EPR paradox: General remarks

For general information on the related problems, check http://www.mtnmath.com/.

So far, there has been no decisive experiment in this field. Hence the discussion may only be held on the conceptual level now, without asserting or denying anything.

I suspect that an experiment to check the EPR issues cannot be staged at all. The problem is not physical, but rather philosophic and methodological. As usual, paradoxes arise when different levels of hierarchy are treated on the same footing, mixed in a single discourse. As soon as there is a clear distinction between the levels of consideration, no contradictions can appear.

1. Any theory has its own limits of applicability, and no theory can be considered as strictly rigorous. So, there may be no "theorems" about the validity of a physical model, since this validity is never absolute, and one can tell in advance that there will be situations where this model won't be applicable. All one can do is to derive the applicability conditions (usually in terms of strong inequality) for a theory within a more general theory. There is no such a generalization of quantum mechanics yet, and hence there may be no inequalities specifying the conditions of its applicability.

2. The main problem of quantum physics is incompatibility with relativism. This incompatibility is inherent in the very idea of quantum mechanics, since it is the extension of the classical physics in the direction opposite to that of relativity. In the relativistic approach, the observer is very small, and all he can observe is his immediate environment - locality. On the contrary, the observer of quantum physics is infinitely big - so that he observes any system from far apart (from infinity), and the parts of the system cannot be discerned. Thus, one can detect particles moving away from the system, but nothing can be said about the association of these particles with particular components of the system (atoms, molecules etc.). One does not know where a particular electron came from: an atom in the experimental device, sun flare or distant galaxy.

   Evidently, it is difficult for the observer to be small and big in the same time, and all the relativistic quantum theories have to involve a kind of compromise. They are inconsistent a priori - but this does not matter, since no science can be consistent enough (including mathematics), and one can always switch to another theory when the old one does not work well. This introduces an element of art into science: the scientist has to find the balance between the various models to achieve make the result meaningful. When such a balance is achieved in a clear and economical way, we speak of scientific beauty.

3. Of course, there can be no action at a distance from the relativistic viewpoint. If two electrons are far enough from each other, they can be distinguished, and the interactions of one of them can have no influence on the other. But this picture is applicable for macroscopic distances only! - and if you act on an electron in a macroscopic way, there will be no quantum effects and no need for immediate communication. For example, electrons behave like macroscopic particles in Millicain-like experiments, in Geiger counters, in electron beams... Also, there are cases when microscopic particles interact among themselves, and only the products of this interaction are observed. Here, the electrons are completely indistinguishable - in the sense that you cannot speak about the action on one particular electron, but rather about the probability of acting on one electron or another. Again, no contradictions arise.

   The discussions of EPR-like experiments often mix physically different levels - and naturally come to paradoxes. In fact, this is just a problem of model applicability.

4. Quantum mechanics is attractive since it seems to advocate the idea of holistic universe. However, this is not really so, since the quantum approach opposes the macro- and microlevels (which is impossible for classical physics). Holism is broken in quantum physics, and it has to be restored with the aid of metaphysical speculations.

   Relativism is another way to break the universality of classical physics. There is still no physical theory that would unite thus abstracted parts (levels) of the universe.