ACCELERATION-INDUCED CARRIER a OF THE IMPRINTS OF GRAVITATION

We exhibit a purely quantum mechanical carrier of the imprints of gravitation by identifying for a relativistic charge a property which (i) is independent of its mass and (ii) expresses the Poincare invariance of spacetime in the absence of gravitation. This carrier is a Klein-Gordon-equation-determined vector eld given by the \Planckian power" and the \r.m.s. thermal uctuation" spectra. Does there exist a purely quantum mechanical carrier of the imprints of gravi-tation? The motivation for considering this question arises from the following historical scenario: Suppose the time is 1907 when Einstein had the \happiest thought of his life", which launched him on the path toward his formulation of gravitation (general relativity). But suppose Einstein already knew relativistic quantum mechanics , and that, in fact, he accepted and appreciated it without any reservations before he started on his journey. How diierent would his theory of gravitation have been from what we have today? Put diierently, how diierent would the course of history have been if Einstein had grafted relativistic quantum mechanics onto the roots of gravitation instead of its trunk or branches? Nontrivial relativistic quantum mechanics starts with the Klein-Gordon equation @ 2 @t 2 ? @ 2 @z 2 + k 2 = 0; (1) where k 2 = k 2 x + k 2 y + m 2. The objective of this brief report is to deduce from this equation a carrier of the imprints of gravitation with the following three fundamental requirements: 1. The imprints must be carried by the evolving dynamics of a quantum mechanical wavefunction. 2. Even though the dynamical system is characterized by its particle mass m, the carrier and imprints must not depend on the particle species, i.e. the carrier must be independent of k 2. This requirement is analogous to the classical one in which the world line of a particle is independent of its mass. 3. In the absence of gravitation the carrier should yield measurable results (expectation values) which are invariant under Lorentz boosts and spacetime translations. In quantum mechanics the wave function plays the role which in Newtonian mechanics is played by a particle trajectory or in relativistic mechanics by a particle world line. That the wave function should also assume the task of carrying the imprints of gravitation is, therefore, a reasonable requirement. Because of the Dicke-Eotvos experiment, the motion of bodies in a gravitational eld is independent of the …