Bell's Theorem
Bell's theorem is a logical argument in support of the completeness of quantum theory. The theorem argues against the existence of any hidden or unknown variables that might deterministically explain otherwise seemingly random events predicted by quantum mechanics.
Bell's theorem was devised in 1964 by British physicist John Stewart Bell. Sometimes known as Bell's inequalities, in quantum mechanics the theorem is an analysis of a paradox first advanced by physicists Albert Einstein, Boris Podolsky and Nathan Rosen (EPR) in a 1935 Physical Review article titled "Can Quantum Mechanical Description of Physical Reality be Considered Complete?" As a consequence, Bell's theorem is used to argue against any incompleteness or hidden variables in the quantum mechanical description of nature.
Bell's theorem examines the expected results of EPR-type experiments when it is assumed that particle properties such as momentum and position have real values prior to measurement. This assumption is made by the hidden-variable theories that have been advanced as alternatives to quantum mechanics and the uncertainty principle. The theorem demonstrates that hidden-variable theories give results that are consistent with quantum mechanics in special cases, but that in more general experimental situations, hidden-variable theories predict results that are inconsistent with quantum mechanics.
For example, examining the correlations between measurements of the two particles in an EPR-type experiment gives statistical predictions of the outcome. By comparing the statistical predictions of a quantum mechanical model of the experiment with the predictions of alternative models that assume variables (e.g., momentum and position) have values prior to measurement, Bell's theorem shows that the predictions of the two models differ by a significant amount unless it is assumed that measurements on one particle can affect those on the other particle instantaneously, no matter how far apart they are separated. Since this condition would involve faster-than-light travel, it would violate special relativity, and thus it suggests that the criticisms of quantum mechanics in the EPR paradox do not seriously threaten the validity of the uncertainty principle.
Experiments by physicist Alain Aspect and others have tended to support Bell's theorem and strengthen arguments particles cannot have simultaneous values for complementary properties such as position and momentum unless physics is non-local and permits particles to interact instantaneously regardless of how far apart they are. David Bohm (1917-1992) and others have constructed such non-local hidden-variable theories, but they have not been widely accepted. Because the quantum mechanical description of nature is so different from everyday experience its interpretation continues to be a subject of debate, and Bell's theorem raises deep questions about the physical world that have yet to be completely answered.
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