Abstract
In this paper we propose a deterministic basis for quantum mechanics and give equations of motion (derivable from an action principle) which describe deterministic trajectories in an extended space that the quantum events are assumed to follow. By applying the laws of classical probability, namely the conservation of probability along the deterministic trajectories, we derive a probability description which is found to be a generalization of the Schrödinger description with built-in probability interpretation. The generalized description admits of an infinite number of wave functions following coupled set of Schrödinger-like equations while the total probability is given by the sum of the modulus squared of all these wave functions, one of which is identified as the Schrödinger function. If all the functions other than the Schrödinger wave function be neglected the Schrödinger description is retrieved. It is thus concluded that the classical probability not only embrances probability in quantum mechanics but allows other new modes for its propagation.
We thus predict new modes of quantum behaviour and we discuss two situations and propose experiments where these modes could be looked for. Finally, our theory also provides an identification for the quantum of action, ħ.
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References
Belinfante F J 1973A Survey of Hidden Variable Theories (Pergamon Press)
Dvoryankin F F, Mityagin A-Yu and Pogorelskii K S 1970Sov. Phys. Solid State 11 1975
Fairbank Jr W M, Hansch T W and Schawlow A L 1975J. Opt. Soc. Am. 65 199
Feynman R P, Leighton R B and Sands M 1963The Feynman Lectures on Physics (Mass: Addison-wesley) vol. 1, 38–2
Fine A 1972 inProblems in the Foundation of Physics ed. Mario Bunge (Berlin: Springer Verlag) Vol. 4, p. 79
Gervais A, Stern R M and Menes M 1969Acta Cryst. A24 191
Hastie R J, Hobbs G D and Taylor J B 1969Proc. Third. Int. Conf. Plasma Phys. Contr. Fusion p. 389
Kinchin A Y 1949Mathematical Foundations of Statistical Mechanics (New York: Dover Pub.) p. 47
Lynden-Bell D 1962Mon. Not. R. Astron. Soc. 124 1
Przibram K 1967Letters on Wave Mechanics (New York: Philosophical Lib.) p. 37
Rosenbluth M N and Simon A 1965Phys. Fluids 8 1300
Rosenbluth M N and Varma R K 1967Nucl. Fusion 7 33
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Varma, R.K. Deterministic model equations of motion for quantum mechanics and some new modes of quantum behaviour. Pramana - J Phys 10, 89–113 (1978). https://doi.org/10.1007/BF02845925
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DOI: https://doi.org/10.1007/BF02845925