On Friday, January 11, 2019 at 10:11:10 AM UTC, Bruno Marchal wrote:
>
>
> On 11 Jan 2019, at 10:54, agrays...@gmail.com <javascript:> 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 <agrays...@gmail.com> 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 <agrays...@gmail.com> 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 <agrays...@gmail.com> 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 other, even if they're probability waves, and this is one of the 
>>> core features of Wave Mechanics. So phase angles must relate to degrees of 
>>> interference. But if the phase angles are arbitrary; ERGO, so is the 
>>> interference; arbitrary and thus NOT well defined. What am I missing? TIA, 
>>> AG
>>>
>>>
>>>
>>> The *global* phase angle is arbitrary: Psi = e^phi Psi.
>>>
>>> The relative phase angle is not arbitrary: you can distinguish all 
>>> states up + e^phi down, when phi varies.
>>>
>>> All this follows from the Born rule.
>>>
>>> Bruno 
>>>
>>  
>> What about the case where the superposition is a sum of many eigenstates? 
>>
>>
>> That is always the case.
>>
>
> * ???*
>
>> How do you *calculate* the phase angle of each eigenstate? I don't see 
>> how Born's rule helps. AG
>>
>> By looking at the interference obtained when preparing many particles in 
>> that superposition states. 
>>
>
> *How can you prepare a system in any superposition state if you don't know 
> the phase angles beforehand? *
>
>
> ?
>
> That is the point of the preparation. It is enough to rotate the polariser 
> (say) in some special direction.
> I can prepare particles in some “up” state, and then I make them passing a 
> polariser with a relative angle alpha, so that I can get the state 
> sin(alpha) up + cos(alpha) down. I can verify this by measuring the density 
> corresponding to the probabilities sin^2(alpha) of being up, and 
> cos^2(alpha) of being down, + some other direction to make the difference 
> with a mixture (as already explained once).
>
>
>
>
> *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 *
>
>
> I have no clue what you mean by calculating.
>

*It means you can use theory to predict the phase differences. This isn't 
what Bruce claimed AFAICT. For a superposition with many eigenstates, what 
is the math that produces the phase differences? I don't understand your 
rotation example. AG*

I postulate QM, and talk about experience done with state which have been 
> prepared, as we can only do that in QM.  I think that all what Bruce said 
> about this is correct. We cannot distinguish Psi from e^phi Psi, but there 
> is no problem distinguishing up + e^phi down from up + down.
>
> Bruno
>
>
>
>
> You will find more explanation on all this in David Albert’s book, which 
>> minimises well the use of mathematics.
>>
>> Bruno
>>
>
>
>
>>
>>
>>
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