The Principle of Relativity 1

The Principle of Relativity

Yutaka Tanaka

1. Einstein's Impact on Modern Science and Philosophy

It is difficult to overestimate the tremendous impact of Einstein's theory of relativity on contemporary physicists. Today, more than half a century after the so-called Einstein revolution, almost every textbook of physics takes his theory for granted. What once seemed paradoxical has become commonsense to students of physics. Taking a retrospective glance, we need a little imaginative power to understand the nature of the paradigm-change from Newton to Einstein. Concerning the drastic effect of Einstein's prediction that rays of light are bent as they pass in the neighborhood of the sun, Whitehead wrote in his memoirs:

"It was my good fortune to be present at the meeting of the Royal Society in London when the Astronomer Royal for England announced that the photographic plates of the famous eclipse, as measured by his colleagues in Greenwich Observatory, has verified the prediction of Einstein . . . The whole atmosphere of tense interest was exactly that of the Greek drama: we are the chorus commenting on the decree of destiny as disclosed in the development of a supreme incident. There was dramatic quality in the very staging: the traditional ceremonial, and in the background the picture of Newton to remind us that the greatest of scientific generalizations was, now, after more than two centuries, to receive its first modification."⁽¹⁾

The crucial point of the above drama was that the new theory, in spite of the risk of refutation, dared to predict that something should happen at the time of the eclipse, which was afterwards confirmed by experimental physicists. Moreover, the admission of the new theory involved abandonment of common notions which physicists had hitherto uncritically accepted. The very validity of Euclidian geometry, as applied to physical space, was now suspect in the light of relativistic theory. In other words, Einstein claimed that non-Euclidian geometry should hold in the presence of a strong gravitational field. The meaning of spatio-temporal magnitudes must be changed in such a way that the length of a rigid body and the lapse of time measured by clocks cannot remain unaltered after the transformation of coordinate systems.

Einstein's infiuence on contemporary philosophy was worth noticing, especially with regard to the logic of scientific research. For example, Karl Popper repeatedly emphasized the importance of Einstein's methodology as a paradigm of critical reason. He claimed that the traditional principles of science which had been thought of as a priori should be reformulated in such a way that they can be tested by empirical data. When he proposed the falsifiability-criterion as the principle of demarcation between science and metaphysics, he was certainly influenced by Einstein. What had impressed him most was that Einstein declared clearly what kind of empirical data should be counted as a refutation of his general theory of relativity. For example, he wrote that "if the red shift on spectrum caused by gravitational potential is not observed, the general relativity cannot be maintained."⁽²⁾ Revolutionary as he was, he admitted the refutability even of his own theory. According to Popper, such a self-critical attitude of Einstein's methodology, which was open to a new horizon of experience, was "radically different from the dogmatic ones of Marx, Freud, and Adler, to say nothing of their uncritical followers."⁽³⁾

Whereas Newton distinguished his principles from hypotheses in his dictum "hypotheses non fingo", Einstein willingly exposed fundamental principles of his own theory to the risk of being refuted. The alleged a prior principles of classical physics became so many empty formulae, devoid of empirical meaning, at the expense of their irrefutability. On the other hand, Einstein's principles, having passed through empirical tests, enables us to get much more information about the actual world. Einstein's theory, In spite of its revolutionary character, contains the principle of self-criticism which can be formulated within itself. It was natural that his theory had broken the dogmatic slumbers of philosophers who rested on a priori principles. The Kantian theory of space and time, which had accepted as a matter of fact the axioms of Euclidian geometry and Newtonian physics, could not embrace Einstein's theory without modifications. So the logical positivist were also under Einstein's influence when they denied the synthetic a priori. H. Reihenbach, A. J. Ayer, and other advocates of this movement treated Einstein as if he were a prophet in the new age of "scientific philosophy". But we must notice that Einstein did not think much of positivism, but held something beyond observable facts in high esteem. For example, he once said to Heisenberg:

"It may be heuristically useful to keep in mind what one has actually observed. But on principle, it is quite wrong to try founding a theory on observable magnitudes alone. In reality the very opposite happens. It is the theory which decides what we can observe . . . You should not seriously believe that none but observable magnitudes must go into a physical theory."⁽⁴⁾

A phenomenalistic approach is not sufficient if we are to go beyond the observable data and reach to the essence of natural knowledge. Nor can we reconstruct what may be called the philosophy of Einstein only by collecting his fragmentary comments on philosophical problems scattered through his writings. His philosophy was not explicitly systematized, so we had rather seek it in his mode of thinking as he grappled with the frontier problems of physics.

In The Meaning of Relativity, Einstein stressed the importance of conceptual analysis which must precede any system-building. Concerning the relation between inertia and gravitation, he said:

"The possibility of explaining the numerical equality of inertia and gravitation by the unity of their nature gives to the general theory of relativity, according to my conviction, such a superiority over the conceptions of classical mechanics, that all the difficulties encountered must be considered as small in comparison with this progress."⁽⁵⁾

It had been a well-known phenomenon since Galileo that material bodies fall with the same acceleration independently of their sizes or masses. Physicists had accepted it as an "irreducible stubborn fact", too commonplace to be posited as a problem. Why this kind of uniform acceleration should happen is beyond the reach of positivists. Tracing back the origin of numerical equality between gravitational and inertial masses to the unity of their essences, Einstein was able to construct the theory of general relativity. This kind of reasoning was, according to Einstein, necessary to the essential development of science. Taking an analogous example from the history of physics, we remember that first the numerical equality between the speed of light and that of electro-magnetic waves was discovered, and then the essential identity between both phenomena was theoretically propounded for the unified system of physics. Such questioning about the origin of measured equality, in spite of its seeming speculative analysis, was characteristic of Einstein's procedure.