Bell's Theorem mathematically demonstrates that any local hidden variable theory of physics makes testably different predictions from those made by quantum mechanics. Whereas quantum mechanics states that the workings of the universe are purely statistical in nature and that the best we can truly do in predicting the behaviour of a system is to calculate the probabilities of various outcomes, a hidden variable theory of physics is one which attempts to model the universe in a deterministic fashion, in which there is only one possible outcome for any experiment in which the conditions of the experiment are specified. Hidden variable theories bear their name because they postulate that the apparent randomness of nature in experiments is due to certain variables being hidden from measurement, in such a way that they're either impossible for a human observer to measure or beyond our present technological capabilities. Albert Einstein was a famous proponent of the hidden variable view of quantum mechanics, acknowledging that the statistical picture may work in practice, but also that "God does not play dice with the universe", and Einstein was also one of the first to recognize that quantum mechanics implies that some form of instantaneous faster-than-light interaction is possible between particles across the universe with his Einstein-Rosen-Podolski paradox.

A "local" hidden variable theory is one which not only suggests that hidden deterministic variables/properties are responsible for the apparently randomized behaviour of nature, but also restricts all forms of communication and interaction to propagating no faster than a certain speed, usually the speed of light. In general, local theories are the only hidden variable theories seriously considered by hidden variables proponents, because nonlocal deterministic theories, in which signals can exceed the speed of light, instantly run into problems with time paradoxes forming inside Relativity, a problem which does not occur in the probabilistic approach of quantum mechanics. The value of Bell's Theorem is that it provides us with a way to conclusively demonstrate that nonlocal effects do indeed occur in nature, thus leaving us with only two choices for an explanation: 1) A nonlocal hidden variable theory which generates time paradoxes in Relativity, or 2) quantum mechanics which, in its modern quantum field theory formulation, incorporates Special Relativity as a vital component, or else some other theory based on a probabilistic interpretation of the universe.

quantum_wave has been promoting his own personal ideas about cosmology for some time, and recently inquired in the Physics & Math forum why there isn't more discussion and speculation there about the unsolved mysteries in theoretical physics as we know it today. As part of my arguments for why his ideas do not merit serious consideration in that sort of setting, as well as why physicists restrict themselves to working with theories largely compatible to and extended from existing knowledge, I propose to demonstrate that quantum_wave's personal cosmological ideas, when analyzed using Bell's Theorem, are in fundamental disagreement with known experiments, whereas quantum mechanics predicts the results of those same experiments accurately to high precision.

So quantum_wave, how would you like to proceed? Would you like me to give a brief overview and derivation of Bell's Theorem in its basic form, or would you like to start by introducing the postulates for your hidden variable theory?