Re: explanation for teleportation/entanglement?

[Kevin de Laplante <***>]

Tim,

 Regarding the use of spin in nonlocality experiments (such as Aspect's), my
> understanding is that spin pairs do not convey the same degree of evidence
> as the original EPR/Bohr discussion based around conjugate variables of
> position and momentum. Basically, that using measurement of, say, momentum
> on one of the pair of an allegedly entangled pair should induce a
> corresponding uncertainty in the position of the other. Allowing the
second
> particle to travel some additional distance should result in a positional
> "spread" or fanning out, measurable over a statistically significant
number
> of samples. On the other hand, spin pairs have no such quality, and rely
> instead on indirect evidence by drawing inference from violations of
Bell's
> inequalities.
>

I think there might be some confusion over how the EPR argument relates to
the indeterminacy relations for noncommuting observables, like position and
momentum.  Bohr defends the completeness of quantum  mechanics as a physical
theory, and hence treats the indeterminacy relations as universal,
unbeatable.  EPR want to argue that quantum mechanics isn't the final story,
that the indeterminacy relations don't describe irreducible indeterminacies
in the values of quantum observables.  They want to defend some form of
common sense realism about physical properties.  The EPR argument starts by
positing a system of correlated particles whose total momentum is zero.
They shoot away from each other, in opposite directions.  By conservation of
momentum, we know that if particle A has momentum x, then particle B has
momentum -x (so they total to zero).  Now, measure the momentum of particle
B.  This yields a definite result, x.  We can now infer with certainty that,
IF we were to measure the momentum of particle A, we WOULD get the result -x
(this is, indeed, what you would measure).

EPR then argue as follows.  If we can predict the result of a measurement of
a quantum property with certainty, then it makes sense to infer that the
particle property being measured had that value ALL ALONG.  This is an
inference from predictability (an epistemological claim) to the existence of
a definite value for a physical property prior to measurement (an
ontological claim).  This the assumption of "realism" that EPR employ.  Now,
EPR consider the possibility that the momentum of particle A might be
genuinely indeterminate prior to the measurement of the momentum of particle
B, and that maybe the measurement of momentum on B somehow renders the
momentum of A determinate.  But they reject this possibility, since it
violates Einstein's own cherished principle of locality, which states that
causal influences cannot propagate faster than the speed of light (much less
instantaneously).  EPR's principle of locality states that nothing  you do
to A can have an instantaneous influence on the physical properties of B, if
A and B are spatially separated (note that you can separate A and B by any
distance you like in this experiment).  EPR state that "no reasonable
definition of reality could be expected to permit this".  The term "spooky
action at a distance" is Einstein's -- he viewed such instantaneous
influences as unintelligible (much as Newton did).

Now, you can measure the position of particle A, and that'll give you a
definite value.  But by the above argument, we're already allowed to assert
that A has a definite momentum at that time.  So, we conclude that particle
A has both a definite position and momentum at the same time.  If we treat
quantum mechanics as a complete theory, then we have a contradiction with
the indeterminacy relations.  EPR conclude that quantum mechanics is not a
complete theory.

Note that this argument doesn't involve a measurement on particle B causing
a property of particle A to become indeterminate.  In particular, it doesn't
involve a measurement of the momentum of particle B causing an uncertainty
in the position of A.

Note also that EPR don't require that you actually measure the position of
particle A to get the same conclusion.  Measurements of angular momentum at
right angles to each other (say, x and y, or x and z, or y and z) fail to
commute, and so they have a corresponding indeterminacy relation between
them as well.  All you need to do is measure one of the values of these
variables on particle B, and you can infer a definite value for particle A.
But the choice of the direction along which you measure angular momentum is
arbitrary; you measured along x, but you COULD have measured y.  Hence, by
the same argument, particle A has definite values for angular momentum along
x and y, in violation of the indeterminacy relations.  (In subsequent
essays, Einstein emphasizes this kind of reasoning.)

The spin experiments are just measurements of angular momentum components.
The arguments have precisely the same structure.

It's important to see that the EPR argument is an argument, not an
experiment.  It either works or doesn't as an argument.  It has the
conclusion that if quantum mechanics is complete then we must deny either
the principle of locality or the minimal principle of realism that EPR
assume (if I can predict the value of an observable property with
probability 1, then that observable property had that value prior to
measurement).  Much of the philosophical work on the foundations of quantum
mechanics assumes that the argument is both valid and sound -- that it
really does establish an inconsistency between the assumptions of
completeness, locality and realism.

Interestingly, in Bohr's response he doesn't challenge the realism
assumption (none of the founding fathers of quantum mechanics, it turns out,
challenged this assumption).  Bohr challenges the locality assumption, or
rather the assumptions of the separability of systems that underlies it.  He
didn't believe in faster than light causal influences.  Bohr's focus was on
the epistemological assumptions that define how "the phenomena" are
specified.  It is in this respect that I see some affinity between Bohr and
Rosen, in that both are concerned with this question.

regards,

Kevin