The Heisenberg uncertainty principle as an endogenous equilibrium property of stochastic optimal control systems in quantum mechanics

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openAccess

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Volume Title

A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä

Date

2020-09

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Mcode

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Language

en

Pages

8

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SYMMETRY, Volume 12, issue 9

Abstract

We provide a natural derivation and interpretation for the uncertainty principle in quantum mechanics from the stochastic optimal control approach. We show that, in particular, the stochastic approach to quantum mechanics allows one to understand the uncertainty principle through the "thermodynamic equilibrium". A stochastic process with a gradient structure is key in terms of understanding the uncertainty principle and such a framework comes naturally from the stochastic optimal control approach to quantum mechanics. The symmetry of the system is manifested in certain non-vanishing and invariant covariances between the four-position and the four-momentum. In terms of interpretation, the results allow one to understand the uncertainty principle through the lens of scientific realism, in accordance with empirical evidence, contesting the original interpretation given by Heisenberg.

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Keywords

Stochastic mechanics, Stochastic optimal control, Thermodynamic equilibrium, Uncertainty principle

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Citation

Lindgren , J & Liukkonen , J 2020 , ' The Heisenberg uncertainty principle as an endogenous equilibrium property of stochastic optimal control systems in quantum mechanics ' , SYMMETRY , vol. 12 , no. 9 , 1533 . https://doi.org/10.3390/SYM12091533