Stochastic quantum mechanics

Stochastic quantum mechanics (or the stochastic interpretation) is an interpretation of quantum mechanics.

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Quantum mechanics

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
Main article: 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]

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See also

References

Notes
  1. See I. Fényes (1946, 1952)
  2. Davidson (1979), p. 1
  3. de la Peña & Cetto (1996), p. 36
  4. de Broglie (1967)
  5. de la Peña & Cetto (1996), p. 36
  6. See E. Nelson (1966, 1985, 1986)
  7. de la Peña & Cetto (1996), p. 36
  8. de la Peña & Cetto (1996), p. 65
  9. Milonni (1994), p. 128
  10. Milonni (1994), p. 290
  11. See T. W. Marshall (1963, 1965)
  12. 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.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 Fur Physik. 132 (1): 81–106. Bibcode:1952ZPhy..132...81F. doi:10.1007/BF01338578. ISSN 1434-6001.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.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: 19984. Bibcode:2019NatSR...919984L. doi:10.1038/s41598-019-56357-3. 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
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