Mach's principle, Action at a Distance and Cosmology

TL;DR

This paper revisits Hoyle and Narlikar's Machian gravity theory with advanced and retarded waves, arguing that considering the cosmic event horizon makes the theory finite and viable, countering previous criticisms about divergence.

Contribution

It demonstrates that incorporating the cosmic event horizon into the HN theory resolves divergence issues, revitalizing a Machian gravitational framework with advanced waves.

Findings

Advanced wave integral is finite when considering the cosmic event horizon.

The HN theory reduces to Einstein's gravity in the fluid approximation.

The theory remains consistent with an expanding, accelerating universe.

Abstract

Hoyle and Narlikar (HN) in the 1960's 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. Unfortunately the theory has been ignored by much of the General Relativity community since it was developed with the static universe in mind. However, it is easy to drop the static universe condition (by dropping the "C"-field matter creation terms) and then you have a perfectly good theory of gravitation. Hawking 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 would like to 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 $H_e$ represents a barrier between future events that can be observed and those which cannot. We maintain that the advanced integral is in fact finite when the cosmic event horizon is taken into account, since the upper limit of the advanced wave integral becomes $H_e/c$. Hawking's objection is no longer valid and the HN theory becomes a working theory once again.