Re: Can isolation break entanglement?

From: Thomas Trotter (thomastrotter2005_at_juno.com)
Date: 09/22/04 

Date: 21 Sep 2004 18:20:14 -0700

puppet_sock@hotmail.com wrote in message news:<c7976c46.0409210631.22ed3df7@posting.google.com>...
> thomastrotter2005@juno.com (Thomas Trotter) wrote in message news:<21970122.0409210148.68be9f7@posting.google.com>...
> [description of experiments similar to Aspect's snipped]
> > Entanglement refers to *correlations*. Instantaneous action at a
> > distance isn't required in the sorts of experiments I mentioned above.
>
> That's not obvious. It *may* be true, but it seems not to be.
>
> The results of the various experiments strongly seem to verify
> quantum mechanics. These seem to say something like so:
>
> Before the measurement, the wave function is some superposition
> like so.
>
> psi = |L+>|R-> + |L->|R+>
>
> That is, before the measurement, there is a superposition of
> the left photon being + polarized and the right being -,
> *and* the left - and the right +.
>
> After the measurement, the photon on the other side is purely
> the opposite. So if the left is measured |L+>, the right is
> suddenly pure |R->.
>
> This is a major point of Bell's theorm. Changing from the entangled
> to the pure state happens only at the point of measurement. And it
> seems to happen instantly. This is the infamous "collapse of the
> wave function." And it has been a source of active dicsussion in
> QM from nearly the moment that QM was propposed.

I would say that the major point of Bell's theorem is that if
you formulate the probability of coincidental detection as the
product of the probability distributions at A and B, then you'll
get expectation values for some mutual polarizer settings that
don't agree with qm expectation values for those settings.

Wrt, for example, experiments that analyze photon pairs produced
via atomic cascades, the emission model provides the basis for
the qm formulation. The model says that, because of conservation
of angular momentum, if photon 1 incident on polarizer A is
right circularly polarized, then photon 2 incident on polarizer B
is also right circularly polarized, and if photon 1 is left
circularly polarized, then so is photon 2. IOW, photon 1 and
photon 2 of any given pair are polarized identically via the
emission process.

What's being analyzed in the experimental context is the
relationship of the polarizations of photon 1 and photon 2 of
any given pair incident on the polarizers.

The observational context is the mutual polarizer settings
for any given pair of emitted photons. This is modeled as
the angular difference (theta) in the settings.

There are two values affecting the rate of
coincidental detection ... (1) the difference in polarization
between the polarizer-incident, paired photons and (2) theta.
If the emission model is correct, then photon 1 and photon 2
of any given pair of photons emitted by the same atom are always
polarized identically (though the polarization of any pair varies
randomly from pair to pair). If the emission model is
correct, (1) is not a variable, and, in the ideal, will not be
a factor in determining the variable rate of coincidental
detection. What's left is theta, and, in the ideal, qm
says that the probability of coincidental detection will
vary as cos^2 theta.

Since experimental results have closely approximated the
correlation curves predicted by qm, there's reason to believe
that the emission model(s) on which the qm formulation(s) are
based are correct.

In short, the entanglement of photons correlated in
polarization has to do with the their being identically
polarized via the emission process. Insofar as the photons
are sufficiently isolated from external influences, then
time and distance should have no effect on their
relationship wrt polarization.

It should be mentioned that the exact polarization of
the polarizer-incident photons (that is, the emission
polarization) is never known. The measurement results
simply tell you whether a photon worth of light was
transmitted by a polarizer or not wrt any given
coincidence or correlation 'window'. But, in the
ideal, if you know the value of theta for some pair
and the result at, say, A, then you know the probability
of detection at B.

There's certainly a lot of confusing language wrt EPR-Bell,
entanglement, etc. I would love it if FTL whatever were
someday demonstrated -- but so far, for some of us anyway,
the prospects don't seem too promising.

Relevant Pages

  • Re: I dont understand EPR
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  • Re: A Look at Quantum "Spookiness"
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  • Re: Quantum entanglement and information transfer
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  • Re: Two EPR questions
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    (sci.physics.research)
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