50 84 v 4 1 0 Se p 20 01 What is general relativity silent on ?

In general relativity the gravitational field is a manifestation of spacetime curvature and unlike the electromagnetic field is not a force field. A body falling toward the Earth is represented by a geodesic worldline which means that no force is acting on it. If a body is on the Earth’s surface, however, its worldline is no longer geodesic and it is subjected to a force. The nature of that force is an open question in general relativity. The aim of this paper is to outline an approach toward resolving it which was initiated by Fermi in 1921. General relativity provides a consistent no-force explanation of gravitational interaction of bodies following geodesic paths. However, it is silent on the nature of the very force we regard as gravitational the force acting upon a body deviated from its geodesic path due to its being at rest in a gravitational field. A non-resistant motion (i.e. motion by inertia) of a body in both special relativity (in flat spacetime) and general relativity (in curved spacetime) is represented by a geodesic worldline whereas a body represented by a non-geodesic worldline is subjected to a force whose nature is inertial in both special and general relativity. It should be specifically stressed that the conclusion of the non-gravitational nature of the force acting on a body at rest in a gravitational field follows from general relativity itself [7]: as a body supported in a gravitational field is deviated from its geodesic path, which means that it is prevented from moving non-resistantly (by inertia), it is subjected to an inertial force (since a body prevented from moving by inertia is subjected to such an inertial force). That is why ”there is no such thing as the force of gravity” in general relativity [8]. What has been traditionally called the gravitational force in the Newtonian gravitational theory (i) the force acting on a body at rest in a gravitational field, and (ii) the force a falling body is subjected to turned out to be (i) an inertial force, and (ii) no force at all in general relativity. That a body falling in a gravitational field is subjected to no force is nicely explained by general relativity in terms of spacetime curvature. However, like the Newtonian physics general relativity provides no insight into the nature of inertial forces. Here it will be shown that a corollary of general relativity that the propagation of electromagnetic signals (for short light) in a gravitational field is anisotropic in conjunction with the classical electromagnetic mass theory [1]-[6] sheds some light on the nature of the force acting on a classical charged particle deviated from its geodesic path. Consider a classical [9] electron at rest in the non-inertial reference frame N of an observer supported in the Earth’s gravitational field. Following Lorentz [4] and Abraham [5] we assume that the electron charge is uniformly distributed on a spherical shell. The repulsion of the charge elements of an electron in uniform motion in flat spacetime cancels out exactly and there is no net force acting on the electron. As we shall see below, however, the anisotropic velocity of light in N (i) gives rise to a self-force acting on an electron deviated from its geodesic path by disturbing the balance of the mutual repulsion of its charge elements, and (ii) makes a free electron fall in N with an acceleration g in order to balance the repulsion of its charge elements. No force is acting upon a falling electron (whose worldline is geodesic) but if it is prevented from falling (i.e. deviated from its geodesic path) the average velocity of light with respect to it becomes anisotropic and disturbs the balance of the mutual repulsion of the elements of its charge which results in a self-force trying to force the electron to fall. This force turns out to be precisely equal to the gravitational force F = mg, where m = U/c represents the passive gravitational mass of the classical electron and U is the energy of its field. As the coefficient m in front of g is precisely equal to U/c