Mach’s Principle, Action at a Distance and Cosmology

Hoyle and Narlikar (HN) in the 1960’s [1]-[3] developed a theory of gravitation which was completely Machian and used both retarded and advanced waves to communicate gravitational influence between particles. The advanced waves, which travel backward in time, are difficult to visualize and although they are mathematically allowed by relativistic wave equations, they never really caught on. The HN theory reduced to Einstein’s theory of gravity in the smooth fluid approximation and a transformation into the rest frame of the fluid. Hawking [4] in 1965 pointed out a possible flaw in the theory. This involved integrating out into the distant future to account for all the advanced waves which might influence the mass of a particle here and now. Hawking used infinity as his upper time limit and showed the integral was divergent. We point out that since the universe is known to be expanding, and accelerating, the upper limit in the advanced wave time integral should not be infinite but is bounded by the Cosmic Event Horizon. This event horizon e H represents a barrier between future events that can be observed and those which cannot. We show that the advanced wave integral is finite when e H c , is used as the upper limit of the advanced wave integral. Hawking’s objection is no longer valid and the HN theory becomes a working theory once again.