Rotating frames from quantum deformed spacetime

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