Quantum variable, hidden

In [6] such variables are called quantum variables , by resemblance with the hidden variables theories of quantum mechanics. 

Bell s Theorem In a celebrated 1935 paper, Einstein, Podolsky and Rosen (EPR) [ein35] argued that quantum mechanics provides an essentially incomplete description of reality unless hidden variables exist. 

Since quantum mechanics allows us to predict, with certainty, the component of the second spin by measuring the same spin component of the first (and remotely positioned) particle - and to do so without in any way disturbing that second particle - BPR s first two assumptions attribute an element of physical reality to the value of any spin component of either particle i.e. the spin components must be determinate. On the other hand, assuming that the particles cannot communicate information any faster than at the speed of light, the only way to stay consistent with BPR s third postulate is to assume the existence of hidden variables. 

Bell s result, made all the more remarkable for the very few assumptions he makes to derive it, rather dramatically asserts that cither EPR s three premises are wrong or quantum mechanics is incorrect. However, recent experiments by A.spect, et.al. ([aspect82a], [aspect82b]). On and Mandel [01188], and others have shown, virtually conclusively, that nature satisfies the quantum mechanical prediction (equation 12.54) and not Bell s inequality (equation 12.55), thus strongly denying the possibility of local hidden variables. We are thus left with what is arguably one of the deepest mysteries in the foundations of physics the existence of a profoundly nonclassical correlation between spatially-far separated systems, or nonscparability. 

Achinstein, P. [1968] Concepts of Science, Baltimore University Press, Baltimore. Bell, J. S. [1966] On the Problem of Hidden Variables in Quantum Mechanics , Reviews of Modern Physics, 38, p. 447. 

In spite of stubborn efforts to reduce it to a statistical probability distribution over states of hidden variables D. Bohm, Phys, Rev. 85, 166 and 180 (1952) F.J. Belinfante, A Survey of Hidden-Variables Theories (Pergamon, Oxford 1973) E. Nelson, Quantum Fluctuations (Princeton University Press, Princeton, NY 1985) J.S. Bell, Speakable and Unspeakable in Quantum Mechanics (Cambridge University Press, Cambridge 1987). 

The final coup de grace against any alternative to the orthodox formulation was supposed to be delivered by John von Neumann (1932) with mathematical proof that dispersion-free states2 and hidden variables are impossible in quantum mechanics. He concluded [29] that ... 

The idea of hidden variables is fairly common in chemical models such as the kinetic gas model. This theory is formulated in terms of molecular momenta that remain hidden, and evaluated against measurements of macroscopic properties such as pressure, temperature and volume. Electronic motion is the hidden variable in the analysis of electrical conduction. The firm belief that hidden variables were mathematically forbidden in quantum systems was used for a long time to discredit Bohm s ideas. Without joining the debate it can be stated that this proof has finally been falsified. 

The idea of action at a distance was resisted both by Newton, and by Einstein [42] who called it "spooky", but it has now been demonstrated experimentally [43, 44] that local realistic theory cannot account for correlations between measurements performed at well separated sites. The conclusion is that quantum theory permits hidden variables and is non-local. This conclusion is at variance with relativity, but, as pointed out by Bohm [34], the nonlocality of quantum theory only applies to complex wave functions and does not imply that the quantum potential can be used to transmit signals faster than light. 

Thus, the wavelength-frequency relation (2.1) implies the Compton-effect formula (2.10). The best we can do is to describe the phenomena constituting the wave-particle duality. There is no widely accepted explanation in terms of everyday experience and common sense. Feynman referred to the experiment with two holes as the central mystery of quantum mechanics. It should be mentioned that a number of models have been proposed over the years to rationalize these quantum mysteries. Bohm proposed that there might exist hidden variables whieh would make the behavior of each photon deterministic, i.e., particle-like. Everett and Wheeler proposed the many worlds interpretation of quantum mechanics in which each random event causes the splitting of the entire universe into disconnected parallel universes in whieh eaeh possibility becomes the reality. 

According to the viewpoint of local realism, the recurring correlations in the Bohm experiment can be attributed to the existence of hidden variables which determine the spin state in every possible direction. It is as if each particle carried a little code book containing all this detailed information, a situation something like the left-hand drawing in Fig. 16.4. It must be concluded—so far—that both local realism and the quantum-mechanical picture of the world are separately capable of giving consistent accounts of the EPR and Bohm experiments. In what follows, we will refer to the two competing worldviews as local realism (LR) and quantum mechanics ("QM). By QM we will understand the conventional formulation of the theory, complete as it stands, without hidden variables or other auxilliary constructs. 

The preceding formalism of SU(2) phase states can be used in a number of problems of quantum physics. As an illustrative example of great importance, consider the so-called Einstein-Podolsky-Rosen (EPR) paradox [73] (see also discussions in Refs. 14, 15, 74, and 75). The EPR paradox touches on the conceptual problems of reality and locality and existence of hidden variables in quantum physics as well as the more technological aspects of quantum cryptography [34]. 

R. Haggarty, Fundamentals of Mathematical Analysis, Addison-Wesley, Reading, MA, 1989, p. 178. The word is also used in quantum physics to denote phenomena, or entities ( hidden variables ), that do not, or do not seem to, violate relativity. See e.g. A. Whitaker, Einstein, Bohr and the Quantum Dilemma, Cambridge University Press, Cambridge, 1996 V. J. Stenger, The Unconscious Quantum, Prometheus, Amherst, New York, 1995. 

Bohm s work was largely ignored for many years partly because the eminent mathematician yon Neumann in 1932 had published a proof that it was impossible for any deterministiG hidden-variable theory to reproduce the same experimental results as quantum mechanics. In 1966, Bell showed that von Neumann s proof contained an unjustified assumption and so was erroneous. In subsequent years, interest in Bohm s theory has increased. For more on Bohm s theory, see D. Z Albert, Quantum Mechanics and Experience, Harvard Univ. Press, 1992, Chapter 7 Whitaker, Chapter 7 P. Holland, The Quantum Theory of Motion, Cambridge Univ. Press, 1S>93 D. Bohm and R J. Hiley, The Undivided Universe, Routledge, 1992 D. Z Albert, Scientific American, May 1S>S>4, p. 58. 

Bohm, D. (1952). A suggested interpretation of the quantum theory in terms of hidden variables. I. Phys Rev 85,166-179 180-193. 

Leggett s theorem A result in quantum mechanics that is a generalization of Bell s theorem. This theorem, which was put forward in 2003 by the British physicist Anthony Leggett (1938- ), states that nonlocal hidden-variables theories make predictions that contradict the predictions of quantum mechanics. It was subsequently found that experiments agree with the predictions of quantum mechanics rather than of nonlocal hidden-variables theories. 

An alternative to the wave mechanical treatment of quantum mechanics is an equivalent formalism called matrix mechanics, which is based on mathematical operators. See also hidden-variables theory Bell s THEOREM. 

During my student days (pre-university, university, PhD), we learned quantum mechanics from the books authored by L. D. Landau and E. M. Lifshitz, A. S. Davydov, D. Bohm, Feynman s course of Lectures on Physics, and from P. A. M. Dirac s Principles . We were exeited with the theories of hidden variables, EPR paradox, decoherence, entanglement, and concerned for a life of immortal Schrodinger s cat - they were in the air at that time Did I understand it Yes - because, due to a conventional wisdom, I used it more than 24 hours a day and every day. I however doubt - doubt together with Feynman who once remarked that Nobody understands it - that I ve actually understood it. I touched and used it throughout the molecular world, which is nowadays inhabited by 21 million molecules, and which I studied as a quantum chemist - in fact, by education, I am a theoretical physicist. 

In 1952, David Bohm (following a suggestion made by de Broglie in 1927 that the wave function might act as a pilot wave guiding the motion of the particle) devised a nonlocal deterministic hidden-variable theory that predicts the same experimental results as quantum mechanics [D. Bohm, Phys. Rev., 85, 166, 180 (1952)]. In Bohm s theory, a... 

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