EPR Paradox: General Remarks
The issues related to the nearly century-old the EPR paradox have recently been reported to find some experimental foundation. However, a closer examination of the experimental techniques and setup reveals a number of serious conceptual difficulties that are still far from being resolved. While there is no decisive experiment, any theorizing is to stick to the conceptual level, without really asserting or denying anything.
I suspect that an experiment that could bring light to the EPR problem is impossible in principle. Such issues do not belong to the physical domain, and even to the realm of science in general; they are the bread of philosophy and methodology. Encountering a paradox, one can be sure that there is a logical fallacy, with the different levels of hierarchy treated on the same footing, confused in the same discourse. As soon as we clearly distinguish the levels viewpoints involved, any contradictions will disappear. The logical aspects of the EPR discussions could be summarized as follows.
Any theory is only valid within the limits of its applicability; there are no absolutely "rigorous" studies in science. That is, the adequacy of a physical theory is not a matter of formal derivation, there are no "theorems" and "proofs", since the inadequacy of the theory beyond the limits of applicability is anticipated from the very beginning, before any formal justification or experimental tests. The maximum one could achieve is to derive the applicability conditions (usually in terms of strong inequality), and this can only be done in the framework of a more general (higher-level) theory. As no fundamental generalizations of quantum mechanics have been suggested, any talk about the conditions of its applicability will remain sheer philosophy, and the suggested formal criteria (like Bell’s inequalities) have no scientific sense. Even if some experiments confirmed their strict validity, this would tell nothing about the limitations of quantum and classical pictures of the world.
One could indicate that many conceptual difficulties of quantum physics come from its logical incompatibility with relativism. Quantum mechanics and relativity extend classical physics in the opposite directions. In the relativistic approach, the observer is very small, and all he can observe is his immediate environment; relativistic physics is essentially local, it cannot compare spatially separated events. On the contrary, the observer of quantum physics is supposed to be infinitely big, viewing a quantum system from far apart (mathematically, from infinity), so that the parts of the system cannot be discerned. Thus, one can detect particles (or waves) moving to and from the system at infinity, where they are no longer belong to the system of interest; however, there is no way to track the history of the interactions of these particles with the individual components of the system (atoms, molecules etc.). As long as an electron is treated in a quantum manner, we cannot know whether it has come from an atom in the experimental device, a sun flare, or a distant galaxy; there are no individual electrons in this sense.
Obviously, simultaneously being both small and big is a nontrivial task, and all the relativistic quantum theories have to seek for a kind of compromise. They are inherently inconsistent; however, no science can be entirely consistent (including mathematics), and this does not much matter, since one can always switch to another theory if the old one does not work well enough. Science thus acquires an element of art: a scientist has to find a delicate balance between the different models, to obtain a meaningful result. When such a balance is achieved in a clear and economical way, we speak of scientific beauty.
From the relativistic standpoint, there can be no action at a distance. If two electrons are far enough from each other, they can be distinguished, and anything happening to one of them can bear no influence on the other. This is an entirely "macroscopic" picture, meaning that each electron enters only macroscopic (uncorrelated) interaction; in that case, there will be no exchange effects and no need to introduce "quantum telepathy", and no paradoxes. For example, electrons behave like plain macroscopic particles in Millikan-like experiments, in Geiger counters, in industrial electron beams...
In the opposite case, on the "microscopic" level, the particles (or fields) interact with each other so that only the macroscopic (well separated from the quantum system) products of this interaction can be observed. Now, the electrons are completely indistinguishable, in the sense that you cannot selectively act on an individual electron and have to consider the probability of acting on one electron or another. Again, there are no conceptual problems.
Mental experiments of the EPR type illegally combine both macroscopic and microscopic description, which takes the form of an apparent contradiction, a paradox. This has nothing to do with physics, but rather with the inconsistency of the model lumping together physically different phenomena.
Quantum mechanics is philosophically attractive since it seems to advocate the idea of an essentially holistic universe. But it does not. On the contrary, the quantum approach splits the whole world into two worlds formally opposed to each other, macroscopic and microscopic levels; this distinction is absent in classical physics, which can therefore be considered as more universal. The broken integrity leads to conceptual difficulties and calls for metaphysical speculations to restore the holistic view.
Relativism breaks the universality of classical physics in yet another way, admitting that some parts of the world can be physically separated due to the final nature of the speed of light.
The elimination of the inherent contradictions in both quantum physics and relativism will be possible in a more general theory synthesizing the traits of the both rather than eclectically mixing them like in quantum field theories.