basis 
>> vectors 
>> themselves. In decoherence, the phase relationships between the 
>> terms in 
>> the original expansion are lost.
>>
>> Bruce 
>>
>
> I appreciate your reply. I was sure you could ascertain my 
> error -- confusing orthogonality with interference and coherence. 
> Let me 
> have your indulgence on a related issue. AG
>

 Suppose the original wf is expressed in terms of p, and its 
 superposition expansion is also expressed in eigenfunctions with 
 variable 
 p. Does the phase of the original wf carry over into the 
 eigenfunctions as 
 identical for each, or can each component in the superposition 
 have 
 different phases? I ask this because the probability determined by 
 any 
 complex amplitude is independent of its phase. TIA, AG 

>>>
>>> The phases of the coefficients are independent of each other.
>>>
>>
>> When I formally studied QM, no mention was made of calculating 
>> the phases since, presumably, they don't effect probability 
>> calculations. 
>> Do you have a link which explains how they're calculated? TIA, AG 
>>
>
> I found some links on physics.stackexchange.com which show that 
> relative phases can effect probabilities, but none so far about how 
> to 
> calculate any phase angle. AG 
>

 

Re: Coherent states of a superposition

2019-01-11 Thread Bruno Marchal

> On 11 Jan 2019, at 10:54, agrayson2...@gmail.com wrote:
> 
> 
> 
> On Friday, January 11, 2019 at 9:07:50 AM UTC, Bruno Marchal wrote:
> 
>> On 10 Jan 2019, at 22:08, agrays...@gmail.com  wrote:
>> 
>> 
>> 
>> On Thursday, January 10, 2019 at 11:07:51 AM UTC, Bruno Marchal wrote:
>> 
>>> On 9 Jan 2019, at 07:58, agrays...@gmail.com <> wrote:
>>> 
>>> 
>>> 
>>> On Monday, January 7, 2019 at 11:37:13 PM UTC, agrays...@gmail.com 
>>>  wrote:
>>> 
>>> 
>>> On Monday, January 7, 2019 at 2:52:27 PM UTC, agrays...@gmail.com <> wrote:
>>> 
>>> 
>>> On Sunday, January 6, 2019 at 10:45:01 PM UTC, Bruce wrote:
>>> On Mon, Jan 7, 2019 at 9:42 AM > wrote:
>>> On Saturday, December 8, 2018 at 2:46:41 PM UTC, agrays...@gmail.com <> 
>>> wrote:
>>> On Thursday, December 6, 2018 at 5:46:13 PM UTC, agrays...@gmail.com <> 
>>> wrote:
>>> On Wednesday, December 5, 2018 at 10:13:57 PM UTC, agrays...@gmail.com <> 
>>> wrote:
>>> On Wednesday, December 5, 2018 at 9:42:51 PM UTC, Bruce wrote:
>>> On Wed, Dec 5, 2018 at 10:52 PM > wrote:
>>> On Wednesday, December 5, 2018 at 11:42:06 AM UTC, agrays...@gmail.com <> 
>>> wrote:
>>> On Tuesday, December 4, 2018 at 9:57:41 PM UTC, Bruce wrote:
>>> On Wed, Dec 5, 2018 at 2:36 AM > wrote:
>>> 
>>> Thanks, but I'm looking for a solution within the context of interference 
>>> and coherence, without introducing your theory of consciousness. Mainstream 
>>> thinking today is that decoherence does occur, but this seems to imply 
>>> preexisting coherence, and therefore interference among the component 
>>> states of a superposition. If the superposition is expressed using 
>>> eigenfunctions, which are mutually orthogonal -- implying no mutual 
>>> interference -- how is decoherence possible, insofar as coherence, IIUC, 
>>> doesn't exist using this basis? AG
>>> 
>>> I think you misunderstand the meaning of "coherence" when it is used off an 
>>> expansion in terms of a set of mutually orthogonal eigenvectors. The 
>>> expansion in some eigenvector basis is written as
>>> 
>>>|psi> = Sum_i (a_i |v_i>)
>>> 
>>> where |v_i> are the eigenvectors, and i ranges over the dimension of the 
>>> Hilbert space. The expansion coefficients are the complex numbers a_i. 
>>> Since these are complex coefficients, they contain inherent phases. It is 
>>> the preservation of these phases of the expansion coefficients that is 
>>> meant by "maintaining coherence". So it is the coherence of the particular 
>>> expansion that is implied, and this has noting to do with the mutual 
>>> orthogonality or otherwise of the basis vectors themselves. In decoherence, 
>>> the phase relationships between the terms in the original expansion are 
>>> lost.
>>> 
>>> Bruce 
>>> 
>>> I appreciate your reply. I was sure you could ascertain my error -- 
>>> confusing orthogonality with interference and coherence. Let me have your 
>>> indulgence on a related issue. AG
>>> 
>>> Suppose the original wf is expressed in terms of p, and its superposition 
>>> expansion is also expressed in eigenfunctions with variable p. Does the 
>>> phase of the original wf carry over into the eigenfunctions as identical 
>>> for each, or can each component in the superposition have different phases? 
>>> I ask this because the probability determined by any complex amplitude is 
>>> independent of its phase. TIA, AG 
>>> 
>>> The phases of the coefficients are independent of each other.
>>> 
>>> When I formally studied QM, no mention was made of calculating the phases 
>>> since, presumably, they don't effect probability calculations. Do you have 
>>> a link which explains how they're calculated? TIA, AG 
>>> 
>>> I found some links on physics.stackexchange.com 
>>>  which show that relative phases can 
>>> effect probabilities, but none so far about how to calculate any phase 
>>> angle. AG 
>>> 
>>> Here's the answer if anyone's interested. But what's the question? How are 
>>> wf phase angles calculated? Clearly, if you solve for the eigenfunctions of 
>>> some QM operator such as the p operator, any phase angle is possible; its 
>>> value is completely arbitrary and doesn't effect a probability calculation. 
>>> In fact, IIUC, there is not sufficient information to solve for a unique 
>>> phase. So, I conclude,that the additional information required to uniquely 
>>> determine a phase angle for a wf, lies in boundary conditions. If the 
>>> problem of specifying a wf is defined as a boundary value problem, then, I 
>>> believe, a unique phase angle can be calculated. CMIIAW. AG 
>>> 
>>> Bruce
>>> 
>>> I could use a handshake on this one. Roughly speaking, if one wants to 
>>> express the state of a system as a superposition of eigenstates, how does 
>>> one calculate the phase angles of the amplitudes for each eigenstate? AG
>>> 
>>> One doesn't. The phases are arbitrary unless one interferes the system with 
>>> some other system.
>>> 
>>> Bruce 
>>> 
>>> If the phases are 

Re: Coherent states of a superposition

2019-01-11 Thread agrayson2000


On Friday, January 11, 2019 at 9:07:50 AM UTC, Bruno Marchal wrote:
>
>
> On 10 Jan 2019, at 22:08, agrays...@gmail.com  wrote:
>
>
>
> On Thursday, January 10, 2019 at 11:07:51 AM UTC, Bruno Marchal wrote:
>>
>>
>> On 9 Jan 2019, at 07:58, agrays...@gmail.com wrote:
>>
>>
>>
>> On Monday, January 7, 2019 at 11:37:13 PM UTC, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Monday, January 7, 2019 at 2:52:27 PM UTC, agrays...@gmail.com wrote:



 On Sunday, January 6, 2019 at 10:45:01 PM UTC, Bruce wrote:
>
> On Mon, Jan 7, 2019 at 9:42 AM  wrote:
>
>> On Saturday, December 8, 2018 at 2:46:41 PM UTC, agrays...@gmail.com 
>> wrote:
>>>
>>> On Thursday, December 6, 2018 at 5:46:13 PM UTC, agrays...@gmail.com 
>>> wrote:

 On Wednesday, December 5, 2018 at 10:13:57 PM UTC, 
 agrays...@gmail.com wrote:
>
> On Wednesday, December 5, 2018 at 9:42:51 PM UTC, Bruce wrote:
>>
>> On Wed, Dec 5, 2018 at 10:52 PM  wrote:
>>
>>> On Wednesday, December 5, 2018 at 11:42:06 AM UTC, 
>>> agrays...@gmail.com wrote:

 On Tuesday, December 4, 2018 at 9:57:41 PM UTC, Bruce wrote:
>
> On Wed, Dec 5, 2018 at 2:36 AM  wrote:
>
>>
>> *Thanks, but I'm looking for a solution within the context of 
>> interference and coherence, without introducing your theory of 
>> consciousness. Mainstream thinking today is that decoherence 
>> does occur, 
>> but this seems to imply preexisting coherence, and therefore 
>> interference 
>> among the component states of a superposition. If the 
>> superposition is 
>> expressed using eigenfunctions, which are mutually orthogonal -- 
>> implying 
>> no mutual interference -- how is decoherence possible, insofar 
>> as 
>> coherence, IIUC, doesn't exist using this basis? AG*
>>
>
> I think you misunderstand the meaning of "coherence" when it 
> is used off an expansion in terms of a set of mutually orthogonal 
> eigenvectors. The expansion in some eigenvector basis is written 
> as
>
>|psi> = Sum_i (a_i |v_i>)
>
> where |v_i> are the eigenvectors, and i ranges over the 
> dimension of the Hilbert space. The expansion coefficients are 
> the complex 
> numbers a_i. Since these are complex coefficients, they contain 
> inherent 
> phases. It is the preservation of these phases of the expansion 
> coefficients that is meant by "maintaining coherence". So it is 
> the 
> coherence of the particular expansion that is implied, and this 
> has noting 
> to do with the mutual orthogonality or otherwise of the basis 
> vectors 
> themselves. In decoherence, the phase relationships between the 
> terms in 
> the original expansion are lost.
>
> Bruce 
>

 I appreciate your reply. I was sure you could ascertain my 
 error -- confusing orthogonality with interference and coherence. 
 Let me 
 have your indulgence on a related issue. AG

>>>
>>> Suppose the original wf is expressed in terms of p, and its 
>>> superposition expansion is also expressed in eigenfunctions with 
>>> variable 
>>> p. Does the phase of the original wf carry over into the 
>>> eigenfunctions as 
>>> identical for each, or can each component in the superposition have 
>>> different phases? I ask this because the probability determined by 
>>> any 
>>> complex amplitude is independent of its phase. TIA, AG 
>>>
>>
>> The phases of the coefficients are independent of each other.
>>
>
> When I formally studied QM, no mention was made of calculating the 
> phases since, presumably, they don't effect probability calculations. 
> Do 
> you have a link which explains how they're calculated? TIA, AG 
>

 I found some links on physics.stackexchange.com which show that 
 relative phases can effect probabilities, but none so far about how to 
 calculate any phase angle. AG 

>>>
>>> Here's the answer if anyone's interested. But what's the question? 
>>> How are wf phase angles calculated? Clearly, if you solve for the 
>>> eigenfunctions of some QM operator such as the p operator, any phase 
>>> angle 
>>> is possible; its value is completely arbitrary and doesn't effect a 
>>> 

Re: Coherent states of a superposition

2019-01-11 Thread Bruno Marchal

> On 10 Jan 2019, at 22:08, agrayson2...@gmail.com wrote:
> 
> 
> 
> On Thursday, January 10, 2019 at 11:07:51 AM UTC, Bruno Marchal wrote:
> 
>> On 9 Jan 2019, at 07:58, agrays...@gmail.com  wrote:
>> 
>> 
>> 
>> On Monday, January 7, 2019 at 11:37:13 PM UTC, agrays...@gmail.com 
>>  wrote:
>> 
>> 
>> On Monday, January 7, 2019 at 2:52:27 PM UTC, agrays...@gmail.com <> wrote:
>> 
>> 
>> On Sunday, January 6, 2019 at 10:45:01 PM UTC, Bruce wrote:
>> On Mon, Jan 7, 2019 at 9:42 AM > wrote:
>> On Saturday, December 8, 2018 at 2:46:41 PM UTC, agrays...@gmail.com <> 
>> wrote:
>> On Thursday, December 6, 2018 at 5:46:13 PM UTC, agrays...@gmail.com <> 
>> wrote:
>> On Wednesday, December 5, 2018 at 10:13:57 PM UTC, agrays...@gmail.com <> 
>> wrote:
>> On Wednesday, December 5, 2018 at 9:42:51 PM UTC, Bruce wrote:
>> On Wed, Dec 5, 2018 at 10:52 PM > wrote:
>> On Wednesday, December 5, 2018 at 11:42:06 AM UTC, agrays...@gmail.com <> 
>> wrote:
>> On Tuesday, December 4, 2018 at 9:57:41 PM UTC, Bruce wrote:
>> On Wed, Dec 5, 2018 at 2:36 AM > wrote:
>> 
>> Thanks, but I'm looking for a solution within the context of interference 
>> and coherence, without introducing your theory of consciousness. Mainstream 
>> thinking today is that decoherence does occur, but this seems to imply 
>> preexisting coherence, and therefore interference among the component states 
>> of a superposition. If the superposition is expressed using eigenfunctions, 
>> which are mutually orthogonal -- implying no mutual interference -- how is 
>> decoherence possible, insofar as coherence, IIUC, doesn't exist using this 
>> basis? AG
>> 
>> I think you misunderstand the meaning of "coherence" when it is used off an 
>> expansion in terms of a set of mutually orthogonal eigenvectors. The 
>> expansion in some eigenvector basis is written as
>> 
>>|psi> = Sum_i (a_i |v_i>)
>> 
>> where |v_i> are the eigenvectors, and i ranges over the dimension of the 
>> Hilbert space. The expansion coefficients are the complex numbers a_i. Since 
>> these are complex coefficients, they contain inherent phases. It is the 
>> preservation of these phases of the expansion coefficients that is meant by 
>> "maintaining coherence". So it is the coherence of the particular expansion 
>> that is implied, and this has noting to do with the mutual orthogonality or 
>> otherwise of the basis vectors themselves. In decoherence, the phase 
>> relationships between the terms in the original expansion are lost.
>> 
>> Bruce 
>> 
>> I appreciate your reply. I was sure you could ascertain my error -- 
>> confusing orthogonality with interference and coherence. Let me have your 
>> indulgence on a related issue. AG
>> 
>> Suppose the original wf is expressed in terms of p, and its superposition 
>> expansion is also expressed in eigenfunctions with variable p. Does the 
>> phase of the original wf carry over into the eigenfunctions as identical for 
>> each, or can each component in the superposition have different phases? I 
>> ask this because the probability determined by any complex amplitude is 
>> independent of its phase. TIA, AG 
>> 
>> The phases of the coefficients are independent of each other.
>> 
>> When I formally studied QM, no mention was made of calculating the phases 
>> since, presumably, they don't effect probability calculations. Do you have a 
>> link which explains how they're calculated? TIA, AG 
>> 
>> I found some links on physics.stackexchange.com 
>>  which show that relative phases can 
>> effect probabilities, but none so far about how to calculate any phase 
>> angle. AG 
>> 
>> Here's the answer if anyone's interested. But what's the question? How are 
>> wf phase angles calculated? Clearly, if you solve for the eigenfunctions of 
>> some QM operator such as the p operator, any phase angle is possible; its 
>> value is completely arbitrary and doesn't effect a probability calculation. 
>> In fact, IIUC, there is not sufficient information to solve for a unique 
>> phase. So, I conclude,that the additional information required to uniquely 
>> determine a phase angle for a wf, lies in boundary conditions. If the 
>> problem of specifying a wf is defined as a boundary value problem, then, I 
>> believe, a unique phase angle can be calculated. CMIIAW. AG 
>> 
>> Bruce
>> 
>> I could use a handshake on this one. Roughly speaking, if one wants to 
>> express the state of a system as a superposition of eigenstates, how does 
>> one calculate the phase angles of the amplitudes for each eigenstate? AG
>> 
>> One doesn't. The phases are arbitrary unless one interferes the system with 
>> some other system.
>> 
>> Bruce 
>> 
>> If the phases are arbitrary and the system interacts with some other system, 
>> the new phases presumably are also arbitrary. So there doesn't seem to be 
>> any physical significance, yet this is the heart of decoherence theory as I 
>> understand it. What am I 

Re: Coherent states of a superposition

2019-01-11 Thread Bruno Marchal

> On 10 Jan 2019, at 21:33, agrayson2...@gmail.com wrote:
> 
> 
> 
> On Thursday, January 10, 2019 at 11:07:51 AM UTC, Bruno Marchal wrote:
> 
>> On 9 Jan 2019, at 07:58, agrays...@gmail.com  wrote:
>> 
>> 
>> 
>> On Monday, January 7, 2019 at 11:37:13 PM UTC, agrays...@gmail.com 
>>  wrote:
>> 
>> 
>> On Monday, January 7, 2019 at 2:52:27 PM UTC, agrays...@gmail.com <> wrote:
>> 
>> 
>> On Sunday, January 6, 2019 at 10:45:01 PM UTC, Bruce wrote:
>> On Mon, Jan 7, 2019 at 9:42 AM > wrote:
>> On Saturday, December 8, 2018 at 2:46:41 PM UTC, agrays...@gmail.com <> 
>> wrote:
>> On Thursday, December 6, 2018 at 5:46:13 PM UTC, agrays...@gmail.com <> 
>> wrote:
>> On Wednesday, December 5, 2018 at 10:13:57 PM UTC, agrays...@gmail.com <> 
>> wrote:
>> On Wednesday, December 5, 2018 at 9:42:51 PM UTC, Bruce wrote:
>> On Wed, Dec 5, 2018 at 10:52 PM > wrote:
>> On Wednesday, December 5, 2018 at 11:42:06 AM UTC, agrays...@gmail.com <> 
>> wrote:
>> On Tuesday, December 4, 2018 at 9:57:41 PM UTC, Bruce wrote:
>> On Wed, Dec 5, 2018 at 2:36 AM > wrote:
>> 
>> Thanks, but I'm looking for a solution within the context of interference 
>> and coherence, without introducing your theory of consciousness. Mainstream 
>> thinking today is that decoherence does occur, but this seems to imply 
>> preexisting coherence, and therefore interference among the component states 
>> of a superposition. If the superposition is expressed using eigenfunctions, 
>> which are mutually orthogonal -- implying no mutual interference -- how is 
>> decoherence possible, insofar as coherence, IIUC, doesn't exist using this 
>> basis? AG
>> 
>> I think you misunderstand the meaning of "coherence" when it is used off an 
>> expansion in terms of a set of mutually orthogonal eigenvectors. The 
>> expansion in some eigenvector basis is written as
>> 
>>|psi> = Sum_i (a_i |v_i>)
>> 
>> where |v_i> are the eigenvectors, and i ranges over the dimension of the 
>> Hilbert space. The expansion coefficients are the complex numbers a_i. Since 
>> these are complex coefficients, they contain inherent phases. It is the 
>> preservation of these phases of the expansion coefficients that is meant by 
>> "maintaining coherence". So it is the coherence of the particular expansion 
>> that is implied, and this has noting to do with the mutual orthogonality or 
>> otherwise of the basis vectors themselves. In decoherence, the phase 
>> relationships between the terms in the original expansion are lost.
>> 
>> Bruce 
>> 
>> I appreciate your reply. I was sure you could ascertain my error -- 
>> confusing orthogonality with interference and coherence. Let me have your 
>> indulgence on a related issue. AG
>> 
>> Suppose the original wf is expressed in terms of p, and its superposition 
>> expansion is also expressed in eigenfunctions with variable p. Does the 
>> phase of the original wf carry over into the eigenfunctions as identical for 
>> each, or can each component in the superposition have different phases? I 
>> ask this because the probability determined by any complex amplitude is 
>> independent of its phase. TIA, AG 
>> 
>> The phases of the coefficients are independent of each other.
>> 
>> When I formally studied QM, no mention was made of calculating the phases 
>> since, presumably, they don't effect probability calculations. Do you have a 
>> link which explains how they're calculated? TIA, AG 
>> 
>> I found some links on physics.stackexchange.com 
>>  which show that relative phases can 
>> effect probabilities, but none so far about how to calculate any phase 
>> angle. AG 
>> 
>> Here's the answer if anyone's interested. But what's the question? How are 
>> wf phase angles calculated? Clearly, if you solve for the eigenfunctions of 
>> some QM operator such as the p operator, any phase angle is possible; its 
>> value is completely arbitrary and doesn't effect a probability calculation. 
>> In fact, IIUC, there is not sufficient information to solve for a unique 
>> phase. So, I conclude,that the additional information required to uniquely 
>> determine a phase angle for a wf, lies in boundary conditions. If the 
>> problem of specifying a wf is defined as a boundary value problem, then, I 
>> believe, a unique phase angle can be calculated. CMIIAW. AG 
>> 
>> Bruce
>> 
>> I could use a handshake on this one. Roughly speaking, if one wants to 
>> express the state of a system as a superposition of eigenstates, how does 
>> one calculate the phase angles of the amplitudes for each eigenstate? AG
>> 
>> One doesn't. The phases are arbitrary unless one interferes the system with 
>> some other system.
>> 
>> Bruce 
>> 
>> If the phases are arbitrary and the system interacts with some other system, 
>> the new phases presumably are also arbitrary. So there doesn't seem to be 
>> any physical significance, yet this is the heart of decoherence theory as I 
>> understand it. What am I 

Re: Coherent states of a superposition

2019-01-10 Thread agrayson2000


On Thursday, January 10, 2019 at 11:07:51 AM UTC, Bruno Marchal wrote:
>
>
> On 9 Jan 2019, at 07:58, agrays...@gmail.com  wrote:
>
>
>
> On Monday, January 7, 2019 at 11:37:13 PM UTC, agrays...@gmail.com wrote:
>>
>>
>>
>> On Monday, January 7, 2019 at 2:52:27 PM UTC, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Sunday, January 6, 2019 at 10:45:01 PM UTC, Bruce wrote:

 On Mon, Jan 7, 2019 at 9:42 AM  wrote:

> On Saturday, December 8, 2018 at 2:46:41 PM UTC, agrays...@gmail.com 
> wrote:
>>
>> On Thursday, December 6, 2018 at 5:46:13 PM UTC, agrays...@gmail.com 
>> wrote:
>>>
>>> On Wednesday, December 5, 2018 at 10:13:57 PM UTC, 
>>> agrays...@gmail.com wrote:

 On Wednesday, December 5, 2018 at 9:42:51 PM UTC, Bruce wrote:
>
> On Wed, Dec 5, 2018 at 10:52 PM  wrote:
>
>> On Wednesday, December 5, 2018 at 11:42:06 AM UTC, 
>> agrays...@gmail.com wrote:
>>>
>>> On Tuesday, December 4, 2018 at 9:57:41 PM UTC, Bruce wrote:

 On Wed, Dec 5, 2018 at 2:36 AM  wrote:

>
> *Thanks, but I'm looking for a solution within the context of 
> interference and coherence, without introducing your theory of 
> consciousness. Mainstream thinking today is that decoherence does 
> occur, 
> but this seems to imply preexisting coherence, and therefore 
> interference 
> among the component states of a superposition. If the 
> superposition is 
> expressed using eigenfunctions, which are mutually orthogonal -- 
> implying 
> no mutual interference -- how is decoherence possible, insofar as 
> coherence, IIUC, doesn't exist using this basis? AG*
>

 I think you misunderstand the meaning of "coherence" when it is 
 used off an expansion in terms of a set of mutually orthogonal 
 eigenvectors. The expansion in some eigenvector basis is written as

|psi> = Sum_i (a_i |v_i>)

 where |v_i> are the eigenvectors, and i ranges over the 
 dimension of the Hilbert space. The expansion coefficients are the 
 complex 
 numbers a_i. Since these are complex coefficients, they contain 
 inherent 
 phases. It is the preservation of these phases of the expansion 
 coefficients that is meant by "maintaining coherence". So it is 
 the 
 coherence of the particular expansion that is implied, and this 
 has noting 
 to do with the mutual orthogonality or otherwise of the basis 
 vectors 
 themselves. In decoherence, the phase relationships between the 
 terms in 
 the original expansion are lost.

 Bruce 

>>>
>>> I appreciate your reply. I was sure you could ascertain my error 
>>> -- confusing orthogonality with interference and coherence. Let me 
>>> have 
>>> your indulgence on a related issue. AG
>>>
>>
>> Suppose the original wf is expressed in terms of p, and its 
>> superposition expansion is also expressed in eigenfunctions with 
>> variable 
>> p. Does the phase of the original wf carry over into the 
>> eigenfunctions as 
>> identical for each, or can each component in the superposition have 
>> different phases? I ask this because the probability determined by 
>> any 
>> complex amplitude is independent of its phase. TIA, AG 
>>
>
> The phases of the coefficients are independent of each other.
>

 When I formally studied QM, no mention was made of calculating the 
 phases since, presumably, they don't effect probability calculations. 
 Do 
 you have a link which explains how they're calculated? TIA, AG 

>>>
>>> I found some links on physics.stackexchange.com which show that 
>>> relative phases can effect probabilities, but none so far about how to 
>>> calculate any phase angle. AG 
>>>
>>
>> Here's the answer if anyone's interested. But what's the question? 
>> How are wf phase angles calculated? Clearly, if you solve for the 
>> eigenfunctions of some QM operator such as the p operator, any phase 
>> angle 
>> is possible; its value is completely arbitrary and doesn't effect a 
>> probability calculation. In fact, IIUC, there is not sufficient 
>> information 
>> to solve for a unique phase. So, I conclude,that the additional 
>> information 
>> required to uniquely determine a phase angle for a wf, lies in boundary 
>> conditions. If the 

Re: Coherent states of a superposition

2019-01-10 Thread agrayson2000


On Thursday, January 10, 2019 at 11:07:51 AM UTC, Bruno Marchal wrote:
>
>
> On 9 Jan 2019, at 07:58, agrays...@gmail.com  wrote:
>
>
>
> On Monday, January 7, 2019 at 11:37:13 PM UTC, agrays...@gmail.com wrote:
>>
>>
>>
>> On Monday, January 7, 2019 at 2:52:27 PM UTC, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Sunday, January 6, 2019 at 10:45:01 PM UTC, Bruce wrote:

 On Mon, Jan 7, 2019 at 9:42 AM  wrote:

> On Saturday, December 8, 2018 at 2:46:41 PM UTC, agrays...@gmail.com 
> wrote:
>>
>> On Thursday, December 6, 2018 at 5:46:13 PM UTC, agrays...@gmail.com 
>> wrote:
>>>
>>> On Wednesday, December 5, 2018 at 10:13:57 PM UTC, 
>>> agrays...@gmail.com wrote:

 On Wednesday, December 5, 2018 at 9:42:51 PM UTC, Bruce wrote:
>
> On Wed, Dec 5, 2018 at 10:52 PM  wrote:
>
>> On Wednesday, December 5, 2018 at 11:42:06 AM UTC, 
>> agrays...@gmail.com wrote:
>>>
>>> On Tuesday, December 4, 2018 at 9:57:41 PM UTC, Bruce wrote:

 On Wed, Dec 5, 2018 at 2:36 AM  wrote:

>
> *Thanks, but I'm looking for a solution within the context of 
> interference and coherence, without introducing your theory of 
> consciousness. Mainstream thinking today is that decoherence does 
> occur, 
> but this seems to imply preexisting coherence, and therefore 
> interference 
> among the component states of a superposition. If the 
> superposition is 
> expressed using eigenfunctions, which are mutually orthogonal -- 
> implying 
> no mutual interference -- how is decoherence possible, insofar as 
> coherence, IIUC, doesn't exist using this basis? AG*
>

 I think you misunderstand the meaning of "coherence" when it is 
 used off an expansion in terms of a set of mutually orthogonal 
 eigenvectors. The expansion in some eigenvector basis is written as

|psi> = Sum_i (a_i |v_i>)

 where |v_i> are the eigenvectors, and i ranges over the 
 dimension of the Hilbert space. The expansion coefficients are the 
 complex 
 numbers a_i. Since these are complex coefficients, they contain 
 inherent 
 phases. It is the preservation of these phases of the expansion 
 coefficients that is meant by "maintaining coherence". So it is 
 the 
 coherence of the particular expansion that is implied, and this 
 has noting 
 to do with the mutual orthogonality or otherwise of the basis 
 vectors 
 themselves. In decoherence, the phase relationships between the 
 terms in 
 the original expansion are lost.

 Bruce 

>>>
>>> I appreciate your reply. I was sure you could ascertain my error 
>>> -- confusing orthogonality with interference and coherence. Let me 
>>> have 
>>> your indulgence on a related issue. AG
>>>
>>
>> Suppose the original wf is expressed in terms of p, and its 
>> superposition expansion is also expressed in eigenfunctions with 
>> variable 
>> p. Does the phase of the original wf carry over into the 
>> eigenfunctions as 
>> identical for each, or can each component in the superposition have 
>> different phases? I ask this because the probability determined by 
>> any 
>> complex amplitude is independent of its phase. TIA, AG 
>>
>
> The phases of the coefficients are independent of each other.
>

 When I formally studied QM, no mention was made of calculating the 
 phases since, presumably, they don't effect probability calculations. 
 Do 
 you have a link which explains how they're calculated? TIA, AG 

>>>
>>> I found some links on physics.stackexchange.com which show that 
>>> relative phases can effect probabilities, but none so far about how to 
>>> calculate any phase angle. AG 
>>>
>>
>> Here's the answer if anyone's interested. But what's the question? 
>> How are wf phase angles calculated? Clearly, if you solve for the 
>> eigenfunctions of some QM operator such as the p operator, any phase 
>> angle 
>> is possible; its value is completely arbitrary and doesn't effect a 
>> probability calculation. In fact, IIUC, there is not sufficient 
>> information 
>> to solve for a unique phase. So, I conclude,that the additional 
>> information 
>> required to uniquely determine a phase angle for a wf, lies in boundary 
>> conditions. If the 

Re: Coherent states of a superposition

2019-01-10 Thread agrayson2000


On Thursday, January 10, 2019 at 11:07:51 AM UTC, Bruno Marchal wrote:
>
>
> On 9 Jan 2019, at 07:58, agrays...@gmail.com  wrote:
>
>
>
> On Monday, January 7, 2019 at 11:37:13 PM UTC, agrays...@gmail.com wrote:
>>
>>
>>
>> On Monday, January 7, 2019 at 2:52:27 PM UTC, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Sunday, January 6, 2019 at 10:45:01 PM UTC, Bruce wrote:

 On Mon, Jan 7, 2019 at 9:42 AM  wrote:

> On Saturday, December 8, 2018 at 2:46:41 PM UTC, agrays...@gmail.com 
> wrote:
>>
>> On Thursday, December 6, 2018 at 5:46:13 PM UTC, agrays...@gmail.com 
>> wrote:
>>>
>>> On Wednesday, December 5, 2018 at 10:13:57 PM UTC, 
>>> agrays...@gmail.com wrote:

 On Wednesday, December 5, 2018 at 9:42:51 PM UTC, Bruce wrote:
>
> On Wed, Dec 5, 2018 at 10:52 PM  wrote:
>
>> On Wednesday, December 5, 2018 at 11:42:06 AM UTC, 
>> agrays...@gmail.com wrote:
>>>
>>> On Tuesday, December 4, 2018 at 9:57:41 PM UTC, Bruce wrote:

 On Wed, Dec 5, 2018 at 2:36 AM  wrote:

>
> *Thanks, but I'm looking for a solution within the context of 
> interference and coherence, without introducing your theory of 
> consciousness. Mainstream thinking today is that decoherence does 
> occur, 
> but this seems to imply preexisting coherence, and therefore 
> interference 
> among the component states of a superposition. If the 
> superposition is 
> expressed using eigenfunctions, which are mutually orthogonal -- 
> implying 
> no mutual interference -- how is decoherence possible, insofar as 
> coherence, IIUC, doesn't exist using this basis? AG*
>

 I think you misunderstand the meaning of "coherence" when it is 
 used off an expansion in terms of a set of mutually orthogonal 
 eigenvectors. The expansion in some eigenvector basis is written as

|psi> = Sum_i (a_i |v_i>)

 where |v_i> are the eigenvectors, and i ranges over the 
 dimension of the Hilbert space. The expansion coefficients are the 
 complex 
 numbers a_i. Since these are complex coefficients, they contain 
 inherent 
 phases. It is the preservation of these phases of the expansion 
 coefficients that is meant by "maintaining coherence". So it is 
 the 
 coherence of the particular expansion that is implied, and this 
 has noting 
 to do with the mutual orthogonality or otherwise of the basis 
 vectors 
 themselves. In decoherence, the phase relationships between the 
 terms in 
 the original expansion are lost.

 Bruce 

>>>
>>> I appreciate your reply. I was sure you could ascertain my error 
>>> -- confusing orthogonality with interference and coherence. Let me 
>>> have 
>>> your indulgence on a related issue. AG
>>>
>>
>> Suppose the original wf is expressed in terms of p, and its 
>> superposition expansion is also expressed in eigenfunctions with 
>> variable 
>> p. Does the phase of the original wf carry over into the 
>> eigenfunctions as 
>> identical for each, or can each component in the superposition have 
>> different phases? I ask this because the probability determined by 
>> any 
>> complex amplitude is independent of its phase. TIA, AG 
>>
>
> The phases of the coefficients are independent of each other.
>

 When I formally studied QM, no mention was made of calculating the 
 phases since, presumably, they don't effect probability calculations. 
 Do 
 you have a link which explains how they're calculated? TIA, AG 

>>>
>>> I found some links on physics.stackexchange.com which show that 
>>> relative phases can effect probabilities, but none so far about how to 
>>> calculate any phase angle. AG 
>>>
>>
>> Here's the answer if anyone's interested. But what's the question? 
>> How are wf phase angles calculated? Clearly, if you solve for the 
>> eigenfunctions of some QM operator such as the p operator, any phase 
>> angle 
>> is possible; its value is completely arbitrary and doesn't effect a 
>> probability calculation. In fact, IIUC, there is not sufficient 
>> information 
>> to solve for a unique phase. So, I conclude,that the additional 
>> information 
>> required to uniquely determine a phase angle for a wf, lies in boundary 
>> conditions. If the 

Re: Coherent states of a superposition

2019-01-10 Thread Bruno Marchal

> On 9 Jan 2019, at 07:58, agrayson2...@gmail.com wrote:
> 
> 
> 
> On Monday, January 7, 2019 at 11:37:13 PM UTC, agrays...@gmail.com wrote:
> 
> 
> On Monday, January 7, 2019 at 2:52:27 PM UTC, agrays...@gmail.com <> wrote:
> 
> 
> On Sunday, January 6, 2019 at 10:45:01 PM UTC, Bruce wrote:
> On Mon, Jan 7, 2019 at 9:42 AM > wrote:
> On Saturday, December 8, 2018 at 2:46:41 PM UTC, agrays...@gmail.com <> wrote:
> On Thursday, December 6, 2018 at 5:46:13 PM UTC, agrays...@gmail.com <> wrote:
> On Wednesday, December 5, 2018 at 10:13:57 PM UTC, agrays...@gmail.com <> 
> wrote:
> On Wednesday, December 5, 2018 at 9:42:51 PM UTC, Bruce wrote:
> On Wed, Dec 5, 2018 at 10:52 PM > wrote:
> On Wednesday, December 5, 2018 at 11:42:06 AM UTC, agrays...@gmail.com <> 
> wrote:
> On Tuesday, December 4, 2018 at 9:57:41 PM UTC, Bruce wrote:
> On Wed, Dec 5, 2018 at 2:36 AM > wrote:
> 
> Thanks, but I'm looking for a solution within the context of interference and 
> coherence, without introducing your theory of consciousness. Mainstream 
> thinking today is that decoherence does occur, but this seems to imply 
> preexisting coherence, and therefore interference among the component states 
> of a superposition. If the superposition is expressed using eigenfunctions, 
> which are mutually orthogonal -- implying no mutual interference -- how is 
> decoherence possible, insofar as coherence, IIUC, doesn't exist using this 
> basis? AG
> 
> I think you misunderstand the meaning of "coherence" when it is used off an 
> expansion in terms of a set of mutually orthogonal eigenvectors. The 
> expansion in some eigenvector basis is written as
> 
>|psi> = Sum_i (a_i |v_i>)
> 
> where |v_i> are the eigenvectors, and i ranges over the dimension of the 
> Hilbert space. The expansion coefficients are the complex numbers a_i. Since 
> these are complex coefficients, they contain inherent phases. It is the 
> preservation of these phases of the expansion coefficients that is meant by 
> "maintaining coherence". So it is the coherence of the particular expansion 
> that is implied, and this has noting to do with the mutual orthogonality or 
> otherwise of the basis vectors themselves. In decoherence, the phase 
> relationships between the terms in the original expansion are lost.
> 
> Bruce 
> 
> I appreciate your reply. I was sure you could ascertain my error -- confusing 
> orthogonality with interference and coherence. Let me have your indulgence on 
> a related issue. AG
> 
> Suppose the original wf is expressed in terms of p, and its superposition 
> expansion is also expressed in eigenfunctions with variable p. Does the phase 
> of the original wf carry over into the eigenfunctions as identical for each, 
> or can each component in the superposition have different phases? I ask this 
> because the probability determined by any complex amplitude is independent of 
> its phase. TIA, AG 
> 
> The phases of the coefficients are independent of each other.
> 
> When I formally studied QM, no mention was made of calculating the phases 
> since, presumably, they don't effect probability calculations. Do you have a 
> link which explains how they're calculated? TIA, AG 
> 
> I found some links on physics.stackexchange.com 
>  which show that relative phases can 
> effect probabilities, but none so far about how to calculate any phase angle. 
> AG 
> 
> Here's the answer if anyone's interested. But what's the question? How are wf 
> phase angles calculated? Clearly, if you solve for the eigenfunctions of some 
> QM operator such as the p operator, any phase angle is possible; its value is 
> completely arbitrary and doesn't effect a probability calculation. In fact, 
> IIUC, there is not sufficient information to solve for a unique phase. So, I 
> conclude,that the additional information required to uniquely determine a 
> phase angle for a wf, lies in boundary conditions. If the problem of 
> specifying a wf is defined as a boundary value problem, then, I believe, a 
> unique phase angle can be calculated. CMIIAW. AG 
> 
> Bruce
> 
> I could use a handshake on this one. Roughly speaking, if one wants to 
> express the state of a system as a superposition of eigenstates, how does one 
> calculate the phase angles of the amplitudes for each eigenstate? AG
> 
> One doesn't. The phases are arbitrary unless one interferes the system with 
> some other system.
> 
> Bruce 
> 
> If the phases are arbitrary and the system interacts with some other system, 
> the new phases presumably are also arbitrary. So there doesn't seem to be any 
> physical significance, yet this is the heart of decoherence theory as I 
> understand it. What am I missing? TIA, AG
> 
>  Also, as we discussed, the phase angles determine interference. If they can 
> be chosen arbitrarily, it seems as if interference has no physical 
> significance. AG
> 
> Puzzling, isn't it? We have waves in Wave Mechanics. Waves interfere with 
> each 

Re: Coherent states of a superposition

2019-01-08 Thread agrayson2000


On Monday, January 7, 2019 at 11:37:13 PM UTC, agrays...@gmail.com wrote:
>
>
>
> On Monday, January 7, 2019 at 2:52:27 PM UTC, agrays...@gmail.com wrote:
>>
>>
>>
>> On Sunday, January 6, 2019 at 10:45:01 PM UTC, Bruce wrote:
>>>
>>> On Mon, Jan 7, 2019 at 9:42 AM  wrote:
>>>
 On Saturday, December 8, 2018 at 2:46:41 PM UTC, agrays...@gmail.com 
 wrote:
>
> On Thursday, December 6, 2018 at 5:46:13 PM UTC, agrays...@gmail.com 
> wrote:
>>
>> On Wednesday, December 5, 2018 at 10:13:57 PM UTC, 
>> agrays...@gmail.com wrote:
>>>
>>> On Wednesday, December 5, 2018 at 9:42:51 PM UTC, Bruce wrote:

 On Wed, Dec 5, 2018 at 10:52 PM  wrote:

> On Wednesday, December 5, 2018 at 11:42:06 AM UTC, 
> agrays...@gmail.com wrote:
>>
>> On Tuesday, December 4, 2018 at 9:57:41 PM UTC, Bruce wrote:
>>>
>>> On Wed, Dec 5, 2018 at 2:36 AM  wrote:
>>>

 *Thanks, but I'm looking for a solution within the context of 
 interference and coherence, without introducing your theory of 
 consciousness. Mainstream thinking today is that decoherence does 
 occur, 
 but this seems to imply preexisting coherence, and therefore 
 interference 
 among the component states of a superposition. If the 
 superposition is 
 expressed using eigenfunctions, which are mutually orthogonal -- 
 implying 
 no mutual interference -- how is decoherence possible, insofar as 
 coherence, IIUC, doesn't exist using this basis? AG*

>>>
>>> I think you misunderstand the meaning of "coherence" when it is 
>>> used off an expansion in terms of a set of mutually orthogonal 
>>> eigenvectors. The expansion in some eigenvector basis is written as
>>>
>>>|psi> = Sum_i (a_i |v_i>)
>>>
>>> where |v_i> are the eigenvectors, and i ranges over the 
>>> dimension of the Hilbert space. The expansion coefficients are the 
>>> complex 
>>> numbers a_i. Since these are complex coefficients, they contain 
>>> inherent 
>>> phases. It is the preservation of these phases of the expansion 
>>> coefficients that is meant by "maintaining coherence". So it is the 
>>> coherence of the particular expansion that is implied, and this has 
>>> noting 
>>> to do with the mutual orthogonality or otherwise of the basis 
>>> vectors 
>>> themselves. In decoherence, the phase relationships between the 
>>> terms in 
>>> the original expansion are lost.
>>>
>>> Bruce 
>>>
>>
>> I appreciate your reply. I was sure you could ascertain my error 
>> -- confusing orthogonality with interference and coherence. Let me 
>> have 
>> your indulgence on a related issue. AG
>>
>
> Suppose the original wf is expressed in terms of p, and its 
> superposition expansion is also expressed in eigenfunctions with 
> variable 
> p. Does the phase of the original wf carry over into the 
> eigenfunctions as 
> identical for each, or can each component in the superposition have 
> different phases? I ask this because the probability determined by 
> any 
> complex amplitude is independent of its phase. TIA, AG 
>

 The phases of the coefficients are independent of each other.

>>>
>>> When I formally studied QM, no mention was made of calculating the 
>>> phases since, presumably, they don't effect probability calculations. 
>>> Do 
>>> you have a link which explains how they're calculated? TIA, AG 
>>>
>>
>> I found some links on physics.stackexchange.com which show that 
>> relative phases can effect probabilities, but none so far about how to 
>> calculate any phase angle. AG 
>>
>
> Here's the answer if anyone's interested. But what's the question? How 
> are wf phase angles calculated? Clearly, if you solve for the 
> eigenfunctions of some QM operator such as the p operator, any phase 
> angle 
> is possible; its value is completely arbitrary and doesn't effect a 
> probability calculation. In fact, IIUC, there is not sufficient 
> information 
> to solve for a unique phase. So, I conclude,that the additional 
> information 
> required to uniquely determine a phase angle for a wf, lies in boundary 
> conditions. If the problem of specifying a wf is defined as a boundary 
> value problem, then, I believe, a unique phase angle can be calculated. 
> CMIIAW. AG 
>
>>
 Bruce

>>>
 I could use a handshake on this one. Roughly speaking, if one wants 

Re: Coherent states of a superposition

2019-01-07 Thread agrayson2000


On Monday, January 7, 2019 at 2:52:27 PM UTC, agrays...@gmail.com wrote:
>
>
>
> On Sunday, January 6, 2019 at 10:45:01 PM UTC, Bruce wrote:
>>
>> On Mon, Jan 7, 2019 at 9:42 AM  wrote:
>>
>>> On Saturday, December 8, 2018 at 2:46:41 PM UTC, agrays...@gmail.com 
>>> wrote:

 On Thursday, December 6, 2018 at 5:46:13 PM UTC, agrays...@gmail.com 
 wrote:
>
> On Wednesday, December 5, 2018 at 10:13:57 PM UTC, agrays...@gmail.com 
> wrote:
>>
>> On Wednesday, December 5, 2018 at 9:42:51 PM UTC, Bruce wrote:
>>>
>>> On Wed, Dec 5, 2018 at 10:52 PM  wrote:
>>>
 On Wednesday, December 5, 2018 at 11:42:06 AM UTC, 
 agrays...@gmail.com wrote:
>
> On Tuesday, December 4, 2018 at 9:57:41 PM UTC, Bruce wrote:
>>
>> On Wed, Dec 5, 2018 at 2:36 AM  wrote:
>>
>>>
>>> *Thanks, but I'm looking for a solution within the context of 
>>> interference and coherence, without introducing your theory of 
>>> consciousness. Mainstream thinking today is that decoherence does 
>>> occur, 
>>> but this seems to imply preexisting coherence, and therefore 
>>> interference 
>>> among the component states of a superposition. If the superposition 
>>> is 
>>> expressed using eigenfunctions, which are mutually orthogonal -- 
>>> implying 
>>> no mutual interference -- how is decoherence possible, insofar as 
>>> coherence, IIUC, doesn't exist using this basis? AG*
>>>
>>
>> I think you misunderstand the meaning of "coherence" when it is 
>> used off an expansion in terms of a set of mutually orthogonal 
>> eigenvectors. The expansion in some eigenvector basis is written as
>>
>>|psi> = Sum_i (a_i |v_i>)
>>
>> where |v_i> are the eigenvectors, and i ranges over the dimension 
>> of the Hilbert space. The expansion coefficients are the complex 
>> numbers 
>> a_i. Since these are complex coefficients, they contain inherent 
>> phases. It 
>> is the preservation of these phases of the expansion coefficients 
>> that is 
>> meant by "maintaining coherence". So it is the coherence of the 
>> particular 
>> expansion that is implied, and this has noting to do with the mutual 
>> orthogonality or otherwise of the basis vectors themselves. In 
>> decoherence, 
>> the phase relationships between the terms in the original expansion 
>> are 
>> lost.
>>
>> Bruce 
>>
>
> I appreciate your reply. I was sure you could ascertain my error 
> -- confusing orthogonality with interference and coherence. Let me 
> have 
> your indulgence on a related issue. AG
>

 Suppose the original wf is expressed in terms of p, and its 
 superposition expansion is also expressed in eigenfunctions with 
 variable 
 p. Does the phase of the original wf carry over into the 
 eigenfunctions as 
 identical for each, or can each component in the superposition have 
 different phases? I ask this because the probability determined by any 
 complex amplitude is independent of its phase. TIA, AG 

>>>
>>> The phases of the coefficients are independent of each other.
>>>
>>
>> When I formally studied QM, no mention was made of calculating the 
>> phases since, presumably, they don't effect probability calculations. Do 
>> you have a link which explains how they're calculated? TIA, AG 
>>
>
> I found some links on physics.stackexchange.com which show that 
> relative phases can effect probabilities, but none so far about how to 
> calculate any phase angle. AG 
>

 Here's the answer if anyone's interested. But what's the question? How 
 are wf phase angles calculated? Clearly, if you solve for the 
 eigenfunctions of some QM operator such as the p operator, any phase angle 
 is possible; its value is completely arbitrary and doesn't effect a 
 probability calculation. In fact, IIUC, there is not sufficient 
 information 
 to solve for a unique phase. So, I conclude,that the additional 
 information 
 required to uniquely determine a phase angle for a wf, lies in boundary 
 conditions. If the problem of specifying a wf is defined as a boundary 
 value problem, then, I believe, a unique phase angle can be calculated. 
 CMIIAW. AG 

>
>>> Bruce
>>>
>>
>>> I could use a handshake on this one. Roughly speaking, if one wants to 
>>> express the state of a system as a superposition of eigenstates, how does 
>>> one calculate the phase angles of the amplitudes for each eigenstate? AG
>>>
>>
>> One doesn't. The phases are arbitrary 

Re: Coherent states of a superposition

2019-01-07 Thread agrayson2000


On Sunday, January 6, 2019 at 10:45:01 PM UTC, Bruce wrote:
>
> On Mon, Jan 7, 2019 at 9:42 AM > wrote:
>
>> On Saturday, December 8, 2018 at 2:46:41 PM UTC, agrays...@gmail.com 
>> wrote:
>>>
>>> On Thursday, December 6, 2018 at 5:46:13 PM UTC, agrays...@gmail.com 
>>> wrote:

 On Wednesday, December 5, 2018 at 10:13:57 PM UTC, agrays...@gmail.com 
 wrote:
>
> On Wednesday, December 5, 2018 at 9:42:51 PM UTC, Bruce wrote:
>>
>> On Wed, Dec 5, 2018 at 10:52 PM  wrote:
>>
>>> On Wednesday, December 5, 2018 at 11:42:06 AM UTC, 
>>> agrays...@gmail.com wrote:

 On Tuesday, December 4, 2018 at 9:57:41 PM UTC, Bruce wrote:
>
> On Wed, Dec 5, 2018 at 2:36 AM  wrote:
>
>>
>> *Thanks, but I'm looking for a solution within the context of 
>> interference and coherence, without introducing your theory of 
>> consciousness. Mainstream thinking today is that decoherence does 
>> occur, 
>> but this seems to imply preexisting coherence, and therefore 
>> interference 
>> among the component states of a superposition. If the superposition 
>> is 
>> expressed using eigenfunctions, which are mutually orthogonal -- 
>> implying 
>> no mutual interference -- how is decoherence possible, insofar as 
>> coherence, IIUC, doesn't exist using this basis? AG*
>>
>
> I think you misunderstand the meaning of "coherence" when it is 
> used off an expansion in terms of a set of mutually orthogonal 
> eigenvectors. The expansion in some eigenvector basis is written as
>
>|psi> = Sum_i (a_i |v_i>)
>
> where |v_i> are the eigenvectors, and i ranges over the dimension 
> of the Hilbert space. The expansion coefficients are the complex 
> numbers 
> a_i. Since these are complex coefficients, they contain inherent 
> phases. It 
> is the preservation of these phases of the expansion coefficients 
> that is 
> meant by "maintaining coherence". So it is the coherence of the 
> particular 
> expansion that is implied, and this has noting to do with the mutual 
> orthogonality or otherwise of the basis vectors themselves. In 
> decoherence, 
> the phase relationships between the terms in the original expansion 
> are 
> lost.
>
> Bruce 
>

 I appreciate your reply. I was sure you could ascertain my error -- 
 confusing orthogonality with interference and coherence. Let me have 
 your 
 indulgence on a related issue. AG

>>>
>>> Suppose the original wf is expressed in terms of p, and its 
>>> superposition expansion is also expressed in eigenfunctions with 
>>> variable 
>>> p. Does the phase of the original wf carry over into the eigenfunctions 
>>> as 
>>> identical for each, or can each component in the superposition have 
>>> different phases? I ask this because the probability determined by any 
>>> complex amplitude is independent of its phase. TIA, AG 
>>>
>>
>> The phases of the coefficients are independent of each other.
>>
>
> When I formally studied QM, no mention was made of calculating the 
> phases since, presumably, they don't effect probability calculations. Do 
> you have a link which explains how they're calculated? TIA, AG 
>

 I found some links on physics.stackexchange.com which show that 
 relative phases can effect probabilities, but none so far about how to 
 calculate any phase angle. AG 

>>>
>>> Here's the answer if anyone's interested. But what's the question? How 
>>> are wf phase angles calculated? Clearly, if you solve for the 
>>> eigenfunctions of some QM operator such as the p operator, any phase angle 
>>> is possible; its value is completely arbitrary and doesn't effect a 
>>> probability calculation. In fact, IIUC, there is not sufficient information 
>>> to solve for a unique phase. So, I conclude,that the additional information 
>>> required to uniquely determine a phase angle for a wf, lies in boundary 
>>> conditions. If the problem of specifying a wf is defined as a boundary 
>>> value problem, then, I believe, a unique phase angle can be calculated. 
>>> CMIIAW. AG 
>>>

>> Bruce
>>
>
>> I could use a handshake on this one. Roughly speaking, if one wants to 
>> express the state of a system as a superposition of eigenstates, how does 
>> one calculate the phase angles of the amplitudes for each eigenstate? AG
>>
>
> One doesn't. The phases are arbitrary unless one interferes the system 
> with some other system.
>
> Bruce 
>

If the phases are arbitrary and the system interacts with some other 
system, the new phases presumably are also arbitrary. So there 

Re: Coherent states of a superposition

2019-01-06 Thread Bruce Kellett
On Mon, Jan 7, 2019 at 9:42 AM  wrote:

> On Saturday, December 8, 2018 at 2:46:41 PM UTC, agrays...@gmail.com
> wrote:
>>
>> On Thursday, December 6, 2018 at 5:46:13 PM UTC, agrays...@gmail.com
>> wrote:
>>>
>>> On Wednesday, December 5, 2018 at 10:13:57 PM UTC, agrays...@gmail.com
>>> wrote:

 On Wednesday, December 5, 2018 at 9:42:51 PM UTC, Bruce wrote:
>
> On Wed, Dec 5, 2018 at 10:52 PM  wrote:
>
>> On Wednesday, December 5, 2018 at 11:42:06 AM UTC,
>> agrays...@gmail.com wrote:
>>>
>>> On Tuesday, December 4, 2018 at 9:57:41 PM UTC, Bruce wrote:

 On Wed, Dec 5, 2018 at 2:36 AM  wrote:

>
> *Thanks, but I'm looking for a solution within the context of
> interference and coherence, without introducing your theory of
> consciousness. Mainstream thinking today is that decoherence does 
> occur,
> but this seems to imply preexisting coherence, and therefore 
> interference
> among the component states of a superposition. If the superposition is
> expressed using eigenfunctions, which are mutually orthogonal -- 
> implying
> no mutual interference -- how is decoherence possible, insofar as
> coherence, IIUC, doesn't exist using this basis? AG*
>

 I think you misunderstand the meaning of "coherence" when it is
 used off an expansion in terms of a set of mutually orthogonal
 eigenvectors. The expansion in some eigenvector basis is written as

|psi> = Sum_i (a_i |v_i>)

 where |v_i> are the eigenvectors, and i ranges over the dimension
 of the Hilbert space. The expansion coefficients are the complex 
 numbers
 a_i. Since these are complex coefficients, they contain inherent 
 phases. It
 is the preservation of these phases of the expansion coefficients that 
 is
 meant by "maintaining coherence". So it is the coherence of the 
 particular
 expansion that is implied, and this has noting to do with the mutual
 orthogonality or otherwise of the basis vectors themselves. In 
 decoherence,
 the phase relationships between the terms in the original expansion are
 lost.

 Bruce

>>>
>>> I appreciate your reply. I was sure you could ascertain my error --
>>> confusing orthogonality with interference and coherence. Let me have 
>>> your
>>> indulgence on a related issue. AG
>>>
>>
>> Suppose the original wf is expressed in terms of p, and its
>> superposition expansion is also expressed in eigenfunctions with variable
>> p. Does the phase of the original wf carry over into the eigenfunctions 
>> as
>> identical for each, or can each component in the superposition have
>> different phases? I ask this because the probability determined by any
>> complex amplitude is independent of its phase. TIA, AG
>>
>
> The phases of the coefficients are independent of each other.
>

 When I formally studied QM, no mention was made of calculating the
 phases since, presumably, they don't effect probability calculations. Do
 you have a link which explains how they're calculated? TIA, AG

>>>
>>> I found some links on physics.stackexchange.com which show that
>>> relative phases can effect probabilities, but none so far about how to
>>> calculate any phase angle. AG
>>>
>>
>> Here's the answer if anyone's interested. But what's the question? How
>> are wf phase angles calculated? Clearly, if you solve for the
>> eigenfunctions of some QM operator such as the p operator, any phase angle
>> is possible; its value is completely arbitrary and doesn't effect a
>> probability calculation. In fact, IIUC, there is not sufficient information
>> to solve for a unique phase. So, I conclude,that the additional information
>> required to uniquely determine a phase angle for a wf, lies in boundary
>> conditions. If the problem of specifying a wf is defined as a boundary
>> value problem, then, I believe, a unique phase angle can be calculated.
>> CMIIAW. AG
>>
>>>
> Bruce
>

> I could use a handshake on this one. Roughly speaking, if one wants to
> express the state of a system as a superposition of eigenstates, how does
> one calculate the phase angles of the amplitudes for each eigenstate? AG
>

One doesn't. The phases are arbitrary unless one interferes the system with
some other system.

Bruce

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Re: Coherent states of a superposition

2019-01-06 Thread agrayson2000


On Saturday, December 8, 2018 at 2:46:41 PM UTC, agrays...@gmail.com wrote:
>
>
>
> On Thursday, December 6, 2018 at 5:46:13 PM UTC, agrays...@gmail.com 
> wrote:
>>
>>
>>
>> On Wednesday, December 5, 2018 at 10:13:57 PM UTC, agrays...@gmail.com 
>> wrote:
>>>
>>>
>>>
>>> On Wednesday, December 5, 2018 at 9:42:51 PM UTC, Bruce wrote:

 On Wed, Dec 5, 2018 at 10:52 PM  wrote:

> On Wednesday, December 5, 2018 at 11:42:06 AM UTC, agrays...@gmail.com 
> wrote:
>>
>> On Tuesday, December 4, 2018 at 9:57:41 PM UTC, Bruce wrote:
>>>
>>> On Wed, Dec 5, 2018 at 2:36 AM  wrote:
>>>

 *Thanks, but I'm looking for a solution within the context of 
 interference and coherence, without introducing your theory of 
 consciousness. Mainstream thinking today is that decoherence does 
 occur, 
 but this seems to imply preexisting coherence, and therefore 
 interference 
 among the component states of a superposition. If the superposition is 
 expressed using eigenfunctions, which are mutually orthogonal -- 
 implying 
 no mutual interference -- how is decoherence possible, insofar as 
 coherence, IIUC, doesn't exist using this basis? AG*

>>>
>>> I think you misunderstand the meaning of "coherence" when it is used 
>>> off an expansion in terms of a set of mutually orthogonal eigenvectors. 
>>> The 
>>> expansion in some eigenvector basis is written as
>>>
>>>|psi> = Sum_i (a_i |v_i>)
>>>
>>> where |v_i> are the eigenvectors, and i ranges over the dimension of 
>>> the Hilbert space. The expansion coefficients are the complex numbers 
>>> a_i. 
>>> Since these are complex coefficients, they contain inherent phases. It 
>>> is 
>>> the preservation of these phases of the expansion coefficients that is 
>>> meant by "maintaining coherence". So it is the coherence of the 
>>> particular 
>>> expansion that is implied, and this has noting to do with the mutual 
>>> orthogonality or otherwise of the basis vectors themselves. In 
>>> decoherence, 
>>> the phase relationships between the terms in the original expansion are 
>>> lost.
>>>
>>> Bruce 
>>>
>>
>> I appreciate your reply. I was sure you could ascertain my error -- 
>> confusing orthogonality with interference and coherence. Let me have 
>> your 
>> indulgence on a related issue. AG
>>
>
> Suppose the original wf is expressed in terms of p, and its 
> superposition expansion is also expressed in eigenfunctions with variable 
> p. Does the phase of the original wf carry over into the eigenfunctions 
> as 
> identical for each, or can each component in the superposition have 
> different phases? I ask this because the probability determined by any 
> complex amplitude is independent of its phase. TIA, AG 
>

 The phases of the coefficients are independent of each other.

>>>
>>> When I formally studied QM, no mention was made of calculating the 
>>> phases since, presumably, they don't effect probability calculations. Do 
>>> you have a link which explains how they're calculated? TIA, AG 
>>>
>>
>> I found some links on physics.stackexchange.com which show that relative 
>> phases can effect probabilities, but none so far about how to calculate any 
>> phase angle. AG 
>>
>
> Here's the answer if anyone's interested. But what's the question? How are 
> wf phase angles calculated? Clearly, if you solve for the eigenfunctions of 
> some QM operator such as the p operator, any phase angle is possible; its 
> value is completely arbitrary and doesn't effect a probability calculation. 
> In fact, IIUC, there is not sufficient information to solve for a unique 
> phase. So, I conclude,that the additional information required to uniquely 
> determine a phase angle for a wf, lies in boundary conditions. If the 
> problem of specifying a wf is defined as a boundary value problem, then, I 
> believe, a unique phase angle can be calculated. CMIIAW. AG 
>
>>
 Bruce

>>>
I could use a handshake on this one. Roughly speaking, if one wants to 
express the state of a system as a superposition of eigenstates, how does 
one calculate the phase angles of the amplitudes for each eigenstate? AG

>
  

>>>

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Re: Coherent states of a superposition

2018-12-08 Thread agrayson2000


On Thursday, December 6, 2018 at 5:46:13 PM UTC, agrays...@gmail.com wrote:
>
>
>
> On Wednesday, December 5, 2018 at 10:13:57 PM UTC, agrays...@gmail.com 
> wrote:
>>
>>
>>
>> On Wednesday, December 5, 2018 at 9:42:51 PM UTC, Bruce wrote:
>>>
>>> On Wed, Dec 5, 2018 at 10:52 PM  wrote:
>>>
 On Wednesday, December 5, 2018 at 11:42:06 AM UTC, agrays...@gmail.com 
 wrote:
>
> On Tuesday, December 4, 2018 at 9:57:41 PM UTC, Bruce wrote:
>>
>> On Wed, Dec 5, 2018 at 2:36 AM  wrote:
>>
>>>
>>> *Thanks, but I'm looking for a solution within the context of 
>>> interference and coherence, without introducing your theory of 
>>> consciousness. Mainstream thinking today is that decoherence does 
>>> occur, 
>>> but this seems to imply preexisting coherence, and therefore 
>>> interference 
>>> among the component states of a superposition. If the superposition is 
>>> expressed using eigenfunctions, which are mutually orthogonal -- 
>>> implying 
>>> no mutual interference -- how is decoherence possible, insofar as 
>>> coherence, IIUC, doesn't exist using this basis? AG*
>>>
>>
>> I think you misunderstand the meaning of "coherence" when it is used 
>> off an expansion in terms of a set of mutually orthogonal eigenvectors. 
>> The 
>> expansion in some eigenvector basis is written as
>>
>>|psi> = Sum_i (a_i |v_i>)
>>
>> where |v_i> are the eigenvectors, and i ranges over the dimension of 
>> the Hilbert space. The expansion coefficients are the complex numbers 
>> a_i. 
>> Since these are complex coefficients, they contain inherent phases. It 
>> is 
>> the preservation of these phases of the expansion coefficients that is 
>> meant by "maintaining coherence". So it is the coherence of the 
>> particular 
>> expansion that is implied, and this has noting to do with the mutual 
>> orthogonality or otherwise of the basis vectors themselves. In 
>> decoherence, 
>> the phase relationships between the terms in the original expansion are 
>> lost.
>>
>> Bruce 
>>
>
> I appreciate your reply. I was sure you could ascertain my error -- 
> confusing orthogonality with interference and coherence. Let me have your 
> indulgence on a related issue. AG
>

 Suppose the original wf is expressed in terms of p, and its 
 superposition expansion is also expressed in eigenfunctions with variable 
 p. Does the phase of the original wf carry over into the eigenfunctions as 
 identical for each, or can each component in the superposition have 
 different phases? I ask this because the probability determined by any 
 complex amplitude is independent of its phase. TIA, AG 

>>>
>>> The phases of the coefficients are independent of each other.
>>>
>>
>> When I formally studied QM, no mention was made of calculating the phases 
>> since, presumably, they don't effect probability calculations. Do you have 
>> a link which explains how they're calculated? TIA, AG 
>>
>
> I found some links on physics.stackexchange.com which show that relative 
> phases can effect probabilities, but none so far about how to calculate any 
> phase angle. AG 
>

Here's the answer if anyone's interested. But what's the question? How are 
wf phase angles calculated? Clearly, if you solve for the eigenfunctions of 
some QM operator such as the p operator, any phase angle is possible; its 
value is completely arbitrary and doesn't effect a probability calculation. 
In fact, IIUC, there is not sufficient information to solve for a unique 
phase. So, I conclude,that the additional information required to uniquely 
determine a phase angle for a wf, lies in boundary conditions. If the 
problem of specifying a wf is defined as a boundary value problem, then, I 
believe, a unique phase angle can be calculated. CMIIAW. AG 

>
>>> Bruce
>>>
>>>  
>>>
>>

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Re: Coherent states of a superposition

2018-12-06 Thread agrayson2000


On Wednesday, December 5, 2018 at 10:13:57 PM UTC, agrays...@gmail.com 
wrote:
>
>
>
> On Wednesday, December 5, 2018 at 9:42:51 PM UTC, Bruce wrote:
>>
>> On Wed, Dec 5, 2018 at 10:52 PM  wrote:
>>
>>> On Wednesday, December 5, 2018 at 11:42:06 AM UTC, agrays...@gmail.com 
>>> wrote:

 On Tuesday, December 4, 2018 at 9:57:41 PM UTC, Bruce wrote:
>
> On Wed, Dec 5, 2018 at 2:36 AM  wrote:
>
>>
>> *Thanks, but I'm looking for a solution within the context of 
>> interference and coherence, without introducing your theory of 
>> consciousness. Mainstream thinking today is that decoherence does occur, 
>> but this seems to imply preexisting coherence, and therefore 
>> interference 
>> among the component states of a superposition. If the superposition is 
>> expressed using eigenfunctions, which are mutually orthogonal -- 
>> implying 
>> no mutual interference -- how is decoherence possible, insofar as 
>> coherence, IIUC, doesn't exist using this basis? AG*
>>
>
> I think you misunderstand the meaning of "coherence" when it is used 
> off an expansion in terms of a set of mutually orthogonal eigenvectors. 
> The 
> expansion in some eigenvector basis is written as
>
>|psi> = Sum_i (a_i |v_i>)
>
> where |v_i> are the eigenvectors, and i ranges over the dimension of 
> the Hilbert space. The expansion coefficients are the complex numbers 
> a_i. 
> Since these are complex coefficients, they contain inherent phases. It is 
> the preservation of these phases of the expansion coefficients that is 
> meant by "maintaining coherence". So it is the coherence of the 
> particular 
> expansion that is implied, and this has noting to do with the mutual 
> orthogonality or otherwise of the basis vectors themselves. In 
> decoherence, 
> the phase relationships between the terms in the original expansion are 
> lost.
>
> Bruce 
>

 I appreciate your reply. I was sure you could ascertain my error -- 
 confusing orthogonality with interference and coherence. Let me have your 
 indulgence on a related issue. AG

>>>
>>> Suppose the original wf is expressed in terms of p, and its 
>>> superposition expansion is also expressed in eigenfunctions with variable 
>>> p. Does the phase of the original wf carry over into the eigenfunctions as 
>>> identical for each, or can each component in the superposition have 
>>> different phases? I ask this because the probability determined by any 
>>> complex amplitude is independent of its phase. TIA, AG 
>>>
>>
>> The phases of the coefficients are independent of each other.
>>
>
> When I formally studied QM, no mention was made of calculating the phases 
> since, presumably, they don't effect probability calculations. Do you have 
> a link which explains how they're calculated? TIA, AG 
>

I found some links on physics.stackexchange.com which show that relative 
phases can effect probabilities, but none so far about how to calculate any 
phase angle. AG 

>
>> Bruce
>>
>>  
>>
>

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Re: Coherent states of a superposition

2018-12-05 Thread agrayson2000


On Wednesday, December 5, 2018 at 9:42:51 PM UTC, Bruce wrote:
>
> On Wed, Dec 5, 2018 at 10:52 PM > wrote:
>
>> On Wednesday, December 5, 2018 at 11:42:06 AM UTC, agrays...@gmail.com 
>> wrote:
>>>
>>> On Tuesday, December 4, 2018 at 9:57:41 PM UTC, Bruce wrote:

 On Wed, Dec 5, 2018 at 2:36 AM  wrote:

>
> *Thanks, but I'm looking for a solution within the context of 
> interference and coherence, without introducing your theory of 
> consciousness. Mainstream thinking today is that decoherence does occur, 
> but this seems to imply preexisting coherence, and therefore interference 
> among the component states of a superposition. If the superposition is 
> expressed using eigenfunctions, which are mutually orthogonal -- implying 
> no mutual interference -- how is decoherence possible, insofar as 
> coherence, IIUC, doesn't exist using this basis? AG*
>

 I think you misunderstand the meaning of "coherence" when it is used 
 off an expansion in terms of a set of mutually orthogonal eigenvectors. 
 The 
 expansion in some eigenvector basis is written as

|psi> = Sum_i (a_i |v_i>)

 where |v_i> are the eigenvectors, and i ranges over the dimension of 
 the Hilbert space. The expansion coefficients are the complex numbers a_i. 
 Since these are complex coefficients, they contain inherent phases. It is 
 the preservation of these phases of the expansion coefficients that is 
 meant by "maintaining coherence". So it is the coherence of the particular 
 expansion that is implied, and this has noting to do with the mutual 
 orthogonality or otherwise of the basis vectors themselves. In 
 decoherence, 
 the phase relationships between the terms in the original expansion are 
 lost.

 Bruce 

>>>
>>> I appreciate your reply. I was sure you could ascertain my error -- 
>>> confusing orthogonality with interference and coherence. Let me have your 
>>> indulgence on a related issue. AG
>>>
>>
>> Suppose the original wf is expressed in terms of p, and its superposition 
>> expansion is also expressed in eigenfunctions with variable p. Does the 
>> phase of the original wf carry over into the eigenfunctions as identical 
>> for each, or can each component in the superposition have different phases? 
>> I ask this because the probability determined by any complex amplitude is 
>> independent of its phase. TIA, AG 
>>
>
> The phases of the coefficients are independent of each other.
>

When I formally studied QM, no mention was made of calculating the phases 
since, presumably, they don't effect probability calculations. Do you have 
a link which explains how they're calculated? TIA, AG 

>
> Bruce
>
>  
>

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Re: Coherent states of a superposition

2018-12-05 Thread Bruce Kellett
On Wed, Dec 5, 2018 at 10:52 PM  wrote:

> On Wednesday, December 5, 2018 at 11:42:06 AM UTC, agrays...@gmail.com
> wrote:
>>
>> On Tuesday, December 4, 2018 at 9:57:41 PM UTC, Bruce wrote:
>>>
>>> On Wed, Dec 5, 2018 at 2:36 AM  wrote:
>>>

 *Thanks, but I'm looking for a solution within the context of
 interference and coherence, without introducing your theory of
 consciousness. Mainstream thinking today is that decoherence does occur,
 but this seems to imply preexisting coherence, and therefore interference
 among the component states of a superposition. If the superposition is
 expressed using eigenfunctions, which are mutually orthogonal -- implying
 no mutual interference -- how is decoherence possible, insofar as
 coherence, IIUC, doesn't exist using this basis? AG*

>>>
>>> I think you misunderstand the meaning of "coherence" when it is used off
>>> an expansion in terms of a set of mutually orthogonal eigenvectors. The
>>> expansion in some eigenvector basis is written as
>>>
>>>|psi> = Sum_i (a_i |v_i>)
>>>
>>> where |v_i> are the eigenvectors, and i ranges over the dimension of the
>>> Hilbert space. The expansion coefficients are the complex numbers a_i.
>>> Since these are complex coefficients, they contain inherent phases. It is
>>> the preservation of these phases of the expansion coefficients that is
>>> meant by "maintaining coherence". So it is the coherence of the particular
>>> expansion that is implied, and this has noting to do with the mutual
>>> orthogonality or otherwise of the basis vectors themselves. In decoherence,
>>> the phase relationships between the terms in the original expansion are
>>> lost.
>>>
>>> Bruce
>>>
>>
>> I appreciate your reply. I was sure you could ascertain my error --
>> confusing orthogonality with interference and coherence. Let me have your
>> indulgence on a related issue. AG
>>
>
> Suppose the original wf is expressed in terms of p, and its superposition
> expansion is also expressed in eigenfunctions with variable p. Does the
> phase of the original wf carry over into the eigenfunctions as identical
> for each, or can each component in the superposition have different phases?
> I ask this because the probability determined by any complex amplitude is
> independent of its phase. TIA, AG
>

The phases of the coefficients are independent of each other.

Bruce

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Re: Coherent states of a superposition

2018-12-05 Thread agrayson2000


On Wednesday, December 5, 2018 at 11:42:06 AM UTC, agrays...@gmail.com 
wrote:
>
>
>
> On Tuesday, December 4, 2018 at 9:57:41 PM UTC, Bruce wrote:
>>
>> On Wed, Dec 5, 2018 at 2:36 AM  wrote:
>>
>>>
>>> *Thanks, but I'm looking for a solution within the context of 
>>> interference and coherence, without introducing your theory of 
>>> consciousness. Mainstream thinking today is that decoherence does occur, 
>>> but this seems to imply preexisting coherence, and therefore interference 
>>> among the component states of a superposition. If the superposition is 
>>> expressed using eigenfunctions, which are mutually orthogonal -- implying 
>>> no mutual interference -- how is decoherence possible, insofar as 
>>> coherence, IIUC, doesn't exist using this basis? AG*
>>>
>>
>> I think you misunderstand the meaning of "coherence" when it is used off 
>> an expansion in terms of a set of mutually orthogonal eigenvectors. The 
>> expansion in some eigenvector basis is written as
>>
>>|psi> = Sum_i (a_i |v_i>)
>>
>> where |v_i> are the eigenvectors, and i ranges over the dimension of the 
>> Hilbert space. The expansion coefficients are the complex numbers a_i. 
>> Since these are complex coefficients, they contain inherent phases. It is 
>> the preservation of these phases of the expansion coefficients that is 
>> meant by "maintaining coherence". So it is the coherence of the particular 
>> expansion that is implied, and this has noting to do with the mutual 
>> orthogonality or otherwise of the basis vectors themselves. In decoherence, 
>> the phase relationships between the terms in the original expansion are 
>> lost.
>>
>> Bruce 
>>
>
> I appreciate your reply. I was sure you could ascertain my error -- 
> confusing orthogonality with interference and coherence. Let me have your 
> indulgence on a related issue. AG
>

Suppose the original wf is expressed in terms of p, and its superposition 
expansion is also expressed in eigenfunctions with variable p. Does the 
phase of the original wf carry over into the eigenfunctions as identical 
for each, or can each component in the superposition have different phases? 
I ask this because the probability determined by any complex amplitude is 
independent of its phase. TIA, AG 

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Re: Coherent states of a superposition

2018-12-05 Thread agrayson2000


On Tuesday, December 4, 2018 at 9:57:41 PM UTC, Bruce wrote:
>
> On Wed, Dec 5, 2018 at 2:36 AM > wrote:
>
>>
>> *Thanks, but I'm looking for a solution within the context of 
>> interference and coherence, without introducing your theory of 
>> consciousness. Mainstream thinking today is that decoherence does occur, 
>> but this seems to imply preexisting coherence, and therefore interference 
>> among the component states of a superposition. If the superposition is 
>> expressed using eigenfunctions, which are mutually orthogonal -- implying 
>> no mutual interference -- how is decoherence possible, insofar as 
>> coherence, IIUC, doesn't exist using this basis? AG*
>>
>
> I think you misunderstand the meaning of "coherence" when it is used off 
> an expansion in terms of a set of mutually orthogonal eigenvectors. The 
> expansion in some eigenvector basis is written as
>
>|psi> = Sum_i (a_i |v_i>)
>
> where |v_i> are the eigenvectors, and i ranges over the dimension of the 
> Hilbert space. The expansion coefficients are the complex numbers a_i. 
> Since these are complex coefficients, they contain inherent phases. It is 
> the preservation of these phases of the expansion coefficients that is 
> meant by "maintaining coherence". So it is the coherence of the particular 
> expansion that is implied, and this has noting to do with the mutual 
> orthogonality or otherwise of the basis vectors themselves. In decoherence, 
> the phase relationships between the terms in the original expansion are 
> lost.
>
> Bruce 
>

I appreciate your reply. I was sure you could ascertain my error -- 
confusing orthogonality with interference and coherence. Let me have your 
indulgence on a related issue. 

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Re: Coherent states of a superposition

2018-12-04 Thread Bruce Kellett
On Wed, Dec 5, 2018 at 2:36 AM  wrote:

>
> *Thanks, but I'm looking for a solution within the context of interference
> and coherence, without introducing your theory of consciousness. Mainstream
> thinking today is that decoherence does occur, but this seems to imply
> preexisting coherence, and therefore interference among the component
> states of a superposition. If the superposition is expressed using
> eigenfunctions, which are mutually orthogonal -- implying no mutual
> interference -- how is decoherence possible, insofar as coherence, IIUC,
> doesn't exist using this basis? AG*
>

I think you misunderstand the meaning of "coherence" when it is used off an
expansion in terms of a set of mutually orthogonal eigenvectors. The
expansion in some eigenvector basis is written as

   |psi> = Sum_i (a_i |v_i>)

where |v_i> are the eigenvectors, and i ranges over the dimension of the
Hilbert space. The expansion coefficients are the complex numbers a_i.
Since these are complex coefficients, they contain inherent phases. It is
the preservation of these phases of the expansion coefficients that is
meant by "maintaining coherence". So it is the coherence of the particular
expansion that is implied, and this has noting to do with the mutual
orthogonality or otherwise of the basis vectors themselves. In decoherence,
the phase relationships between the terms in the original expansion are
lost.

Bruce

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Re: Coherent states of a superposition

2018-12-04 Thread 'scerir' via Everything List

> Il 4 dicembre 2018 alle 16.36 agrayson2...@gmail.com ha scritto:
> 
> 
> 
> On Tuesday, December 4, 2018 at 10:13:38 AM UTC, Bruno Marchal wrote:
> 
> > > 
> > 
> > > > > On 3 Dec 2018, at 20:57, agrays...@gmail.com 
> > wrote:
> > > 
> > > 
> > > 
> > > On Sunday, November 18, 2018 at 1:05:26 PM UTC, 
> > > agrays...@http://gmail.com wrote:
> > > 
> > > > > > > 
> > > > 
> > > > On Saturday, November 17, 2018 at 7:39:14 PM UTC, 
> > > > agrays...@gmail.com wrote:
> > > > 
> > > > > > > > > If you write a 
> > > > superposition as a sum of eigenstates, why is it important, or 
> > > > relevant, or even true that the component states are coherent since 
> > > > eigenstates with distinct eigenvalues are orthogonal. This means there 
> > > > is no interference between the components of the superposition. AG
> > > > > 
> > > > > > > > > 
> > > > Put another way; from what I've read, coherence among 
> > > > components of a superposition is necessary to guarantee interference, 
> > > > but since an eigenstate expansion of the superposition consists of 
> > > > orthogonal, non interfering eigenstates, the requirement of coherence 
> > > > seems unnecessary. AG
> > > > 
> > > > > > > 
> > > For decoherence to occur, one needs, presumably, a coherent 
> > > superposition. But when the wf is expressed as a sum of eigenstates with 
> > > unique eigenvalues, those eigenstates are mutually orthogonal; hence, 
> > > IIUC, there is no coherence. So, how can decoherence occur when the state 
> > > function, expressed as a sum of eigenstates with unique eigenvalues, is 
> > > not coherent? I must be missing something, but what it is I have no clue. 
> > > AG
> > > 
> > > > > 
> > 
> > 
> > Decoherence never occurs, except in the mind or memory of the 
> > observer. Take the state up + down (assuming a factor 1/sqrt(2)). And O is 
> > an observer (its quantum state).
> > 
> > > 
> > > 
> > O has the choice to measure in the base {up, down}, in which case 
> > the Born rule says that he will see up, or down with a probability 1/2. He 
> > will *believe* that decoherence has occurred, but if we long at the 
> > evolution of the whole system O + the particle, all we get is
> > 
> > O-up up + O-down down, 
> > 
> > And some other observer could in principle test this. (O-up means O 
> > with the memory of having seen the particle in the up position).
> > 
> > But O could measure that particle in the base {up+down, up-down). 
> > He has just to rotate a little bit its polariser or Stern-Gerlach device. 
> > In that case he obtains up+down with the probability one, which souls not 
> > be the case with a mixture of up and down. In that case, coherence of up 
> > and down do not disappear, even from the pot of the observer.
> > 
> > Decoherence is just the contagion of the superposition to anything 
> > interacting with it, including the observer, and if we wait long enough the 
> > whole causal cone of the observer.
> > 
> > Bruno
> > 
> > > 
> Thanks, but I'm looking for a solution within the context of interference 
> and coherence, without introducing your theory of consciousness. Mainstream 
> thinking today is that decoherence does occur, but this seems to imply 
> preexisting coherence, and therefore interference among the component states 
> of a superposition. If the superposition is expressed using eigenfunctions, 
> which are mutually orthogonal -- implying no mutual interference -- how is 
> decoherence possible, insofar as coherence, IIUC, doesn't exist using this 
> basis? AG
> 

There are instruments like the MZI (Mach-Zehnder Interferometer).. In this 
insrtrument one (spli)amplitude goes through path A, the other (plit)amplitude 
goes through par'th B. At the end of their travef both amplitudes recombine 
interferentially giving *always a single* outome. As for the de-coherence 
frankly i did not realize its conceptual meaning.

> 
> > > 
> > > > > -- You received this message because you are 
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> > > 
> > > > > 
> > 
> > > 
>  
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Re: Coherent states of a superposition

2018-12-04 Thread agrayson2000


On Tuesday, December 4, 2018 at 10:13:38 AM UTC, Bruno Marchal wrote:
>
>
> On 3 Dec 2018, at 20:57, agrays...@gmail.com  wrote:
>
>
>
> On Sunday, November 18, 2018 at 1:05:26 PM UTC, agrays...@gmail.com wrote:
>>
>>
>>
>> On Saturday, November 17, 2018 at 7:39:14 PM UTC, agrays...@gmail.com 
>> wrote:
>>>
>>> If you write a superposition as a sum of eigenstates, why is it 
>>> important, or relevant, or even true that the component states are coherent 
>>> since eigenstates with distinct eigenvalues are orthogonal. This means 
>>> there is no interference between the components of the superposition. AG
>>>
>>
>> Put another way; from what I've read, coherence among components of a 
>> superposition is necessary to guarantee interference, but since an 
>> eigenstate expansion of the superposition consists of orthogonal, non 
>> interfering eigenstates, the requirement of coherence seems unnecessary. AG 
>>
>
> *For decoherence to occur, one needs, presumably, a coherent 
> superposition. But when the wf is expressed as a sum of eigenstates with 
> unique eigenvalues, those eigenstates are mutually orthogonal; hence, IIUC, 
> there is no coherence. So, how can decoherence occur when the state 
> function, expressed as a sum of eigenstates with unique eigenvalues, is not 
> coherent? I must be missing something, but what it is I have no clue. AG *
>
>
>
>
> Decoherence never occurs, except in the mind or memory of the observer. 
> Take the state up + down (assuming a factor 1/sqrt(2)). And O is an 
> observer (its quantum state). 
>

> O has the choice to measure in the base {up, down}, in which case the Born 
> rule says that he will see up, or down with a probability 1/2. He will 
> *believe* that decoherence has occurred, but if we long at the evolution of 
> the whole system O + the particle, all we get is
>
> O-up up + O-down down, 
>
> And some other observer could in principle test this. (O-up means O with 
> the memory of having seen the particle in the up position).
>
> But O could measure that particle in the base {up+down, up-down). He has 
> just to rotate a little bit its polariser or Stern-Gerlach device. In that 
> case he obtains up+down with the probability one, which souls not be the 
> case with a mixture of up and down. In that case, coherence of up and down 
> do not disappear, even from the pot of the observer.
>
> Decoherence is just the contagion of the superposition to anything 
> interacting with it, including the observer, and if we wait long enough the 
> whole causal cone of the observer.
>
> Bruno
>

*Thanks, but I'm looking for a solution within the context of interference 
and coherence, without introducing your theory of consciousness. Mainstream 
thinking today is that decoherence does occur, but this seems to imply 
preexisting coherence, and therefore interference among the component 
states of a superposition. If the superposition is expressed using 
eigenfunctions, which are mutually orthogonal -- implying no mutual 
interference -- how is decoherence possible, insofar as coherence, IIUC, 
doesn't exist using this basis? AG*

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Re: Coherent states of a superposition

2018-12-04 Thread Bruno Marchal

> On 3 Dec 2018, at 20:57, agrayson2...@gmail.com wrote:
> 
> 
> 
> On Sunday, November 18, 2018 at 1:05:26 PM UTC, agrays...@gmail.com wrote:
> 
> 
> On Saturday, November 17, 2018 at 7:39:14 PM UTC, agrays...@gmail.com <> 
> wrote:
> If you write a superposition as a sum of eigenstates, why is it important, or 
> relevant, or even true that the component states are coherent since 
> eigenstates with distinct eigenvalues are orthogonal. This means there is no 
> interference between the components of the superposition. AG
> 
> Put another way; from what I've read, coherence among components of a 
> superposition is necessary to guarantee interference, but since an eigenstate 
> expansion of the superposition consists of orthogonal, non interfering 
> eigenstates, the requirement of coherence seems unnecessary. AG 
> 
> For decoherence to occur, one needs, presumably, a coherent superposition. 
> But when the wf is expressed as a sum of eigenstates with unique eigenvalues, 
> those eigenstates are mutually orthogonal; hence, IIUC, there is no 
> coherence. So, how can decoherence occur when the state function, expressed 
> as a sum of eigenstates with unique eigenvalues, is not coherent? I must be 
> missing something, but what it is I have no clue. AG 



Decoherence never occurs, except in the mind or memory of the observer. Take 
the state up + down (assuming a factor 1/sqrt(2)). And O is an observer (its 
quantum state).

O has the choice to measure in the base {up, down}, in which case the Born rule 
says that he will see up, or down with a probability 1/2. He will *believe* 
that decoherence has occurred, but if we long at the evolution of the whole 
system O + the particle, all we get is

O-up up + O-down down, 

And some other observer could in principle test this. (O-up means O with the 
memory of having seen the particle in the up position).

But O could measure that particle in the base {up+down, up-down). He has just 
to rotate a little bit its polariser or Stern-Gerlach device. In that case he 
obtains up+down with the probability one, which souls not be the case with a 
mixture of up and down. In that case, coherence of up and down do not 
disappear, even from the pot of the observer.

Decoherence is just the contagion of the superposition to anything interacting 
with it, including the observer, and if we wait long enough the whole causal 
cone of the observer.

Bruno








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Re: Coherent states of a superposition

2018-12-03 Thread agrayson2000


On Sunday, November 18, 2018 at 1:05:26 PM UTC, agrays...@gmail.com wrote:
>
>
>
> On Saturday, November 17, 2018 at 7:39:14 PM UTC, agrays...@gmail.com 
> wrote:
>>
>> If you write a superposition as a sum of eigenstates, why is it 
>> important, or relevant, or even true that the component states are coherent 
>> since eigenstates with distinct eigenvalues are orthogonal. This means 
>> there is no interference between the components of the superposition. AG
>>
>
> Put another way; from what I've read, coherence among components of a 
> superposition is necessary to guarantee interference, but since an 
> eigenstate expansion of the superposition consists of orthogonal, non 
> interfering eigenstates, the requirement of coherence seems unnecessary. AG 
>

*For decoherence to occur, one needs, presumably, a coherent superposition. 
But when the wf is expressed as a sum of eigenstates with unique 
eigenvalues, those eigenstates are mutually orthogonal; hence, IIUC, there 
is no coherence. So, how can decoherence occur when the state function, 
expressed as a sum of eigenstates with unique eigenvalues, is not coherent? 
I must be missing something, but what it is I have no clue. AG *

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Re: Coherent states of a superposition

2018-11-18 Thread agrayson2000


On Saturday, November 17, 2018 at 7:39:14 PM UTC, agrays...@gmail.com wrote:
>
> If you write a superposition as a sum of eigenstates, why is it important, 
> or relevant, or even true that the component states are coherent since 
> eigenstates with distinct eigenvalues are orthogonal. This means there is 
> no interference between the components of the superposition. AG
>

Put another way; from what I've read, coherence among components of a 
superposition is necessary to guarantee interference, but since an 
eigenstate expansion of the superposition consists of orthogonal, non 
interfering eigenstates, the requirement of coherence seems unnecessary. AG 

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