Re: Quantum entanglement and information transfer

From: Tom Trotter (tom129_at_juno.com)
Date: 07/28/04 

Date: 28 Jul 2004 04:59:01 -0400

"Caroline Thompson" <ch.thompson1@virgin.net> wrote in message news:<GvTMc.551$Go2.507@newsfe3-gui.ntli.net>...
> "Tom Trotter" <tom129@juno.com> wrote in message
> news:29df3039.0407240733.405f6c1a@posting.google.com...
> > "Caroline Thompson" <ch.thompson1@virgin.net> wrote
>
> > > But the assumed relationship is merely that lambda is the
> > > same for each photon in a pair: that lambda_A = lambda_B.
> > > Knowing this has no effect on what happens to the photons
> > > individually.
> >
> > That's right. Knowing this relationship will not allow
> > you to more accurately predict individual results,
> > if you're just considering A, or just considering B.
> >
> > And, knowing the polarization for photons incident
> > on the polarizers won't increase your ability
> > to predict coincidental detections, as long as
> > you know how the photons are related.
>
> But knowing the result of the measurement at A *does*
> give you a little information re the likely result at B.

Then you wouldn't be just considering A or just
considering B, would you?

[snip]

> > The 'something extra' is the emission-dependent *relationship*
> > between photon 1 and photon 2, if what's being analyzed is
> > entangled. But, it isn't really extra. It's just the only
> > thing circumscribed by Bell's lambda that's relevant
> > to coincidental detection. You just eliminate from
> > consideration all the extraneous stuff, like how the
> > photons are polarized ...
>
> Sorry, Tom, but the polarisation direction of the individual
> photon is all you've got. We're not making progress, are we?

What you have (empirically) is that a detector registered
during a coincidence window, or it didn't.

For increasing the accuracy of predictions of individual
results, you would need to know the emission-produced polarization.
But, this is never known.

For accurately predicting coincidence rates in the combined
context, you don't need to know the emission-produced
polarization. You just need to know that they're polarized
identically -- hence the efforts made to ensure that
coincidence counters are dealing with photons emitted by
the same atom wrt any given coincidence window.

>
> > ... photons that are emitted in opposite directions are
> > what are selected. And, if they're emitted by the same
> > atom, then they have to be polarized identically,
> > according to the emission model, in order to comply with
> > the law of conservation of angular momentum.
>
> I'm not disputing this.
>
> > Wrt this scenario, in the combined context, the only variable
> > that matters is the angular difference in polarizer settings.
>
> Not necessarily so. There may, for instance, be more photon
> pairs polarised vertically than at any other angle.

[snip]

It doesn't matter. In the combined context, it's not the
polarization, but the relationship between photon 1 and
photon 2 that's being observed.

>
> > > > ... As long as photon 1 and photon 2 of any given pair are
> > > > identically polarized, then the orientation of the polarizers
> > > > wrt each other is the only relevant variable in the
> > > > observational context, and a circular function of this
> > > > changing angular difference is what determines rates of
> > > > coincidental detection.
> > >
> > > But this is true only if we have rotational invariance.
> >
> > I don't think so. Remember, Bell's unknown parameter
> > affecting individual results can have any value.
>
> Yes, but it can also have any distribution.

[snip]

That's right, and the point is that this distribution
(re polarization) is irrelevant wrt determining coincidence
rates as long as photon 1 and photon 2 of an emitted
pair are polarized identically.

[snip]

> > Bell's analysis says that the coincidence rate, cr, for 2Theta,
> > can't exceed cr/2 for Theta.
>
> No, Bell never said that! I think maybe you are following Nick Herbert? I
> haven't read his book but keep on coming upon misconceptions on behalf of
> those who have.

It's a corollary of Bell's theorem.

>
> > But, experimentally, this doesn't
> > hold for all tested values of Theta. The qm formulation, on the
> > other hand, says that cr will vary as a circular, rather than
> > a linear, function of Theta -- and experiments bear this out.
>
> Yes, and the local realist model appropriate to optical Bell tests says the
> same. (See quant-ph/9903066)

That's because the qm formulation doesn't violate local
reality. It's just that some interpretations of it say
that it does.

[snip]

> > As long as you're dealing with opposite moving photons emitted
> > by the same atom, then the angular difference of the settings
> > of the analyzers is the only thing that matters wrt predicting
> > rates of coincidental detection in the combined context.
>
> >From physical considerations this does not make sense. Suppose *all*
> photons are V. Then if our fixed polariser is set vertically we get a
> beautiful full-visibility coincidence curve as we vary the other. If, on
> the other hand, we set it horizontally, we don't get any coincidences at
> all, whatever the angle of the other polariser.

Not so. The coincidence curve will still be a circular function
of the angular difference between the polarizer settings (Theta), as
long
as photon 1 and photon 2 of any given pair are polarized identically.
A mutual non-detection is also a coincidence.

No matter what the polarization of any given pair is, the
rate of coincidental detection attributes will increase as
Theta decreases, and will decrease as Theta increases.

[snip]
 

> > Maybe that's what he was worried about, but that's not what
> > he proved. He proved that if you include parameters that
> > would affect individual measurements in a formulation concerning
> > combined measurements, then you get results that are inconsistent
> > with qm
> > or (after tweaking so that it's consistent with the statistical
> > predictions of qm)
> > results that are inconsistent with the assumptions of standard physics
> > regarding a limitation on signal velocity (thereby violating Einstein
> > causality or Lorentz invariance).
>
> No, his inequality is one that is obeyed under standard physics.

Bell adjusted his formulation so that it would be
consistent with the predictions of qm. In this formulation
the setting at a can affect the result at B, and the setting
at b can affect the result at A -- which would require it, in
Bell's words, to be "non Lorentz invariant".

[snip]
 
> > Either way, you get nonsense. Sort of a reduction to absurdities.
> > The conclusion that follows from this is that the added parameters,
> > while relevant wrt individual contexts, simply aren't relevant wrt
> > combined contexts. That's all. Nothing has been said about the
> > predictions of qm being inconsistent with the *existence*
> > of hidden variables, or being consistent with the *necessity* of
> > ftl signals.
>
> Sorry, Tom, but a lot has been said about the above! The whole point of
> Bell's theorem is that the predictions of qm are incompatible with the
> existence of hidden variables.

That's the normal interpretation, and, as stated, it's just
wrong.

The hidden variables that would allow for more accurate
predictions of individual results don't vanish from existence
just because you're looking at things wrt a different
context. It's just that they're not relevant in the combined
context.

Predictions of qm wrt combined contexts such as Bell tests
are inconsistent with those of formulations that include a term,
eg., lambda, that is irrelevant wrt determining coincidental
detection. The qm formulation, taken by itself without reference to
misinterpretations of Bell's work, isn't incompatible with
Einstein locality or the existence of hidden variables.
(See the emission models.)

[snip]

> > >
> > > I agree that there has been a lot of misinterpretation of Bell's
> > > work, but this is mainly on the behalf of science journalists.
> > > Judging by his PhD thesis, and known communication between
> > > them, I think Aspect understood Bell very well.
> >
> > I'm not sure he understood that it's *not* their obedience to
> > Einstein causality that makes supplementary-parameter theories
> > incompatible with qm and experiment. The qm formulation, and
> > the experiments, also obey Einstein causality.
>
> Hmmm ... If so why did Richard Feynman and Niels Bohr both come out with
> statements to the effect that nobody understands qm -- that if you think you
> do then you are mistaken?

What's this got to do with ... anything?

[snip]

> > > All we have in the Bell tests is lambda values set at the source
> > > and carried with the photons to their respective detectors. A
> > > purely local action takes place at each detector.
> >
> > Well, that's not *all* you have. You're forgetting the observational
> > context. :-)
>
> What is this "observational context"? Remember that in real life the two
> stations may, as in Tittel's experiments at Geneva, be separated by several
> miles.

As long as you can preserve the emission-produced relationship
(the entanglement of photons emitted by the same atom), then
it doesn't matter how far apart they are when you analyze
them. Observation context doesn't necessarily have anything
to do with distance.

The "observational context" is (1) opposite moving photons correlated
in polarization via emission, and (2) analysis of this common
polarization
(this *relationship") for paired photons via corresponding, joint
settings of separated polarizers.

Relevant Pages

  • Re: I dont understand EPR
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