On Mon, Jan 7, 2019 at 9:42 AM <agrayson2...@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.
>>>>> 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.


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