The Theory of Relativity and a Priori Knowledge

// The Theory ofRelativity -:::=-- and A Priori I(nowledg~ By llA S REICHE BACH./ / Translated and edited, wi.th an introduction, by Maria Reichenbach UNIVERSITY OF CALIFOR IA PRESS Berkeley and Los Angeles 1965 (~C Dedicated to ALBERT EINSTEIN <0 , R3\~~! UNIVERSITY OF CALIFOR IA PRESS BERKELEY AND Los ANGELES, CAu.FORNlA CAMBRIDGE UNIVERSITY PREss, LoNDON, E 'GLAND First published in German under the title Relativitiitsthem-je und Erkenntnis Apriori THIS TRANSLATION © 1965 BY THE RECENTS OF THE UNIVERSITY OF CALIFORNIA Library of Congress Catalog Card Number: 65-28456 DESIGNED BY DAVID PAULY PRINTED IN THE UNITED STATES OF AMERICA Contents Introduction to the English Edition Xl I. Introduction 1 II. The Contradictions Asserted by the Spe- cial Theory of Relativity 6 III. The Contradictions Asserted by the Gen- eral Theory of Relativity 22 IV. Knowledge as Coordination 34 V. Two Meanings of "A priori" and Kant's Implicit Presupposition 48 VI. The Refutation of Kant's Presupposition by the Theory of Relativity 61 VII. The Answer to the Critical Question by the Method of Logical Analysis 74 VIII. The Concept of Knowledge of the The- ory of Relativity as an Example of the Development of the Concept of Object 93 Reference Notes 109 I ., Introduction* Einstein's theory of relativity has greatly affected the fundamental principles of epistemology. It will not serve any purpose to deny this fact or to pretend that the physical theory changed only the concepts of physics while the philosophical truths remained in violate. Even though the theory of relativity concerns only relations of physical measurability and physical magnitudes, it must be admitted that these physical assertions contradict general philosophical principle. The philosophical axioms, even in their critical form, were always formulated in such a way that they re mained invariant with respect to specific interpreta tions but definitely excluded certain kinds of physical statements. Yet the theory of relativity selected exactly ., In regard to notes: the author's explanatory notes, which -f{ are not numbered, are printed as footnotes; so are the editor's notes, but the latter are numbered, the numbers being set in brackets. Finally, the author's reference notes, which are numbered consecutively, not chapter by chapter, will be found at the end of the book. .r 2 THE THEORY OF RELATIVITY § I TRODUCTION 3 those statements that had been regarded as inadmissible The general theory of relativity has greatly in and made them the guiding principles of its physical creased these difficulties. It has asserted nothing less as umptions. than that Euclidean geometry is not applicable to The special theory of relativity already made diffi physics. One should clearly understand the far-reach cult demands upon the tolerance of a critical philoso ing implications of this statement. Actually, for the last pher. It deprived time of its character of an irreversi hundred years tlle a priori. character of Euclidean ble proce s and asserted that eve.nts exist wh.ose ~em geometry had no longer been taken for granted. The poral succession may be assumed m the opposIte dIrec construction of non-Euclidean geometries had shown tion. This interpretation contradicts previous concepts, the possibility of conceptual systems contradicting the including the concept of time held by Kant. Occa well-known, intuitively evident axioms of Euclid. Rie sionally, philosophers have attempted to eliminate mann had developed a general theory of manifold in these difficulties through a distinction between "physi analytic form which contained "plane" space as a spe cal time" and "phenomenal time," by pointing out cial case. After Euclidean geometry had been deprived that time as subjective eXjJerience always remains an of its necessary character, its privileged character could irreversible sequence. But this distinction is not in be justified only if its intuitive evidence distinguished the Kantian tradition. For Kant, an essential trait of it from the other manifolds. This distinction became the a priori type of knowledge is that it constitutes a the only basis-in conformity with Kant-for the re presupposition of scientific knowledge and not merely quirement that specifically this geometry ought to be a subjective property of our sensations. Even though applied to the description of reality, that is, in physics. he speaks occasionally of the manner in which the Thus the refutation of Euclidean geometry was re objects "affect" our perceptions, he always believes duced to an objection to its purely conceptual justifi that this subjective form is simultaneously an objec cation. At the same time the empiricists expressed tive form of knowledge because the subjective com their doubt anew; from the possibility of constructing ponent is necessarily contained in the concept of other geometries they wanted to derive that the the object. He would not have conceded that one could orems of Euclidean geometry had received their intui apply a time order to physical events which was di~er tively evident character merely through experience ent from that inherent in the nature of the knowmg and familiarity. In the third place, mathematicians subject. It was, therefore, consistent when certain asserted that a geometrical system was established ac 0 .';. philosophical circles were already attacking the special cording to conventions and represented an empty theory of relativity by objections that had their roots schema that did not contain any statements about the in the logical constructions of Kant's philosophy. physical world. It was chosen on purely formal grounds 4 THE THEORY OF RELATIVITY § INTRODUCTION 5 and might equally well be replaced by a non-Euclidean still so much under discussion. We shall, therefore, schema.! In the face of these criticisms the objection choose the following procedure. First, we shall estab of the general theory of relativity embodies a com lish the contradictions existing between the theory pletely new idea. This theory asserts simply and of relativity and critical philosophy and indicate the clearly that the theorems of Euclidean geometry do assumptions and empirical data that the theory of not apply to our physical space. This statement differs relativity adduces for its assertions.s Subsequently, essentially from the other three points of view, which starting with an analysis of the concept of knowledge, have in common that they do not question the validity we shall investigate what assumptions are inherent of the Euclidean axioms and differ only with respect in Kant's theory of knowledge. By confronting these to the justification of this validity and its epistemologi assumptions with the results of our analysis of the cal interpretation. It is obvious that thereby critical theory of relativity, we shall decide in what sense philosophy, too, is faced with a brand-new question. Kant's theory has been refuted by experience. Finally, There is no doubt that Kant's transcendental aesthetics we shall modify the concept of a priori in such a way starts from the self-evident validity of the Euclidean that it will no longer contradict the theory of relativ axioms. Even though one might dispute whether Kant ity, but will, on the contrary, be confirmed by it on sees in their intuitive evidence the proof of his theory the basis of the theory's own concept of knowledge. of a priori space, or, conversely, in the a priori charac The method of this investigation is called the method ter of space the proof of their evidence, it remains of logical analysis. quite certain that his theory is incompatible with the invalidity of these axioms. Therefore, there are only two possibilities: either the theory of relativity is false, or Kant's philosophy needs to be modified in those parts which contradict Einstein.2 The present study is devoted to the investi gation of this question. The first possibility appears to be very doubtful because of the tremendous suc cess of the theory of relativity, its repeated empirical confirmation and its fertility for the formation of theoretical concepts. Yet we do not want to accept this physical theory unconditionally, especially since the epistemological interpretation of its statements is § SPECIAL THEORY OF RELATIVITY 7 unless, in addition to the transformation of the spatial II coordinates, a time transformation is performed which in turn leads to the relativization of simultaneity and the partial Teversibility of time. This contradiction 1he Contradictions Asserted certainly exists. We ask: What assumptions support Einstein's principles? by the Special Theory Galileo's principle of inertia is an empirical state ment. It is not intuitively obvious why a body that ofRelativity is not affected by a force should move uniformly. If we had not become so accustomed to this idea, we would at first probably assert the opposite. Accord ing to Galileo, the stationary state is also free of forces; but this implies the far-reaching assertion that uni form motion is mechanically equivalent to the state of rest. A force is defined in terms of physical relations. In the present as well as in the following chapter we It is not a priori evident, however, that a force occurs shall use the term "a priori" in Kant's sense; that is, only if it is accompanied by a change of velocity, that we shall call a priori what the forms of intuition or '; is, that the phenomena which we call the effects of a the concept of knowledge require as self-evident. We force are dependent upon the occurrence of accelera are doinO' this in order to arrive at exactly those con- o ..•. tion. 'tVith this interpretation Galileo's principle of tradictions that occur with respect to a pnon pnnCI- inertia is undoubtedly an empirical statement. pIes; for, of course, the theory of relativity contradicts But this principle can be formulated in another many other principles of traditional physics.

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