On 12/8/2017 12:01 AM, agrayson2...@gmail.com wrote:
On Thursday, December 7, 2017 at 11:54:39 PM UTC, Bruce wrote:
On 8/12/2017 10:40 am, agrays...@gmail.com <javascript:> wrote:
On Thursday, December 7, 2017 at 4:44:01 PM UTC, Bruno Marchal
wrote:
Yes, but only if the phase are indeed different at each
slits, I would say. The interference pattern would shift.
*I had a confusing and testy response from Bruce on this issue.
To recapitulate:
AG> Are the phase angles of components of a superposition
identical? If so, is this the definition of coherence? TIA, AG
BK> No, why should they be equal. You really do have to learn
some basic quantum mechanics, Alan, and stop bothering the list
with such questions.
I might be mistaken, but In the double slit I think the phase
angles must be equal to get the interference pattern observed,
and if they're different at each slit, we won't get what's
observed. And if each component of a superposition with many
components has an arbitrary phase angle, I don't see how we get
coherent waves. I know this is not an interesting issue for
Bruce, but maybe he will clarify the situation. IIRC, on another
message list, Roahn, a Ph'D physicist known to Bruce, claimed the
phase angles of components of a superposition are equal. It would
seem so, for if one has a solution of the SWE and assigns a phase
angle arbitrarily, and then expands the solution in some basis, I
think the basis vectors would inherit the same phase angles.
Still studying Bruce's link! *
Bruno is right on this -- the only effect of changing the phase in
one arm of the superposition would be to shift the interference
pattern to the side, it would still be the same pattern.
*That's what I was trying to say above; shifting the pattern would be
a new result IMO, same form but shifted in one direction. What I was
puzzled about was the relation of the phase factors to coherence. If
the superposition consists of three components with each pair of
phases being multiples of each other, but not all three. Would the
resultant superposition still be considered to be coherent? (not
discussed in any links I can find). AG*
The superposition is considered to be not coherent in the FAPP limit
where there are many components with different varying phases (different
frequencies) so the cross-terms of the density matrix tend to average to
zero. This is the situation when the system includes the instrument and
the environment. In theory the system+instrument+environment is in a
superposition but almost all of its components are unobservable so we
regard it as decohered.
Brent
This is explained in the Wikipedia page I referenced. Linearity of
the SWE means that the sum of any two solutions is also a
solution, but the individual solutions can be added with arbitrary
complex weights (phases). The overall phase has no physical
consequences, but the relative phase is all-important. There is no
reason for the relative phases to be equal, they can be anything
at all. So in the two-slit experiment, putting a phase changer in
one arm simply shifts the pattern to the left or the right. This
experiment has been done.
This is elementary quantum mechanics, and the details are readily
available on-line or in text books.
Bruce
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