In 1907 Einstein had the insight that bodies in free fall do not “feel” their own weight. This has been formalized in what is called “the principle of equivalence.” The principle motivated a critical analysis of the Newtonian and special-relativistic concepts of inertia, and it was indispensable to Einstein’s development of his theory of gravitation. A great deal has been written about the principle. Nearly all of this work has focused on the content of the principle and whether it has (...) any content in Einsteinian gravitation, but more remains to be said about its methodological role in the development of the theory. I argue that the principle should be understood as a kind of foundational principle known as a criterion of identity. This work extends and substantiates a recent account of the notion of a criterion of identity by William Demopoulos. Demopoulos argues that the notion can be employed more widely than in the foundations of arithmetic and that we see this in the development of physical theories, in particular space–time theories. This new account forms the basis of a general framework for applying a number of mathematical theories and for distinguishing between applied mathematical theories that are and are not empirically constrained. (shrink)

This chapter contains sections titled: Highlights of Past Literature Current Work Future Work.

Following Einstein's prediction of the gravitational bending of light, and in the course of experimental work aimed at its verification, only sporadic and at times misleading references have been made to Johann Georg von Soldner. In a paper published in 1804, Soldner derived the gravitational bending of light on the classical Newtonian basis and calculated its value around the sun with remarkable accuracy. Soldner's paper, inaccessible even in German, is now presented in English translation and put in the perspective of (...) Soldner's life and the science of his day and ours. (shrink)

Newton's methodology is significantly richer than the hypothetico-deductive model. It is informed by a richer ideal of empirical success that requires not just accurate prediction but also accurate measurement of parameters by the predicted phenomena. It accepts theory-mediated measurements and theoretical propositions as guides to research. All of these enrichments are exemplified in the classical response to Mercury's perihelion problem. Contrary to Kuhn, Newton's method endorses the radical transition from his theory to Einstein's. The richer themes of Newton's method are (...) strikingly realized in a challenge to general relativity from a new problem posed by Mercury's perihelion. †To contact the author, please write to: Talbot College, University of Western Ontario, London, Ontario, Canada N6A 3K7; e-mail: [email protected]. (shrink)

Ideas for explaining the mechanism of gravity involving the expansion of matter have been proposed several times since the 1890’s. Due to their radical nature and other reasons, these ideas have not gotten much attention. Another essential feature needed to augment the viability of the model proposed here---even more important than matter expansion---is that of space generation. I.e., the production of space by matter, involving motion into or outfrom a fourth spatial dimension. An experiment is proposed whose result would unequivocally (...) either falsify the model or support it. Analyses of star cluster velocity dispersions suggest that some support already exists. The simplest, most definitive way to test the model is to build and operate an apparatus that may be called a Small Low-Energy Non-Collider. Essentially the same experiment was proposed by Galileo in 1632. We are way overdue to at last bring to fruition this idea put forth by the Father of Modern Science so long ago. (shrink)