On a Theoretical Proof of the Weak Equivalence Principle from within the confines of Newtonian Gravitation.

Abstract

The great Italian scientist and philosopher, Galileo Galilee, is reported to have stood at the learning tower of Pisa in Italy and famously dropped objects of different masses (and compositions), thereby demonstrating that the motion of matter in a gravitational field is independent of the body’s composition since these objects, despite their different masses (and compositions), their free-fall time was practically equal. By so doing, Galileo demolished a more than one and a half millennium of dogma that had been set forth by the Greek philosopher, Aristotle, namely that, in a gravitational field, heavier objects fall faster than lighter ones. Galileo’s conclusion is a posteriori justified current scientific dogma, we all accept this as a durable fact of experience. Gently and modestly, this reading appears to furnish this hypothesis. We unambiguously demonstrate beyond any shadow of doubt that Newtonian gravitation implies that gravitational and inertial mass are equal.