Exact quantum Rindler frames from an algebraic approach

We have developed the Heisenberg picture approach to quantum mechanics in spacetime with an arbitrary metric and obtained quantum geodesic equations in a previous publication. The picture naturally fits in with the recently popular topic of quantum reference frame transformations, suggesting treating the different position observables as coordinate observables of spacetime. We see that as an approach to quantum physics that is very much along the original idea of Heisenberg and Dirac, completed now with explicit mathematical expressions for Dirac’s notion of q-number values of observables. Quantum physics can be analyzed as such, independent of any Schrödinger picture. Beyond the Cartesian coordinate pictures, correspondence between the Heisenberg and the Schrödinger picture is generally nontrivial, depending on the metric expression and the frame of reference. We focus on the algebraic approach for the Heisenberg-Dirac picture to formulate transformations to exact quantum Rindler frames with quantum proper accelerations. The latter has been considered by various authors in semiclassical treatments. Analyses of some interesting results are presented. The characteristic feature of quantum reference frame transformations in giving rise to entanglement features when the particle to serve as the new frame is in a nontrivial superposition of eigenstates for the observable defining the transformation, the proper acceleration in this case, is illustrated. The notion of other ‘quantum Rindler observers’ is also analyzed. The metric in the quantum Rindler frame is illustrated to become a nonlocal observable with profound implications of which are also discussed. The question about unitarity of the transformations is carefully addressed. Discussions about a consistent perspective on the general subject matter with a quantum picture of spacetime and its Quantum Relativity Principle are also presented.