Why gravity experiments are so exciting

Abstract
Being the most fundamental interaction gravity not only describes a particular interaction between matter, but also covers issues like the notion of space and time, the role of the observer and the relativistic measurement process. Gravity is geometry and, as a consequence, allows for the existence of black holes, non-trivial topologies, a cosmological big bang, time-travel, warp drive, and other phenomena not known from non-relativistic physics. Here we present the experimental basis of General Relativity, in particular its foundations encoded in the Einstein Equivalence Principle and its predictions in the weak and strong gravity regime. We discuss various routes to search for effects possibly signaling effects of the looked for quantum theory of gravity. We lay emphasis on assumptions to be tested which are only rarely discussed in the literature like tests of Newton's axioms, tests of conservation laws, etc. We propose an experiment testing the order of time derivatives in the equation of motion.