# Re: Coherent states of a superposition

```> On 13 Jan 2019, at 07:24, agrayson2...@gmail.com wrote:
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>
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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:
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> 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 ```
```

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

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