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

Jussi Lindgren*, Jukka Liukkonen

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

2 Citations (Scopus)
25 Downloads (Pure)

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.

Original languageEnglish
Article number1533
Number of pages8
JournalSYMMETRY
Volume12
Issue number9
DOIs
Publication statusPublished - Sep 2020
MoE publication typeA1 Journal article-refereed

Keywords

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

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