Motivation
Under the orthodox Copenhagen interpretation, quantum mechanics is nondeterministic, meaning that it generally does not predict the outcome of any measurement with certainty. Instead, it indicates what the probabilities of the outcomes are, with the indeterminism of observable quantities constrained by the uncertainty principle. This leads to the situation where measurements of a certain property done on two apparently identical systems can give different answers. The question arises whether there might be some deeper reality hidden beneath quantum mechanics, to be described by a more fundamental theory that can always predict the outcome of each measurement with certainty: if the exact properties of every subatomic particle were known the entire system could be modeled exactly using deterministic physics similar to classical physics, a la Laplace's demon.
In other words, it is conceivable that the Copenhagen interpretation of quantum mechanics is an incomplete description of reality. The designation of variables as underlying "hidden" variables depends on the level of physical description (so, for example, "if a gas is described in terms of temperature, pressure, and volume, then the velocities of the individual atoms in the gas would be hidden variables".). Physicists supporting de Broglie-Bohm theory maintain that underlying the observed probabilistic nature of the universe is a deterministic objective foundation/property — the hidden variable. Others, however, believe that there is no deeper deterministic reality in quantum mechanics — experiments have shown a vast class of hidden variable theories to be incompatible with observations. Kirchmair and colleagues have shown that, in a system of trapped ions, quantum mechanics conflicts with hidden variable theories regardless of the quantum state of the system.
Although determinism was initially a major motivation for physicists looking for hidden variable theories, nondeterministic theories trying to explain what the supposed reality underlying the quantum mechanics formalism looks like are also considered hidden variable theories; for example Edward Nelson's stochastic mechanics.
Read more about this topic: Hidden Variable Theory
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