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Local Realism - what does it mean?

Models of Reality

Quantum mechanics has often been presented as an anti-realistic
theory. This seems very strange to me, as I don't think that it means anything.
Science often describes how things work in terms of some sort of model, maybe a
mathmatical model or maybe something more concrete. Realists think that this
model describes what is really there, for instance that there is some sort of
quantumstuff making up the universe, while antirealists point out that this
makes no sense as it implies that there could be a further level of theory
describing the internal workings of the quantumstuff. However one expects the
model to be something definite, even if its connection with reality isn't. But
in the case of quantum mechanics the antirealism seems to have infected the
model - not only is the model said not to describe reality, it seems that there
is no real description of the model itself.

Bell's inequality

Realities
Artist: Carole Bécam

Suppose we have a source of particles which sends out pairs of
particles, with one in the opposite direction to the other. Suppose also that we
are interested in some property of the particles which can be expressed in terms
of an angle, such as spin or polarisation. We place a filter at a given angle
and use a detector to see whether the particle goes through - this is done for
both particles, and the two measuring apparatuses may be widely separated. Now
such experiments have been done where it has been found that the source
generates the particles in such a way that whether they go through the filter or
not is random. However, when the two filters are at the same angle then the
results at each detector always agree. OK, we say, the particles have some
internal property, which is randomly set by the source, but which is the same
for both particles. When the angles of the filter differ by 22½° the results
disagree around 1/7 of the time. There's no problem explaining that in terms of
the internal property of the particles. Now suppose the angles differ by 45°.
Then you can think of what the result for each would be if they were both at the
halfway angle, 22½° from their actual position. The each actual result would
disagree with this hypothetical result 1/7 of the time, so a bit of thought says
that the two actual results can only disagree with each other at most 2/7 of the
time. That is a special case of Bell's inequality.

The only trouble is that when you do the experiment, the results at the two
detectors differ from each other half of the time. The only way to
explain this is if there is some secret communication between the two widely
spaced measurements to fix the result. However, we can never use this
communication to send actual information between the two locations.

Incomplete models

So where does randomness fit in with all this - after all we're
constantly being told that quantum theory shows the intrinsic randomness
of the universe. Is this where the antirealism comes in? Well not really -
it is perfectly possible to have a realist model with intrinsically random
events. The trouble is that it doesn't fit very well with quantum theory.
Certainly the possibility of nonlocal correlations excludes the simple
notion of each quantum collapse being random

Einstein was a strong critic of some of the ideas of quantum
mechanics. One of his claims was that it is an incomplete theory. This has
always been taken to mean that he thought that particles had definite properties
such as position and momentum, and if so then he has been shown to be wrong.
However, it is possible to view the claim in a wider context, saying that the
models of quantum theory don't fully describe what happens, and always require
something to be put in by hand. The (original) Copenhagen interpretation says
that what happens on a quantum level is separate from what happens on a
classical level, but is very vague about how the two interact. The collapse
interpretation says the normal behaviour of a system follows the Schrödinger
equation, but that when a measurement occurs there is a collapse of the
wavefunction. Unfortuneately, this doesn't specify precisely what sort of
behaviuor is a measurement and what is normal. The Many-worlds interpretation
appears to provide a direct mathematical descripton of the universe. However
when you try to see what it actually predicts, then you get involved in the
splitting of your mind into many copies, which makes it as bad as, if not worse
than, the other interpretations. So maybe the charge of incompleteness does
stand up after all. This is important, because when someone proposes a different
theory (rather than a different interpretation), it is important to know what
the standard theory predicts. Penrose has proposed experimetns which would test
his ideas. However, I can't help feeling that the standard theory doesn't
actually predict what would happen in these experiments, and so whatever happens
someone could claim that it agreed with the standard theory.

Nonlocality and Bohm's theory

One interpretation which seems to fare better than the others
is that devised by David Bohm in 1952. There is still something fishy going on
here in that it is hard to see how the collapse of the wave function fits in
with this theory. However it does give a model where one can see better what is
going on - in the model that is, not necessarily in reality. In particular it
makes explicit the nonlocal transmission of information. What I find strange is
that people seemed really surprised at the creation of an interpretation of
quantum theory which was compatible with realism. To me it seems obvious that
given a mathematical theory then it is possible to postulate the existence of
some stuff which obeys that mathematics (Of course Bohm's theory does a great
deal more than that). But some people apparently persuaded themselves that it
was impossible.

Too much philosophising

If you are interested in finding out more about these subjects then
the EPR_paradox, Bell_test_experiments
and Bohm_interpretation
Wikipedia articles would be a good
place to start. You might also be interested in the page on Bell's
Inequality from the Usenet Physics
FAQ

My feeling is that we should get away from philosophising about
antirealism, and concentrate on the mathematics. If you claim that there is a
collapse of the wave function then you should be able to model it
mathematically. Furthermore, if we can see in the model how something travels
faster than light, then we will get a better understanding of why we can't use
it to transmit useful information.

Finally I would note that the claim that quantum theory is totally
incompatible with local realism isn't strictly true. It is possible to postulate
a model where a system can use what information it has from its past light cone
to predict what happens elsewhere, and so can 'know' the setting of a distant
apparatus. However, this model would exclude freewill. Now there's something to
philosophise about!

CHRONON CRITICAL POINTS

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