Kinetic energy and the equivalence principle

Abstract

According to the general theory of relativity, kinetic energy contributes to gravitational mass. Surprisingly, the observational evidence for this prediction does not seem to be discussed in the literature. I reanalyze existing experimental data to test the equivalence principle for the kinetic energy of atomic electrons, and show that fairly strong limits on possible violations can be obtained. I discuss the relationship of this result to the occasional claim that "light falls with twice the acceleration of ordinary matter." *

Is gravitational mass of a composite quantum body equivalent to its energy?

“…(7) is equal to zero due to the classical virial theorem. Thus, we conclude that in classical physics averaged over time passive gravitational mass of a composite body is equivalent to its energy, taken in the absence of gravitational field [7,8].…”

“…In a weak centrosymmetric gravitational field (2), wave function (11) is not anymore a ground state of the Hamiltonian (8), (9), where we treat gravitational field as a small perturbation in an inertial system [7,8,[10][11][12][13]. It is important that for an inertial observer, in accordance with Eq.…”

“…More precisely, it is shown [6] that averaged over time active gravitational mass of a photon in a container with mirror walls is E/ 2 , where E is photon energy. Importance of the classical virial theorem for the equivalence between averaged over time gravitational mass and energy of different composite classical bodies is stressed in [7,8]. In particular, it is shown that electrostatic binding energy, U, contributes to passive and active gravitational masses as 2U/ 2 , whereas kinetic energy, K , contribution to the gravitational masses is 3K / 2 [7,8].…”

“…Importance of the classical virial theorem for the equivalence between averaged over time gravitational mass and energy of different composite classical bodies is stressed in [7,8]. In particular, it is shown that electrostatic binding energy, U, contributes to passive and active gravitational masses as 2U/ 2 , whereas kinetic energy, K , contribution to the gravitational masses is 3K / 2 [7,8]. Application of the classical virial theorem to electrostatitally bound two bodies, which claims that averaged over time potential energy, < U > , equals to -2 < K > , results in the equivalence between averaged over time gravitational mass and energy,…”

Pressure as a source of gravity

“…This issue was discussed by Steven Carlip in the weak field approximation independent of any details of the box by using the virial theorem [9].…”