The Use and Ultimate Validity of Invariance Principles

Abstract

Let me first mention the three fundamental concepts of physics of which the invariance principle is one: initial conditions, laws of nature, invariance principles or symmetries. All of them underwent enormous changes in our century, the invariance principles perhaps least. The separation of initial conditions and laws of nature was made with great clarity by Newton and I consider this his greatest accomplishment, perhaps even greater than the discovery of his gravitational law. The symmetries seem to have been discovered and well formulated first by Galileo, perhaps independently by Newton. Some of them are obvious from everyday life, such as the laws of both space and time displacement invariances. If it would require a different kind of effort to pick up this pencil in this room from that of picking it up in the next room, or if had to be done in a different way tomorrow from the way it can be done today, our whole life would be different — if at all possible. But the invariance with respect to a uniform motion along a straight line does not manifest itself in everyday life — Aristotles’ laws of physics surely deny it and the lack of its recognition led to much of the opposition to railroads. Perhaps I mention also that the assumption of the existence of ether also led to questioning this invariance even by rather recent outstanding scientists. Since the days of Galileo and Einstein the only significant change in the invariance principles was Einstein’s introduction of the relativity theories.