The early history of the problem about “hidden variables” in quantum mechanics

“Early history” means the period from the beginning of the thirties to the beginning of the eighties of the twenty century. It comprises the following stages according to the most important publications:

- Its explicit formulation: Neumann (1932); Einstein, Podolsky, and Rosen (1935); Bohr (1935); Schrödinger (1935)

- Neumann’s theorem (1932: 167-173) about the absence of hidden variables in quantum mechanics

- The articulation of the ways for experimental test: Bell (1964); Clauser, Horn, Shimony, Holt (1969)

- Kochen and Specker’s theorem (1968) about the absence of hidden variables in quantum mechanics

- The first experiments convincingly confirming that absence: Clauser, Horn (1974); Aspect, Grangier, and Roger (1981 and 1982)

A short formulation of the problem: The mathematical formalism of quantum mechanics based on the complex Hilbert space needs and requires only the half variables in comparison with the exhausted description of the same mechanical system in classical mechanics. What is the physical meaning of the other half of variables seeming “hidden” in quantum mechanics?

Meaning of the problem in history of philosophy of science: It concentrates in a single scientific problem a series of philosophical problems in quantum mechanics, physics, and science about:

- Determinism
- Holism
- Measurement
- The relation of model and reality
- Space-time and energy-matter universality

- The locality (or globality) and separability (or inseparability) of the apparatus and researched object

- Information as a philosophical concept as a physical ground of the universe
- Too many others

Even more, that single scientific problem could be experimentally resolved and thus this assists indirectly the elucidation of those problems in philosophy of science. The problem has been exceptionally widely discussed in philosophical literature.

Meaning of the problem in history of quantum mechanics: It generates a new and booming physical discipline: (theory of) quantum information studying the phenomena of entanglement and quantum correlations, the physical existence of which is implied by the absence of hidden variables in quantum mechanics as well as an interdisciplinary area of the same name studying and developing the mathematical formalism underlying the former and its implementation in other domains. The theory of quantum information allows of a complete informational reinterpretation of quantum mechanics and by means of it, of other physical and chemical disciplines and its technical application by the theory of quantum computer.

References:
Aspect, A, Grangier, R, Roger G. (1981) Physical Review Letters, 47(7): 460-463.
Aspect, A, Grangier, R, Roger G. (1982) Physical Review Letters, 49(2): 91-94.
Bell, J. (1964) Physics, 1(3): 195-200.
Bohr, N. (1935) Physical Review, 48(8): 696-702.
Clauser, J. Horne, M, Shimony, A, Holt, R. (1969) Physical Review Letters, 23(15): 880-884.
Clauser, J, Horne, M. (1974) Physical Review D, 10(2): 526-535.
Einstein, A, Podolski, B, Rosen, N. (1935) Physical Review, 47, 777-780.
Kochen, S, Specker, E. (1968) Journal of Mathematics and Mechanics, 17(1): 59-87
Neumann, J. (1932) Grundlagen of Quantenmechanik, Springer.
Schrödinger, E. (1935) Die Naturwissenschaften, 23(48): 807-812; 23(49): 823-828; 23(50): 844-849.

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