UNIFIED EQUATION-OF-MOTION OF A TEST CHARGE IN ELECTROMAGNETIC AND GRAVITATIONAL-FIELDS

This work starts by generalizing in a gravitational field the fundamen tal quantum mechanical commutation relations between the coordinates o f a charged test particle and its momentum. Assuming that the componen ts of the momentum of this test charge obey a noncommutative algebra i n the presence of an electromagnetic field, it is proved that the comm utator can be identified with the electromagnetic field tensor. Using these results, the equation of motion of this charged object in the pr esence of both the electromagnetic and gravitational fields is derived from their field equations. In this work, the laws of motion of a par ticle in the electromagnetic and gravitational fields has been unified with the field equations. Although the field equations themselves are not directly unified, this work strongly suggests that the scheme may act as a possible framework for the unification of at least gravitati onal and electromagnetic interactions.