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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.
Though Einstein did not formulate his own standpoints in philosophical terminology, we may tentatively summarise them as follows:
(1) The immanent epistemology in the forma/ principles of Einstein's theory, especially the special and the general principles of relativity. According to this epistemology, such entities as absolute space, absolute time, and absolute inertial systems, should be excluded from the physical theories. Natural phenomena, observed from a certain standpoint (coordinate system of reference), should not be considered as absolute, but always as relative to some observers. But the same principle prohibits the existence of a privileged observer. All observers are equal, for it is postulated that the natural laws should be formulated in such a way that the same mathematical forms hold in every system of reference.
(2) The essentialism implicit in the material principles of Einstein's theory, such as the constant velocity of light, and the principle of equivalence. These principles, though empirically refutable, should give some information about the essential structures of the world. For example, the constant velocity of light plays the essential role of mediation between mass and energy. The principle of equivalence, if accepted, would necessarily reform our ideas of space and time. We must adopt the curved space of non-Euclidean geometry in the presence of a gravitational field.
(3) The deterministic world-view in the background of Einstein's cosmology. The characteristic of relativistic cosmology is that uncertainty, or contingency totally disappears in the four dimensional space-time: everything should be determined sub specie aeternitatis. The appearance of contingency is due to our ignorance of necessity. It was this kind of Spinozism that forced Einstein to reject the non-deterministic interpretation of quantum mechanics.
In order to estimate a physical theory, it is not enough to understand its philosophical background. We must also know to what extent it has passed through the empirical tests. What we must bear in mind is that while the special theory of relativity, with its abundant empirical supports, has won the approval of almost every physicist, the general theory of relativity, in spite of its philosophical importance, has been treated, not as decisive, but as one of many competing gravitational theories. This is because of the comparatively few number of crucial tests, whose accuracy has often proved not sufficient enough to be reliable. It is not without reason that the general theory has been isolated from other advanced fields of physics. But thanks to the improvement of experimental techniques and the development of astronomy, the general theory of relativity has again become the center of interest among experimental physicists.
There are many theories of gravitation known as varieties of Einstein's theory, e.g. Brans-Dicke theory. famous for being faithful to Mach's principle, scalar- and vector-tensor theories, etc. From the philosophical point of view, the most interesting is Whitehead's theory of relativity. This theory, originally published in 1922, has a different paradigm from Einstein's, elegant and simple in mathematical formulation with its own philosophical background. It has been called as "a thorn in Einstein's side", because it agrees with Einstein in its prediction for all the classical tests. Whitehead's theory is closely connected with his philosophy of nature and his metaphysics. We cannot understand it without paying due attention to his philosophy. Comparing it with Einstein's theory, we may summarize the main oppositions between them as follows:
( 1) Whitehead's theory does not presuppose "the principle of relativity" in Einstein's sense. It contains a subsystem which corresponds to Einstein's theory of special relativity, but it can do without "the principle of special relativity" and "the principle of the constant velocity of light." For example, it derives the Lorentz Transformation only in terms of the weak condition concerning the symmetry and uniformity of space-time. Moreover, "the principle of general relativity" does not hold in Whitehead's theory of gravitation, in which the inertial systems are not equivalent to the rotating systems of reference.
(2) Whitehead rejected "the principle of equivalence" which was the cornerstone of Einstein's theory oj'genera/ relativity. According to Whitehead, there is no reason why we should give privileged status to gravitational fields with respect to the space-time metric. They should be treated on a par with other physical fields. The gravitational and inertial forces are, therefore on principle, distinguished from each other in his theory.
(3) Whitehead did not adopt the deterministic world-view in his background cosmology. According to his philosophy of nature, natural laws only partially restrict future contingency. The concept of matter as the substance of nature disappears with his rejection both of Cartesian dualism and of Spinoza's monism. The concept of event, or of duration which is the field of creative becoming, plays the central role in his theory.
Thus we have to say that Whitehead's theory is different from Einstein's with respect both to the formal and to the material principles, in addition to the difference of world-views in the background.
I don't intend to decide by an outside criterion which theory is better, but to consider each in its own context. It is not easy for us to compare between theories with different paradigms, and the simple data cannot tell us crucial matters by themselves. What we want is the integration of the two paradigms. This does not mean that the problem of empirical tests might well be devalued. On the contrary, as long as we discuss physics, we must try to formulate theories in such a way that they are refutable by possible observation. The problem is that there exists a difference between them concerning the kind of principles that are subject to empirical refutation.
Whitehead once said of Einstein that "the worst homage we can pay to genius is to accept uncritically formulations of truths which we owe to it." This kind of critical spirit will become the guiding thread in the following consideration, with proviso that it should be the case with Whitehead as well.
What we must notice before discussing empirical
tests is that Whitehead's principle of relativity has a different
meaning from that of Einstein's. Taking into consideration the
importance of the Whiteheadian relativity principle, we must first
make clear what he means by it in the context of his own philosophy.