Measuring the Gravitational Interaction of Elementary Particles

Abstract

An approach to the measurement of static gravitational couplings is discussed. A plausible mathematical treatment of the nongravitational interactions of particles in the presence of a small, constant, classical tensor field without the assumption of universal coupling to the field is outlined. Some nonstandard features, principally the breakdown of strict Lorentz covariance, are pointed out. Calculations based on this formalism, or, alternatively, on simple energy-momentum conservation, indicate that some particle processes which are forbidden if the coupling to the tensor field is universal are allowed if it is not. The processes considered in some detail are spontaneous emission of a photon by a free particle, spontaneous photo-production of a particle-antiparticle pair, and spontaneous neutrino decay. These occur under certain conditions involving the energies and the coupling constants to the tensor field. The tensor field is identified with the local gravitational field and rates are estimated. Certain existing data on the absence of such reactions give evidence that the gravitational coupling of the muon in particular is equal to that of the photon to within parts per ten thousand, and that all particles with $m{c}^{2}$ less than a few GeV, excepting possibly the neutrinos and the graviton itself, have gravitational coupling which is at most the normal amount---to varying degrees of accuracy. The latter result is subject to an assumption that the algebraic sign of the local gravitational field is what one expects on intuitive grounds.