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Fictitious forces and simulated magnetic fields in rotating reference frames.

W H Klink1, S Wickramasekara

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PubMed
Summary

We extended quantum mechanics to noninertial frames using the Galilean line group. This framework explains experimental observations in neutron interferometry and optical lattices by analyzing loop prolongations.

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Area of Science:

  • Physics
  • Quantum Mechanics
  • Group Theory

Background:

  • The Wigner-Bargmann program grounds quantum mechanics in Galilei group representations.
  • Existing frameworks primarily address inertial reference frames.

Purpose of the Study:

  • To extend the Wigner-Bargmann program to noninertial reference frames.
  • To develop a theoretical framework encompassing all accelerating frames.

Main Methods:

  • Introduced the Galilean line group and its representations.
  • Utilized cocycle structures and loop prolongations (nonassociative extensions).
  • Constrained representations to reduce to Galilei group representations for inertial frames.

Main Results:

  • Developed representations for the Galilean line group, accommodating noninertial frames.
  • Demonstrated that these representations are nonassociative extensions (loop prolongations) determined by three-cocycles.
  • Showed these representations explain observed phase shifts in neutron interferometry and simulated magnetic fields in optical lattices.

Conclusions:

  • The Galilean line group and its loop prolongations provide a comprehensive framework for quantum mechanics in noninertial frames.
  • This extension rigorously derives experimental observations previously unexplained by standard Galilean invariance.
  • The study unifies the treatment of inertial and noninertial frames within quantum mechanics.