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Quantum Mechanics can be understood through stochastic optimization on spacetimes.

Jussi Lindgren1, Jukka Liukkonen2

  • 1Aalto University, Department of Mathematics and Systems Analysis, Espoo, Finland. jussi.lindgren@aalto.fi.

Scientific Reports
|December 29, 2019
PubMed
Summary

This study explains the origin of quantum mechanics' imaginary structure, linking it to relativistic invariance and spacetime geometry. It derives fundamental quantum equations from a coordinate-invariant stochastic optimization problem.

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Area of Science:

  • Theoretical Physics
  • Quantum Mechanics Foundations
  • Relativistic Quantum Theory

Background:

  • The origins of the imaginary unit in quantum mechanics remain a foundational question.
  • Existing quantum mechanics postulates often lack a clear derivation from first principles.
  • Understanding the interplay between relativity and quantum theory is crucial.

Purpose of the Study:

  • To elucidate the source of the imaginary structure in quantum mechanics.
  • To demonstrate the fundamental roles of relativistic invariance and spacetime geometry.
  • To derive quantum mechanical equations from a coordinate-invariant stochastic optimization problem.

Main Methods:

  • Derivation of the Stueckelberg covariant wave equation from first principles using a stochastic control scheme.
  • Deduction of the Telegrapher's equation from the Stueckelberg equation.
  • Derivation of classical relativistic and nonrelativistic quantum mechanics equations.

Main Results:

  • The imaginary structure in quantum mechanics is explained through relativistic invariance and spacetime geometry.
  • The Stueckelberg covariant wave equation is derived from a stochastic control scheme.
  • Classical quantum mechanical equations are shown to emerge from the derived Telegrapher's equation.

Conclusions:

  • Quantum mechanics concepts can be meaningfully derived from a coordinate-invariant stochastic optimization problem.
  • Relativistic invariance and spacetime geometry are fundamental to quantum mechanics' structure.
  • This approach offers a principled foundation for quantum mechanics, moving beyond postulates.