Rotating frames from quantum deformed spacetime

Abstract

In a sense of deformation quantization, noncommutative (NC) geometry introduces a quantum structure of spacetime. Using the twist-deformation formalism, we show that the dynamical effects of spacetime noncommutativity can amount to a transition to a rotating frame of reference. In particular, we study the dynamics of charged matter (scalars and spinors) on the curved background of Melvin's electric universe in the framework of NC gauge field theory. Melvin's electric/magnetic universe is an exact sourceless solution of the Einstein-Maxwell field equations that is both static and axially symmetric, and it represents a parallel bundle of self-gravitating electric/magnetic flux. Due to its axial symmetry, it allows for a special kind of Killing twist that does not affect the coupling of the matter fields to the background metric. Focusing on the perturbative NC equations of motion for charged scalars and Dirac spinors coupled to Melvin's electric background, we show that they have the same form as the corresponding classical (undeformed) equations of motion coupled to the same geometric background but in a uniformly rotating frame whose angular velocity is determined by the NC scale and the electric charge of the matter field. In principle, this NC rotation effect can be experimentally tested by setting up the Sagnac interferometry apparatus to measure the Sagnac phase shift for charged versus electrically neutral particles, thus placing a bound on the scale of spacetime noncommutativity.