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.

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.

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.

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.

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!