The principle of equivalence is partly abandoned as a basis for general relativity, and cosmic time is introduced as a new field variable. Field equations are obtained which take account of the self-energy of the gravitational field. The central symmetrical solution of the new field equations shows a significant deviation from the well-known Schwarzschild solution. It is free from singularities and gives a slightly smaller value for the perihelion motion of planetary orbits. Other consequences of the new formalism are:

(a) A rigorous definition can be given to the concept of ether.

(b) The energy-stress tensor of gravitational fields can be defined in a satisfactory manner.

(c) The gravitational field energy of a particle is distributed continuously over the space and its integral is equal to the gravitational mass of the particle.

(d) There are proper gravitational waves, generated by oscillating matter and propagating with the velocity of light.

(e) There is a noticable ether drift which tends to increase the gravitational mass of a body of given intertial mass.

(f) The ratio of gravitational and inertial mass of radiating energy is twice the corresponding ratio for neutral static matter.

(g) Hubble's recession constant is equal to the reciprocal of the age of the universe.

An outstanding problem is to determine the coupling constant between the gravitational field and the cosmic time field. The value $\beta =1\mathrm{}$ is strongly suggested by cosmological considerations. An experimental determination is possible if the rate of advance of the perihelion of the Mercury orbit is known more accurately.

• Received 23 February 1954

DOI:https://doi.org/10.1103/PhysRev.97.212