A Lorentz-Poincaré Type Interpretation of the Weak Equivalence Principle

Abstract

The validity of the Weak Equivalence Principle relative to a local inertial frame is detailed in a scalar-vector gravitation model with Lorentz-Poincaré type interpretation. Given the previously established first Post-Newtonian concordance of dynamics with General Relativity, the principle is to this order compatible with GRT. The gravitationally modified Lorentz transformations, on which the observations in physical coordinates depend, are shown to provide a physical interpretation of parallel transport. A development of "geodesic" deviation in terms of the present model is given as well.

Lorentz-Poincaré type aspects of the matter Lagrangian in General Relativity Theory

“…The ensuing Hamiltonian formalism verifies till 1-PN correctly the gravitational phenomenology of GRT [3,4,5,6].…”

Is Spacetime as Physical as Is Space?

“…By the definition (21), this is the constant x ′ = φ(x) ∈ R 3 , whenever X = (T, x ′ ) remains in a given line l x v . Note that x is the position in the space 6 If one changes the time chart by (9), the definition (21) applied with θ ′ in the place of θ gives l ′…”

“…(Changing the origin of time is accomplished by changing the time chart θ, see Eq. (9).) This allows us to define the velocity, with respect to the uniformly moving space M v , of the particle having the general world line (10), parameterized by the time t according to (12).…”

“…(Light clocks can also be used to justify the "clock hypothesis" which states that a clock measures the proper time along a trajectory, and which is used not only in SR but also in relativistic gravity [15].) Once the "relativistic" effects of SR can thus be derived from "absolute" metrical effects of the motion through an "ether", it suggests itself to search for an L-P type theory of gravitation, in which gravitation also has metrical effects [1,9]. The foregoing introduction of the Minkowski spacetime as the product spacetime A 1 × A 3 endowed with the metric ( 35) is a way to formalize the L-P version of special relativity, as well as to define the background spacetime for L-P type theories of gravitation.…”

“…(The projection tensor has been defined by Cattaneo [10], it too depends on the reference fluid.) 9 But this other concept (used also after Cattaneo [10], e.g. [20,21,22,17]) is far less simple, especially when it comes to the definition of a relevant covariant derivative of spatial tensors.…”