> 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 <javascript:> wrote:
>> On Monday, January 7, 2019 at 11:37:13 PM UTC, agrays...@gmail.com 
>> <http://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 
>> <http://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 
> Born's rule calculates a complex conjugate, in which case any phase angle 
> cancels out in the calculation. I don't see how it could be used to 
> *calculate* a phase angle.  Moreover, Bruce is most knowledgeable here about 
> QM (along with Brent) and he indicates otherwise; that phase angles cannot be 
> calculated. AG

The global phase cannot be calculated. The relative phase is what we calculate 
all the time when doing quantum mechanics. Psi is not experimentally 
distinguishable from e^phi Psi. But (up + down) can be distinguished from (up + 
e^phi down).

Have you got the book by David Albert?


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