The Equivalence Principle as a Symmetry

Abstract

It is shown that the extra coordinate of 5D induced-matter and membrane theory is related in certain gauges to the inertial rest mass of a test particle.This implies that the Weak Equivalence Principle is a geometric symmetry, valid only in the limit in which the test mass is negligible compared to the source mass. Exact solutions illustrate this, and show the way to possible resolutions of the cosmological-constant and hierarchy problems.

On the 5D Extra-Force according to Basini–Capozziello–Ponce De Leon Formalism and five important features: Kar–Sinha Gravitational Bending of Light, Chung–Freese Superluminal Behaviour, Maartens–Clarkson Black Strings, experimental measures of Extra Dimensions on board International Space Station (ISS) and the existence of the Particle Z due to a higher dimensional spacetime

“…Note that this equation is almost the same of Kar-Sinha(see pg 1780 eq 13 in [3]) but without the Warp Field Φ.The M depicted here is the 4D rest-mass m 0 projection of a 5D rest-mass M 5 according to 85 see table of elementary particles at section 9 86 since we consider induced STM formalism our Einstein Equations would be given by eqs 3 in [9],9 in [12] and pg 1346(the appendix) of [13].We will consider the presented equation due to the Gregory-Laflamme stability conditions but future studies could be used to analyze in parallel both RS and STM formalisms 87 this is not new since both are describing the 5D Schwarzschild Black Hole…”

“…∂x u (50) 16 we will give the complete process 17 note that eq 49 resulting from this process will match [9] eq 24 and look also to [12] eq 3 18 we will give as in the previous case the complete process 19 compare eq 55 with [9] eq 24 and look for the + signal in this equation while [9] eq 24 only have the -sign…”

“…43 Working with diagonalized metrics the terms α,λ,µ,β and ν are all equal 44 see pg 129 in [1] and pg 2230 in [5] 45 see also pg 311 in [12] 46 Chung-Freese depends on the Extra Coordinate y but our Universe is in the Bulk y = 0 [4] eq 1 47 see pg 2038 in [4] Now we have a clear picture of why we cannot perceive the 5D dimension in empty space:The EinsteinHilbert Action reduces itself to a ordinary Action of a 3 + 1 spacetime ds 2 = g αβ dx α dx β .Of course if our Universe lies in the Bulk y = 0 a 5D motion will imply in a y = 0.…”

“…Also according to Basini-Capozziello the effective mass can be geometrically derived in a way that is valid for both flat and curved spacetime as follows:([1] eq 83, [5] eq 77 and [12] eq 19) 57 55 signature (+,-,-,-,-) and diagonalized metric 56 g 44 = − 1 Φ 2 .sign is -57 note that in this case we must also know the "shape" of the function χ(y)…”

“…58 see also [12] eq 20 59 in Basini-Capozziello work the Warp Factor Ω(y) = 1 or simplifying the notation:…”