Re: Quantum entanglement and information transfer

From: Caroline Thompson (ch.thompson1_at_virgin.net)
Date: 07/29/04 

Date: 29 Jul 2004 05:59:33 -0400

"Tom Trotter" <tom129@juno.com> wrote in message
news:29df3039.0407271103.333d99a3@posting.google.com...
>
> "Caroline Thompson" <ch.thompson1@virgin.net> wrote >

> > > [TT:] Wrt this scenario, in the combined context, the only
> > > variable that matters is the angular difference in polarizer settings.
> >
> > [CT:] 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.

I'm afraid I can prove you're wrong, Tom. Have you read my paper on
rotational invariance, http://arxiv.org/abs/quant-ph/9912082 ?

> > > > > ... 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.

It's all very well you "thinking so", but I have actually worked through the
details, assuming that we are dealing with light that comes in pulses, each
with a definite polarisation direction (the same on both sides of the
experiment, only varying between pairs).

> > > 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.

What inequality are you assuming? There a quite a few different ones all
going by that name, all derived with the same intention but in fact often
differing in their assumptions. Many are true only if there are no
non-detections.

> > > 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.

But the QM formula violates Bell's inequality! If the real world actually
did this it would mean the end of rational physics. It would mean that you
can't depend on being able to multiply independent probabilities to get the
combined one. It's not just a matter of interpretation.

> > >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.

But hang on a minute, Tom! Do read that paper of mine. The situation I've
just described is one in which on one side you get *no* detections,
therefore you get no positive coincidences. But neither do you get "mutual
non-detections", since, as you vary the angle, you do get some detections on
the other side.

In point of fact, though, it is not safe to count mutual non-detections as
coincidences. That is the path to confusion.

> 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.

Not if it is fixed at zero! But you get more interesting possibilities
arising if your source is in fact producing a 50-50 mix of photons, half in
one state, half the opposite. The case likely to arise in real life is when
the hidden variable is the phase difference between vertically and
horizontally polarised components.

> > > 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.

Perhaps you are looking only at Bell's 1964 paper? The inequalities used in
real experiments do not require his assumption that when detectors are
parallel there will be perfect correlation.

> > ... 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.)

Where do I find these? Do I take it that you can give me a definite example
of a hidden variable model that agrees with QM?

> > > ... The qm formulation, and
> > > the experiments, also obey Einstein causality.

I agree that the experiments do (by virtue of the looholes, and because I
can give an actual local realist explanation), but can you prove that qm
does? As far as I can see your argument amounts to hand-waving about this
"relationship" that is something more than a mere zero difference in
polarisation directions.

> 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.

Polarisation direction has no physical reason to change 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.

But can you actually show me the details? What are you saying is the
physical cause of the high correlations that violate various Bell's
inequalities? I can show you the details of local hidden variable models
that, in perfect conditions, can't violate a Bell inequality. Given
appropriate imperfections, though, they can.

Caroline

Caroline H Thompson

ch.thompson1@virgin.net
http://freespace.virgin.net/ch.thompson1/