Re: Coherent states of a superposition

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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*
>```
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*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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