Part of the theoretical motivation for improving the present level of testing of the equivalence principle is reviewed. The general rationale for optimizing the choice of pairs of materials to be tested is presented. One introduces a simpliied rationale based on a trichotomy of competing classes of theoretical models. 1. Why testing the equivalence principle ? Einstein introduced in 1907 1] wha...

In four-dimensional general relativity the spacetime outside of an isolated spherical star is described by an unique line element, which is the Schwarzschild metric. However, theories that envision our world as embedded in a larger universe, with more than four dimensions, lead to a number of possible non-Schwarzschild exteriors. In five-dimensional Kaluza-Klein gravity the condition that in th...

We introduce a Π1-uniformization principle and establish its equivalence with the set-theoretic hypothesis (ω1) = ω1. This principle is then applied to derive the equivalence, to suitable set-theoretic hypotheses, of the existence of Π1 maximal chains and thin maximal antichains in the Turing degrees. We also use the Π1-uniformization principle to study Martin’s conjectures on cones of Turing d...

We introduce a Π1-uniformization principle and establish its equivalence with the set-theoretic hypothesis (ω1) = ω1. This principle is then applied to derive the equivalence, to suitable set-theoretic hypotheses, of the existence of Π1 maximal chains and thin maximal antichains in the Turing degrees. We also use the Π1-uniformization principle to study Martin’s conjecture on cones of Turing de...

We discuss our understanding of the equivalence principle in both classical mechanics and quantum mechanics. We show that not only does the equivalence principle hold for the trajectories of quantum particles in a background gravitational field, but also that it is only because of this that the equivalence principle is even to be expected to hold for classical particles at all. While the equiva...

We discuss our understanding of the equivalence principle in both classical mechanics and quantum mechanics. We show that not only does the equivalence principle hold for the trajectories of quantum particles in a background gravitational field, but also that it is only because of this that the equivalence principle is even to be expected to hold for classical particles at all. While the equiva...