An embedding for general relativity with variable rest mass

There is considerable interest currently in theories of gravity where rest masses vary slowly with time. A new theory of this type is proposed which is believed to be superior to others, and which contains Einstein's theory embedded within it. The theory is five dimensional, where the extra coordinate is x4 is equivalent to Gm/c2 (G is the Newtonian gravitational parameter, c the velocity of light, and m the mass). The theory reduces to Einstein's if w is equivalent to (G/c3) dm/dt = O and the fifth dimension is absent. The theory agrees with observation provided w << 1, but the size of w in the real world can only be determined by experiment. (author)