# Re: Coherent states of a superposition

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On Sunday, January 13, 2019 at 7:12:31 PM UTC, agrays...@gmail.com wrote:
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> On Sunday, January 13, 2019 at 3:04:10 PM UTC, Bruno Marchal wrote:
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>> On 13 Jan 2019, at 07:24, agrays...@gmail.com wrote:
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>> On Sunday, January 13, 2019 at 4:13:24 AM UTC, agrays...@gmail.com wrote:
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>>> On Saturday, January 12, 2019 at 8:41:23 AM UTC, agrays...@gmail.com
>>> wrote:
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>>>> 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*
>>>>
>>>
>>> *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*
>>>
>>
>> *IOW, if I change the phase angles, the interference changes and
>> therefore the probability density changes, but this seems to contradict the
>> fact that changing the phase angles has no effect on the probability of
>> occurrences of the measured eigenvalues. AG *
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>>
>>
>> I have some difficulties to understand what you don’t understand. You
>> seem to know the Born rule.
>>
>> Imagine some superposition, 1/(sqrt(2)(up + down) say. If you multiply
>> this by any complex number e^phi, the Born rule will show that the
>> probabilities does not change. But if, by using Stern Gerlach device, or
>> David Albert’s nothing-box, which is just a phase shifter, place on the
>> path of the "down-particle”, to get
>> 1/(sqrt(2)(up + e^phi down), the Born rule shows that this does change
>> the probability of the outcome, in function of phi.
>>
>> Yes, it is hard to believe that a photon or an election “split” on two
>> different path, and we can shift the phase of just one path, using that
>> phase-shifter “nothing box”. Albert called it a “nothing box” because, for
>> any particle going through it, it does not change any possible measurement
>> result that you can do on the particles, unless it is put on the term of a
>> vaster superposition, like in an interferometer.
>>
>> Bruno
>>
>
> Thanks. Here's a thought experiment that might explain my issue/confusion.
> Suppose we imagine a double slit experiment where the wf is a superposition
> of states as I've previously described. Now imagine another thought
> experiment where each component of the superposition is multiplied by an
> arbitrary phase angle. Will the interference patterns of these two
> experiment be the same or different? AG
>```
```
You'll notice that if we cast the experiments as a double slit experiments,
the eigenvalues being measured are transverse momenta along the screen. You
will also notice that using Born's rule, the probability of measuring any
eigenvalue is independent of the arbitrary phase angle multiplied by each
component of the superposition. IOW, it surely seems as if the arbitrary
phase angles have no effect on the statistical pattern of impacts along the
screen. This means, to me, that the arbitrary phase angles have absolutely
no effect on the resultant interference pattern which is observed. But
isn't this what the phase angles are supposed to effect? AG

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