A "Lorentz-Poincare"-Type Interpretation of Relativistic Gravitation

TL;DR

This paper explores a Lorentz-Poincaré interpretation of relativistic gravitation, extending it into General Relativity at first Post-Newtonian order using modified Lorentz transformations and scalar fields.

Contribution

It demonstrates that a Lorentz-Poincaré framework can be extended into GRT with gravitationally modified Lorentz transformations maintaining light speed invariance.

Findings

Model obeys the Weak Equivalence Principle

Acceleration transformations match those of GRT

First Post-Newtonian approximation is recovered

Abstract

The nature of 'time', 'space' and 'reality' are to large extent dependent on our interpretation of Special (SRT) and General Relativity Theory (GRT). In SRT essentially two distinct interpretations exist; the "geometrical" interpretation by Einstein based on the Principle of Relativity and the Invariance of the velocity of light and, the "physical" Lorentz-Poincar\'e interpretation with underpinning by rod contractions, clock slowing and light synchronization, see e.g. (Bohm 1965, Bell 1987). It can be questioned whether the "Lorentz-Poincar\'e"-interpretation of SRT can be continued into GRT. We have shown that till first Post-Newtonian order this is indeed possible (Broekaert 2004). This requires the introduction of gravitationally modified Lorentz transformations, with an intrinsical spatially-variable speed of light $c(r)$, a scalar scaling field $\Phi$ and induced velocity field $w$. Still the invariance of the locally observed velocity of light is maintained (Broekaert 2005). The Hamiltonian description of particles and photons recovers the 1-PN approximation of GRT. At present we show the model does obey the Weak Equivalence Principle from a fixed perspective, and that the implied acceleration transformations are equivalent with those of GRT.