dorsal/arxiv
View SchemaNew derivation of quantum equations from classical stochastic arguments
| Authors | H. Bergeron |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0303153 |
| URL | https://arxiv.org/abs/quant-ph/0303153 |
Abstract
In a previous article [H. Bergeron, J. Math. Phys. 42, 3983 (2001)], we presented a method to obtain a continuous transition from classical to quantum mechanics starting from the usual phase space formulation of classical mechanics. This procedure was based on a Koopman-von Neumann approach where classical equations are reformulated into a quantumlike form. In this article, we develop a different derivation of quantum equations, based on purely classical stochastic arguments, taking some elements from the Bohm-Fenyes-Nelson approach. This study starts from a remark noticed by different authors [M. Born, Physics in My Generation (Pergamon Press, London, 1956); E. Prugovecki, Stochastic Quantum Mechanics and Quantum Spacetime (Reidel, Dordrecht, 1986)], suggesting that physical continuous observables are stochastic by nature. Following this idea, we study how intrinsic stochastic properties can be introduced into the framework of classical mechanics. Then we analyze how the quantum theory can emerge from this modified classical framework. This approach allows us to show that the transition from classical to quantum formalism (for a spinless particle) does not require real postulates, but rather soft generalizations.
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"abstract": "In a previous article [H. Bergeron, J. Math. Phys. 42, 3983 (2001)], we\npresented a method to obtain a continuous transition from classical to quantum\nmechanics starting from the usual phase space formulation of classical\nmechanics. This procedure was based on a Koopman-von Neumann approach where\nclassical equations are reformulated into a quantumlike form. In this article,\nwe develop a different derivation of quantum equations, based on purely\nclassical stochastic arguments, taking some elements from the\nBohm-Fenyes-Nelson approach. This study starts from a remark noticed by\ndifferent authors [M. Born, Physics in My Generation (Pergamon Press, London,\n1956); E. Prugovecki, Stochastic Quantum Mechanics and Quantum Spacetime\n(Reidel, Dordrecht, 1986)], suggesting that physical continuous observables are\nstochastic by nature. Following this idea, we study how intrinsic stochastic\nproperties can be introduced into the framework of classical mechanics. Then we\nanalyze how the quantum theory can emerge from this modified classical\nframework. This approach allows us to show that the transition from classical\nto quantum formalism (for a spinless particle) does not require real\npostulates, but rather soft generalizations.",
"arxiv_id": "quant-ph/0303153",
"authors": [
"H. Bergeron"
],
"categories": [
"quant-ph"
],
"title": "New derivation of quantum equations from classical stochastic arguments",
"url": "https://arxiv.org/abs/quant-ph/0303153"
},
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