Hidden variable theory

Hidden variable theory

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Historically, in physics
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...

, hidden variable theories were espoused by some physicists who argued that quantum mechanics
Quantum mechanics
Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...

 is incomplete. These theories argue against the orthodox interpretation of quantum mechanics
Quantum mechanics
Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...

, which is the Copenhagen Interpretation
Copenhagen interpretation
The Copenhagen interpretation is one of the earliest and most commonly taught interpretations of quantum mechanics. It holds that quantum mechanics does not yield a description of an objective reality but deals only with probabilities of observing, or measuring, various aspects of energy quanta,...

. Albert Einstein
Albert Einstein
Albert Einstein was a German-born theoretical physicist who developed the theory of general relativity, effecting a revolution in physics. For this achievement, Einstein is often regarded as the father of modern physics and one of the most prolific intellects in human history...

, the most famous proponent of hidden variables, famously insisted that, "I am convinced God does not play dice", but whether he objected to the statistical nature of quantum mechanics is disputed. Einstein, Podolsky
Boris Podolsky
Boris Yakovlevich Podolsky , was an American physicist of Russian Jewish descent.-Education:In 1896, Boris Podolsky was born into a poor Jewish family in Taganrog, in what was then the Russian Empire, and he moved to the United States in 1913...

, and Rosen
Nathan Rosen
Nathan Rosen was an American-Israeli physicist noted for his study on the structure of the hydrogen molecule and his work with Albert Einstein and Boris Podolsky on entangled wave functions and the EPR paradox.-Background:Nathan Rosen was born into a Jewish family in Brooklyn, New York...

 argued that "elements of reality" (hidden variables) must be added to quantum mechanics to explain entanglement
Quantum entanglement
Quantum entanglement occurs when electrons, molecules even as large as "buckyballs", photons, etc., interact physically and then become separated; the type of interaction is such that each resulting member of a pair is properly described by the same quantum mechanical description , which is...

 without action at a distance. Later, Bell's theorem
Bell's theorem
In theoretical physics, Bell's theorem is a no-go theorem, loosely stating that:The theorem has great importance for physics and the philosophy of science, as it implies that quantum physics must necessarily violate either the principle of locality or counterfactual definiteness...

 would suggest (in the opinion of most physicists and contrary to Einstein's assertion) that local hidden variables
Local hidden variable theory
In quantum mechanics, a local hidden variable theory is one in which distant events are assumed to have no instantaneous effect on local ones....

 are impossible.

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
David Bohm
David Joseph Bohm FRS was an American-born British quantum physicist who contributed to theoretical physics, philosophy, neuropsychology, and the Manhattan Project.-Youth and college:...

. It is most commonly known as the Bohm interpretation
Bohm interpretation
The de Broglie–Bohm theory, also called the pilot-wave theory, Bohmian mechanics, and the causal interpretation, is an interpretation of quantum theory. In addition to a wavefunction on the space of all possible configurations, it also includes an actual configuration, even in situations where...

 or the Causal Interpretation of quantum mechanics. In Bohm's interpretation, the (nonlocal) quantum potential
Quantum potential
The quantum potential is a central concept of the de Broglie–Bohm formulation of quantum mechanics, introduced by David Bohm in 1952.Initially presented under the name quantum-mechanical potential, subsequently quantum potential, it was later elaborated upon by Bohm and Basil Hiley in its...

 constitutes an implicate (hidden) order, and may itself be the result of yet a further implicate order (superimplicate order). Nowadays Bohm's theory is considered to be one of many interpretations of quantum mechanics which give a realist
Scientific realism
Scientific realism is, at the most general level, the view that the world described by science is the real world, as it is, independent of what we might take it to be...

 interpretation, and not merely a positivistic
Positivism
Positivism is a a view of scientific methods and a philosophical approach, theory, or system based on the view that, in the social as well as natural sciences, sensory experiences and their logical and mathematical treatment are together the exclusive source of all worthwhile information....

 one, to quantum-mechanical calculations. By some it is considered the simplest
Simplicity
Simplicity is the state or quality of being simple. It usually relates to the burden which a thing puts on someone trying to explain or understand it. Something which is easy to understand or explain is simple, in contrast to something complicated...

 theory to explain the orthodox quantum mechanics formalism. Nevertheless it is a hidden variable theory.

The major reference for Bohm's theory today is his posthumous book with Basil Hiley
Basil Hiley
Basil Hiley, born 1935, is a British quantum physicist and professor emeritus of the University of London.- Work :Hiley published a paper in 1961 on the random walk of a macromolecule, which was followed by further papers on the Ising model, and lattice constant systems defined in graph theoretical...

.

Motivation


Under the Copenhagen interpretation, 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 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. In other words if the exact properties of every subatomic particle and smaller were known the entire system could be modeled exactly using deterministic physics similar to classical physics.

In other words, the Copenhagen interpretation of quantum mechanics might be an incomplete description of reality. Physicists supporting the Bohmian interpretation of quantum mechanics 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. Kirchmair and colleagues show 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
Edward Nelson
Edward Nelson is a professor in the Mathematics Department at Princeton University. He is known for his work on mathematical physics and mathematical logic...

's stochastic mechanics
Stochastic interpretation
The stochastic interpretation is an interpretation of quantum mechanics.The modern application of stochastics to quantum mechanics involves the assumption of spacetime stochasticity, the idea that the small-scale structure of spacetime is undergoing both metric and topological fluctuations , and...

.

EPR Paradox & Bell's Theorem


In 1935, Einstein
Albert Einstein
Albert Einstein was a German-born theoretical physicist who developed the theory of general relativity, effecting a revolution in physics. For this achievement, Einstein is often regarded as the father of modern physics and one of the most prolific intellects in human history...

, Podolsky
Boris Podolsky
Boris Yakovlevich Podolsky , was an American physicist of Russian Jewish descent.-Education:In 1896, Boris Podolsky was born into a poor Jewish family in Taganrog, in what was then the Russian Empire, and he moved to the United States in 1913...

 and Rosen
Nathan Rosen
Nathan Rosen was an American-Israeli physicist noted for his study on the structure of the hydrogen molecule and his work with Albert Einstein and Boris Podolsky on entangled wave functions and the EPR paradox.-Background:Nathan Rosen was born into a Jewish family in Brooklyn, New York...

 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
EPR paradox
The EPR paradox is a topic in quantum physics and the philosophy of science concerning the measurement and description of microscopic systems by the methods of quantum physics...

 as proof. In 1964, John Bell
John Stewart Bell
John Stewart Bell FRS was a British physicist from Northern Ireland , and the originator of Bell's theorem, a significant theorem in quantum physics regarding hidden variable theories.- Early life and work :...

 showed through his famous theorem
Bell's theorem
In theoretical physics, Bell's theorem is a no-go theorem, loosely stating that:The theorem has great importance for physics and the philosophy of science, as it implies that quantum physics must necessarily violate either the principle of locality or counterfactual definiteness...

 that if local hidden variables exist, certain experiments could be performed where the result would satisfy a Bell inequality
Bell's theorem
In theoretical physics, Bell's theorem is a no-go theorem, loosely stating that:The theorem has great importance for physics and the philosophy of science, as it implies that quantum physics must necessarily violate either the principle of locality or counterfactual definiteness...

. If, on the other hand, Quantum entanglement
Quantum entanglement
Quantum entanglement occurs when electrons, molecules even as large as "buckyballs", photons, etc., interact physically and then become separated; the type of interaction is such that each resulting member of a pair is properly described by the same quantum mechanical description , which is...

 is correct the Bell inequality would be violated. Another no-go theorem
No-go theorem
In theoretical physics, a no-go theorem is a theorem that states that a particular situation is not physically possible.-Examples of no-go theorems:* Bell's theorem* Coleman–Mandula theorem* Haag-Lopuszanski-Sohnius theorem* Earnshaw's theorem...

 concerning hidden variable theories is the Kochen-Specker theorem
Kochen-Specker theorem
In quantum mechanics, the Kochen–Specker theorem is a "no go" theorem proved by Simon B. Kochen and Ernst Specker in 1967. It places certain constraints on the permissible types of hidden variable theories which try to explain the apparent randomness of quantum mechanics as a deterministic model...

.

Physicists such as Alain Aspect
Alain Aspect
Alain Aspect is a French physicist noted for his experimental work on quantum entanglement....

 and Paul Kwiat have performed experiments
Bell test experiments
The Bell test experiments serve to investigate the validity of the entanglement effect in quantum mechanics by using some kind of Bell inequality...

 that have found violations of these inequalities up to 242 standard deviations(excellent scientific certainty). This rules out local hidden variable theories, but does not rule out non-local ones (which would refute quantum entanglement
Quantum entanglement
Quantum entanglement occurs when electrons, molecules even as large as "buckyballs", photons, etc., interact physically and then become separated; the type of interaction is such that each resulting member of a pair is properly described by the same quantum mechanical description , which is...

). Theoretically, there could be experimental problems that affect the validity of the experimental findings.

Non-local hidden-variable theory


Assuming the validity of Bell's theorem, any classical hidden-variable theory which is consistent with quantum mechanics
Quantum mechanics
Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...

 would have to be non-local
Principle of locality
In physics, the principle of locality states that an object is influenced directly only by its immediate surroundings. Experiments have shown that quantum mechanically entangled particles must violate either the principle of locality or the form of philosophical realism known as counterfactual...

, maintaining the existence of instantaneous or faster-than-light acausal relations (correlations) between physically separated entities. The first hidden-variable theory was the pilot wave theory
Pilot wave
In theoretical physics, the Pilot Wave theory was the first known example of a hidden variable theory, presented by Louis de Broglie in 1927. Its more modern version, the Bohm interpretation,...

of Louis de Broglie, dating from 1927. The currently best-known hidden-variable theory, the Causal Interpretation
Bohm interpretation
The de Broglie–Bohm theory, also called the pilot-wave theory, Bohmian mechanics, and the causal interpretation, is an interpretation of quantum theory. In addition to a wavefunction on the space of all possible configurations, it also includes an actual configuration, even in situations where...

, of the physicist and philosopher David Bohm
David Bohm
David Joseph Bohm FRS was an American-born British quantum physicist who contributed to theoretical physics, philosophy, neuropsychology, and the Manhattan Project.-Youth and college:...

, 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, unknowingly rediscovering (and extending) the idea that Louis de Broglie had proposed and abandoned, 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
Double-slit experiment
The double-slit experiment, sometimes called Young's experiment, is a demonstration that matter and energy can display characteristics of both waves and particles...

 (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 nonlocal correlations (that is information travel is still restricted to the speed of light). It points to a view of a more holistic
Holism in science
Holism in science, or Holistic science, is an approach to research that emphasizes the study of complex systems. This practice is in contrast to a purely analytic tradition which aims to gain understanding of systems by dividing them into smaller composing elements and gaining understanding of the...

, 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 of Jiddu Krishnamurti
Jiddu Krishnamurti
Jiddu Krishnamurti or J. Krishnamurti or , was a renowned writer and speaker on philosophical and spiritual subjects. His subject matter included: psychological revolution, the nature of the mind, meditation, human relationships, and bringing about positive change in society...

. 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. (Indeed, Bohm thought this of his original formulation of the theory.) 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.

Gerard 't Hooft has disputed the validity of Bell's theorem on the basis of the superdeterminism
Superdeterminism
In the context of quantum mechanics, superdeterminism is a term that has been used to describe a hypothetical class of theories which evade Bell's theorem by virtue of being completely deterministic. Bell's theorem depends on the assumption of counterfactual definiteness, which technically does...

 loophole and proposed some ideas to construct local deterministic models.

In August 2011, Roger Colbeck and Renato Renner published a proof that any extension of quantum mechanical theory, whether using hidden variables or otherwise, cannot provide a more accurate description of outcomes, assuming that observers have free will
Free will
"To make my own decisions whether I am successful or not due to uncontrollable forces" -Troy MorrisonA pragmatic definition of free willFree will is the ability of agents to make choices free from certain kinds of constraints. The existence of free will and its exact nature and definition have long...

.

See also

  • Local hidden variable theory
    Local hidden variable theory
    In quantum mechanics, a local hidden variable theory is one in which distant events are assumed to have no instantaneous effect on local ones....

  • Bell's theorem
    Bell's theorem
    In theoretical physics, Bell's theorem is a no-go theorem, loosely stating that:The theorem has great importance for physics and the philosophy of science, as it implies that quantum physics must necessarily violate either the principle of locality or counterfactual definiteness...

  • Bell test experiments
    Bell test experiments
    The Bell test experiments serve to investigate the validity of the entanglement effect in quantum mechanics by using some kind of Bell inequality...

  • Quantum mechanics
    Quantum mechanics
    Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...

  • Bohm interpretation
    Bohm interpretation
    The de Broglie–Bohm theory, also called the pilot-wave theory, Bohmian mechanics, and the causal interpretation, is an interpretation of quantum theory. In addition to a wavefunction on the space of all possible configurations, it also includes an actual configuration, even in situations where...