- Hidden variable theory
Historically, in

physics ,**hidden variable theories**were espoused by a minority ofphysicists who argued that the statistical nature ofquantum mechanics indicated thatquantum mechanics is "incomplete".Albert Einstein , the most famous proponent of hidden variables, insisted that, "I am convinced God does not play dice" [*private letter to*] — meaning that he believed that physical theories must be deterministic to be complete. [Max Born ,4 December ,1926 , [*http://www.alberteinstein.info/db/ViewDetails.do?DocumentID=38009 Albert Einstein Archives*] reel 8, item 180*Einstein, A., Podolsky, B. and Rosen, N. (1935) [*] Later,*http://prola.aps.org/abstract/PR/v47/i10/p777_1 Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?*] , "Phys. Rev."**47**, 777-780Bell's theorem would prove (in the opinion of most physicists and contrary to Einstein's assertion) that local hidden variables are impossible. It was thought that if hidden variables exist, new physical phenomena beyond quantum mechanics are needed to explain the universe as we know it.The most famous such theory (because it gives the same answers as quantum mechanics, thus invalidating the famous theorem by

von Neumann that no hidden variable theory reproducing the statistical predictions of QM is possible) is that ofDavid Bohm , also known as the Causal Interpretation of quantum mechanics. Bohm's (nonlocal) hidden variable is called the quantum potential. Nowadays Bohm's theory is considered to be one of manyinterpretations of quantum mechanics which give a philosophical or realist interpretation, and not merely a positivistic one, to quantum-mechanical calculations. It is in fact just a reformulation of conventional quantum mechanics obtained by rearranging the equations and renaming the variables. Nevertheless it "is" a hidden variable theory.The major reference for Bohm's theory today is his posthumous book with Basil Hiley [

*D.Bohm and B.J.Hiley, The Undivided Universe, Routledge, 1993, ISBN 0-415-06588-7.*] .**Motivation**Quantum mechanics is nondeterministic, meaning that it generally does not predict the outcome of any measurement with certainty. Instead, it tells us what the probabilities of the outcomes are. This leads to the situation where measurements of a certain property done on two "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.

In other words, quantum mechanics as it stands "might be" an incomplete description of reality. Some physicists maintain that underlying the probabilistic nature of the universe is an objective foundation/property — the hidden variable. Others, however, believe that there is no deeper reality in quantum mechanics — experiments have shown a vast class of hidden variable theories to be incompatible with observations.

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.**EPR Paradox & Bell's Theorem**In 1935, Einstein, Podolsky and Rosen wrote a four-page paper titled "Can quantum-mechanical description of physical reality be considered complete?" that argued that such a theory was in fact necessary, proposing the EPR Paradox as proof. In 1964, John Bell showed through his famous theorem that if local hidden variables exist, certain experiments could be performed where the result would satisfy a Bell inequality. If, on the other hand,

Quantum entanglement is correct the Bell inequality would be violated. Anotherno-go theorem concerning hidden variable theories is theKochen-Specker theorem .Physicists such as

Alain Aspect and Paul Kwiat have performed experiments that have found violations of these inequalities up to 242 standard deviations [*Kwiat, P. G., "et al." (1999) Ultrabright source of polarization-entangled photons, "Physical Review A"*] (excellent scientific certainty). This rules out local hidden variable theories, but does not rule out non-local ones (which would refute**60**, R773-R776quantum entanglement ). Theoretically, there could be experimental problems that affect the validity of the experimental findings.**Some hidden-variable theories**A hidden-variable theory which is consistent with

quantum mechanics would have to be non-local, maintaining the existence of instantaneous or faster than light "non"causal relations (correlations) between physically separated entities. The first hidden-variable theory was the**pilot wave theory**ofLouis de Broglie , dating from the late 1920s. The currently best-known hidden-variable theory, the Causal Interpretation, of the physicist and philosopherDavid Bohm , created in 1952, is a non-local hidden variable theory. Those who believe the Bohm interpretation to be actually true (rather than a mere model or interpretation), and the quantum potential to be real, refer to "Bohmian mechanics".What Bohm did, on the basis of an idea of

Louis de Broglie , was to posit "both" the quantum particle, e.g. an electron, and a hidden 'guiding wave' that governs its motion. Thus, in this theory electrons are quite clearly particles. When you perform adouble-slit experiment (seewave-particle duality ), they go through one slit rather than the other. However, their choice of slit is not random but is governed by the guiding wave, resulting in the wave pattern that is observed.Such a view does not contradict the idea of local events that is used in both classical atomism and

relativity theory as Bohm's theory (and indeed quantum mechanics, with which it is exactly equivalent) are still locally causal but allow nonlocal correlations (that is information travel is still restricted to the speed of light). It points to a view of a more holistic, mutually interpenetrating and interacting world. Indeed Bohm himself stressed the holistic aspect of quantum theory in his later years, when he became interested in the ideas ofJiddu Krishnamurti . The Bohm interpretation (as well as others) has also been the basis of some books which attempt to connect physics withEastern mysticism andconsciousness . Nevertheless this nonlocality is seen as a weakness of Bohm's theory by some physicists.Another possible weakness of Bohm's theory is that some feel that it looks contrived. It was deliberately designed to give predictions which are in all details identical to conventional quantum mechanics. Bohm's aim was not to make a serious counterproposal but simply to demonstrate that hidden-variable theories are indeed possible. His hope was that this could lead to new insights and experiments that would lead beyond the current quantum theories.

Another type of deterministic theory [

*'t Hooft, G. (1999) [*] was recently introduced by Gerard 't Hooft. This theory is motivated by the problems that are encountered when one tries to formulate a unified theory of*http://xxx.lanl.gov/abs/gr-qc/9903084 Quantum Gravity as a Dissipative Deterministic System*] , "Class. Quant. Grav."**16**, 3263-3279quantum gravity .**References****ee also***

Local hidden variable theory

*Bell's theorem

*Bell test experiments

*Quantum mechanics

*Bohm interpretation

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