A Modified Lorentz-Transformation–Based Gravity Model Confirming Basic GRT Experiments

Abstract

Implementing Poincaré's geometric conventionalism a scalar Lorentz-covariant gravity model is obtained based on gravitationally modified Lorentz transformations (or GMLT). The modification essentially consists of an appropriate space-time and momentum-energy scaling ("normalization") relative to a nondynamical flat background geometry according to an isotropic, nonsingular gravitational affecting function Φ(r). Elimination of the gravitationally unaffected S 0 perspective by local composition of space-time GMLT recovers the local Minkowskian metric and thus preserves the invariance of the locally observed velocity of light. The associated energy-momentum GMLT provides a covariant Hamiltonian description for test particles and photons which, in a static gravitational field configuration, endorses the four 'basic' experiments for testing General Relativity Theory: gravitational i) deflection of light, ii) precession of perihelia, iii) delay of radar echo, iv) shift of spectral lines. The model recovers the Lagrangian of the Lorentz-Poincaré gravity model by Torgny Sjödin and integrates elements of the precursor gravitational theories, with spatially Variable Speed of Light (VSL) by Einstein and Abraham, and gravitationally variable mass by Nordström.

A Lorentz-Poincaré Type Interpretation of the Weak Equivalence Principle

“…These transformations give the Hamiltonian expressions for particles and photons in the unaffected perspective by simply assuming the special relativistic expressions in the affected perspective. With the resulting Hamiltonian, the equations of motion verify till 1-PN the gravitational phenomenology of GRT [5]. In fact, in the L-P model each quantity with different physical dimension is expected to transform according to a different power of the scaling function and according to covariant or contravariant GMLT's, the former aspect is similar to the gravitation model by Dicke [15].…”

“…In the latter model the acceleration was obtained by a coordinate transformation; from coordinate space and time to local coordinates of the static observer [4], while the coordinate space acceleration itself was obtained by a Hamiltonian principle [5].…”

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].…”

A look at the abandoned contributions to cosmology of Dirac, Sciama, and Dicke

“…[25,26,27]), the representations in terms of a spatially varying speed of light (e.g. [20,28,15,29,30]) have to gain yet broad acceptance.…”

“…[25][26][27]), the representations in terms of a spatially varying speed of light (e.g. [15,20,[28][29][30]) have to gain yet broad acceptance. 21 In general, there is a wide-ranging observational agreement with conventional cosmology due to the dynamics of physical units, whose relations to each other change so slowly that observational differences, if any, remain minute.…”