Equivalence Principle for Quantum Mechanics in the Heisenberg Picture

Abstract

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 $p_{\mu }$, rather than $p^{\mu }$. 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.

19 pages in Revtex, no figure; proof-read version published

References in corpus (3)

• Composite system in noncommutative space and the equivalence principle
• Group Theoretical Approach to Pseudo-Hermitian Quantum Mechanics with Lorentz Covariance and $c\to \infty$ Limit
• $E=m{c}^2$ versus Symmetry for Lorentz Covariant Physics