Equivalence principle for quantum mechanics in the Heisenberg picture

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We present an exact quantum observable analog of the weak equivalence principle for a ‘relativistic’ quantum particle. The quantum geodesic equations are obtained from Heisenberg equations of motion as an exact analog of a fully covariant classical Hamiltonian evolution picture, with the proper identification of the canonical momentum variables as p µ , rather than p µ . We discuss the meaning of the equations in relation to projective measurements as well as equations with solution curves as ones in the noncommutative geometric picture of spacetime, and a plausible approach to quantum gravity as a theory about quantum observables as physical quantities including the notion of quantum coordinate transformation.

Original languageEnglish
Article number085013
JournalClassical and Quantum Gravity
Issue number8
StatePublished - 18 Apr 2024


  • Heisenberg picture
  • equivalence principle
  • noncommutative geometry
  • quantum geodesic equation
  • quantum gravity
  • quantum reference frame transformation


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