Galilei proposed the principle of relativity, but not the “Galilean transformation”

Abstract

Galileo Galilei was the first scientist to hypothesize a universal principle of relativity, but he neither proposed, nor limited his principle to, the so-called “Galilean transformation.” The danger in calling the classical transformation “Galilean” is that students begin to believe that Galilei's principle of relativity is somehow limited to the classical transformation and classical mechanics, thus neglecting its universality. Because Galilei's 1632 statement [Dialogue Concerning the Two Chief World Systems—Ptolemaic and Copernican, 2nd ed., translated by S. Drake (University of California Press, Berkeley, 1967), pp. 186–188] of the principle is remarkably similar to Poincaré's well accepted statement [Proceedings of the Congress of Arts and Science, Universal Exposition, St. Louis, 1904, edited by H. J. Rogers (Houghton Mifflin and Company, Boston, 1904), Vol. 1, pp. 604–622], Galilei should be given greater recognition for it. However, the so-called Galilean transformation might be better named the “Euclidean space-time transformation” since it is shown here that universal Euclidean space actually requires time to be universal, that is, t′ = t. It is not usually realized that the Euclidean transformation assumes lightspeed to be infinite. Pedagogical thought should be given to combining the Galilean principle of relativity, the Euclidean transformation and Newton's mechanics as “Ordinary Relativity” to distinguish it from “Special Relativity.” This would have pedagogical and conceptual value as a model and precursor to special relativity. Finally, it is suggested that the current use of “relativistic” is incorrect when applied exclusively to special relativity, for it implies that classical mechanics is non-relativistic.