Stochastic quantum mechanics
Stochastic quantum mechanics (or the stochastic interpretation) is an interpretation of quantum mechanics.
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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 (John Archibald Wheeler's "quantum foam"), and that the averaged result of these fluctuations recreates a more conventional-looking metric at larger scales that can be described using classical physics, along with an element of nonlocality that can be described using quantum mechanics. A stochastic interpretation of quantum mechanics is due to persistent vacuum fluctuation. The main idea is that vacuum or spacetime fluctuations are the reason for quantum mechanics and not a result of it as it is usually considered.
Stochastic mechanics
The first relatively coherent stochastic theory of quantum mechanics was put forward by Hungarian physicist Imre Fényes[1] who was able to show the Schrödinger equation could be understood as a kind of diffusion equation for a Markov process.[2][3]
Louis de Broglie[4] felt compelled to incorporate a stochastic process underlying quantum mechanics to make particles switch from one pilot wave to another.[5] Perhaps the most widely known theory where quantum mechanics is assumed to describe an inherently stochastic process was put forward by Edward Nelson[6] and is called stochastic mechanics. This was also developed by Davidson, Guerra, Ruggiero and others.[7]
Stochastic electrodynamics
Stochastic quantum mechanics can be applied to the field of electrodynamics and is called stochastic electrodynamics (SED).[8] SED differs profoundly from quantum electrodynamics (QED) but is nevertheless able to account for some vacuum-electrodynamical effects within a fully classical framework.[9] In classical electrodynamics it is assumed there are no fields in the absence of any sources, while SED assumes that there is always a constantly fluctuating classical field due to zero-point energy. As long as the field satisfies the Maxwell equations there is no a priori inconsistency with this assumption.[10] Since Trevor W. Marshall[11] originally proposed the idea it has been of considerable interest to a small but active group of researchers.[12]
See also
References
Notes
- See I. Fényes (1946, 1952)
- Davidson (1979), p. 1
- de la Peña & Cetto (1996), p. 36
- de Broglie (1967)
- de la Peña & Cetto (1996), p. 36
- See E. Nelson (1966, 1985, 1986)
- de la Peña & Cetto (1996), p. 36
- de la Peña & Cetto (1996), p. 65
- Milonni (1994), p. 128
- Milonni (1994), p. 290
- See T. W. Marshall (1963, 1965)
- Milonni (1994), p. 129
Papers
- de Broglie, L. (1967). "Le Mouvement Brownien d'une Particule Dans Son Onde". C. R. Acad. Sci. B264: 1041.CS1 maint: ref=harv (link)
- Davidson, M. P. (1979). "The Origin of the Algebra of Quantum Operators in the Stochastic Formulation of Quantum Mechanics". Letters in Mathematical Physics. 3 (5): 367–376. arXiv:quant-ph/0112099. Bibcode:1979LMaPh...3..367D. doi:10.1007/BF00397209. ISSN 0377-9017. S2CID 6416365.CS1 maint: ref=harv (link)
- Fényes, I. (1946). "A Deduction of Schrödinger Equation". Acta Bolyaiana. 1 (5): ch. 2.CS1 maint: ref=harv (link)
- Fényes, I. (1952). "Eine wahrscheinlichkeitstheoretische Begründung und Interpretation der Quantenmechanik". Zeitschrift für Physik. 132 (1): 81–106. Bibcode:1952ZPhy..132...81F. doi:10.1007/BF01338578. ISSN 1434-6001. S2CID 119581427.CS1 maint: ref=harv (link)
- Marshall, T. W. (1963). "Random Electrodynamics". Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 276 (1367): 475–491. Bibcode:1963RSPSA.276..475M. doi:10.1098/rspa.1963.0220. ISSN 1364-5021. S2CID 202575160.CS1 maint: ref=harv (link)
- Marshall, T. W. (1965). "Statistical Electrodynamics". Mathematical Proceedings of the Cambridge Philosophical Society. 61 (2): 537–546. Bibcode:1965PCPS...61..537M. doi:10.1017/S0305004100004114. ISSN 0305-0041.CS1 maint: ref=harv (link)
- Lindgren, J.; Liukkonen, J. (2019). "Quantum Mechanics can be understood through stochastic optimization on spacetimes". Scientific Reports. 9 (1): 19984. Bibcode:2019NatSR...919984L. doi:10.1038/s41598-019-56357-3. PMC 6934697. PMID 31882809.
- Nelson, E. (1966). Dynamical Theories of Brownian Motion. Princeton: Princeton University Press. OCLC 25799122.CS1 maint: ref=harv (link)
- Nelson, E. (1985). Quantum Fluctuations. Princeton: Princeton University Press. ISBN 0-691-08378-9. LCCN 84026449. OCLC 11549759.CS1 maint: ref=harv (link)
- Nelson, E. (1986). "Field Theory and the Future of Stochastic Mechanics". In Albeverio, S.; Casati, G.; Merlini, D. (eds.). Stochastic Processes in Classical and Quantum Systems. Lecture Notes in Physics. 262. Berlin: Springer-Verlag. pp. 438–469. doi:10.1007/3-540-17166-5. ISBN 978-3-662-13589-1. OCLC 864657129.CS1 maint: ref=harv (link)
Books
- de la Peña, Luis; Cetto, Ana María (1996). van der Merwe, Alwyn (ed.). The Quantum Dice: An Introduction to Stochastic Electrodynamics. Dordrecht; Boston; London: Kluwer Academic Publishers. ISBN 0-7923-3818-9. LCCN 95040168. OCLC 832537438.CS1 maint: ref=harv (link)
- Jammer, M. (1974). The Philosophy of Quantum Mechanics: The Interpretations of Quantum Mechanics in Historical Perspective. New York: Wiley. ISBN 0-471-43958-4. LCCN 74013030. OCLC 613797751.CS1 maint: ref=harv (link)
- Namsrai, K. (1985). Nonlocal Quantum Field Theory and Stochastic Quantum Mechanics. Dordrecht; Boston: D. Reidel Publishing Co. doi:10.1007/978-94-009-4518-0. ISBN 90-277-2001-0. LCCN 85025617. OCLC 12809936.CS1 maint: ref=harv (link)
- Milonni, Peter W. (1994). The Quantum Vacuum: An Introduction to Quantum Electrodynamics. Boston: Academic Press. ISBN 0-12-498080-5. LCCN 93029780. OCLC 422797902.CS1 maint: ref=harv (link)
