Next Article in Journal
Dark Matter as Variations in the Electromagnetic Zero-Point Field Induced by Baryonic Matter
Next Article in Special Issue
Algebraic DVR Approaches Applied to Describe the Stark Effect
Previous Article in Journal
A Dynamic Failure Time Degradation-Based Model
Previous Article in Special Issue
Symmetry, Transactions, and the Mechanism of Wave Function Collapse
Open AccessArticle

The Heisenberg Uncertainty Principle as an Endogenous Equilibrium Property of Stochastic Optimal Control Systems in Quantum Mechanics

1
Department of Mathematics and Systems Analysis, Aalto University, 02150 Espoo, Finland
2
Nuclear and Radiation Safety Authority, STUK, 00880 Helsinki, Finland
*
Author to whom correspondence should be addressed.
Symmetry 2020, 12(9), 1533; https://doi.org/10.3390/sym12091533
Received: 26 August 2020 / Revised: 14 September 2020 / Accepted: 15 September 2020 / Published: 17 September 2020
(This article belongs to the Special Issue Symmetries in Quantum Mechanics)
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. View Full-Text
Keywords: stochastic optimal control; stochastic mechanics; thermodynamic equilibrium; uncertainty principle stochastic optimal control; stochastic mechanics; thermodynamic equilibrium; uncertainty principle
Show Figures

Figure 1

MDPI and ACS Style

Lindgren, J.; Liukkonen, J. The Heisenberg Uncertainty Principle as an Endogenous Equilibrium Property of Stochastic Optimal Control Systems in Quantum Mechanics. Symmetry 2020, 12, 1533.

Show more citation formats Show less citations formats
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Search more from Scilit
 
Search
Back to TopTop