Hidden variable theory
From Wikipedia, the free encyclopedia
Historically, in Physics, Hidden Variable Theories were espoused by a minority of physicists who argued that the statistical nature of quantum mechanics indicated that quantum mechanics is "incomplete". Albert Einstein, the most famous proponent of hidden variables, insisted that, "I am convinced God does not play dice"[1] — meaning that he believed that physical theories must be deterministic to be complete.[2] Later, Bell's theorem would prove (in most physicists opinions 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 of David 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 many Interpretations of Quantum Mechanics which give a philosophical or realist meaning to the positivistic calculations of the Quantum Mechanical procedure. 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[3].
Contents |
[edit] 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. A minority[citation needed] of physicists maintain that underlying the probabilistic nature of the universe is an objective foundation/property — the hidden variable. Most believe[citation needed], however, 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, non deterministic theories trying to explain what the supposed reality underlying quantum mechanics formalism looks like are also considered hidden variable theories; for example Edward Nelson's stochastic mechanics.
[edit] 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 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. Another no-go theorem on hidden variable theories is the Kochen-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[4](excellent scientific certainty). This rules out local hidden variable theories, but does not rule out non-local ones. Theoretically, there could be experimental problems that affect the validity of the experimental findings.
[edit] Hidden-Variable Theory
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 noncausal relations (correlations) between physically separated entities. The first hidden-variable theory was the pilot wave theory by Louis de Broglie from the late 1920s. The currently best-known hidden-variable theory, the Causal Interpretation, of the physicist and philosopher David Bohm, created in 1952, is a non-local hidden variable theory. Those who believe the Bohm Interpretation to be actually true (rather than just a model or interpretation) refer to it as Bohmian Mechanics. We say they "reify" (make real) the Quantum Potential.
What Bohm did, based on an idea originally by 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 a double-slit experiment (see wave-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 only nonlocal correlations (that is information travel is still restricted to the speed of light). It points to a more holistic, mutually interpenetrating and interacting view of the world. Indeed Bohm himself stressed the holistic aspect of quantum theory in his later years, when he became interested in the ideas of Jiddu Krishnamurti. The Bohm interpretation (as well as others) has also been the basis of some books which attempt to connect physics with Eastern mysticism and consciousness.
Nevertheless this nonlocality is seen as a weakness of Bohm's theory by some physicists[5] despite the fact that Quantum Mechanics itself is equally nonlocal.
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. His aim was not to make a serious counterproposal but simply to demonstrate that hidden-variables 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[6] 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 quantum gravity.
[edit] References
- ^ private letter to Max Born, 4 December 1926, Albert Einstein Archives reel 8, item 180
- ^ Einstein, A., Podolsky, B. and Rosen, N. (1935) Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?, Phys. Rev. 47, 777-780
- ^ D.Bohm and B.J.Hiley, The Undivided Universe, Routledge, 1993, ISBN 0-415-06588-7.
- ^ Kwiat, P. G., et al. (1999) Ultrabright source of polarization-entangled photons, Physical Review A 60, R773-R776
- ^ "There is a certain irony here associated with the fact that most physicists (at least, among those who have even heard of it) reject the de Broglie - Bohm theory because it is explicitly non-local." Comment on Experimental realization of Wheeler’s delayed-choice GedankenExperiment - Travis Norsen
- ^ 't Hooft, G. (1999) Quantum Gravity as a Dissipative Deterministic System, Class. Quant. Grav. 16, 3263-3279
