Mach, Einstein, and the Search for Reality

In the history of ideas of our century, there is a chapter that might be entitled ‘The Philosophical Pilgrimage of Albert Einstein’, a pilgrimage from a philosophy of science in which sensationism and empiricism were at the center, to one in which the basis was a rational realism. This essay,* a portion of a more extensive study1, is concerned with Einstein’s gradual philosophical reorientation, particularly as it has become discernible during the work on his largely unpublished scientific correspondence.2

Ostwald "most highly among all scholars currently active in physics." 4 The choice of Ostwald was significant. He was, of course, not only one of the foremost chemists, but also an active "philosopher scientist" during the 1890's and 1900's, a time of turmoil in the physical sciences as well as in the philosophy of science. The op ponents of kinetic, mechanical, or materialistic views of natural phenomena were vociferous. They objected to atomic theory and gained great strength from the victories of thermodynamics, a field in which no knowledge or assumption was needed concerning the detailed nature of material substances (for example, for an under standing of heat engines ).
Ostwald was a major critic of the mechanical interpretation of physical phenomena, as were Helm, Stallo, and Mach. Their form of positivism?as against the sophisticated logical positivism de veloped later in Carnap and Ayer s work?provided an epistemol ogy for the new phenomenologically based science of correlated observations, linking energetics and sensationism. In the second (1893) edition of his influential textbook on chemistry, Ostwald had given up the mechanical treatment of his first edition for Helm's "energetic" one. "Hypothetical" quantities such as atomic entities were to be omitted; instead, these authors claimed they were satisfied, as Merz wrote around 1904, with "measuring such quantities as are presented directly in observation, such as energy, mass, pressure, volume, temperature, heat, electrical potential, etc., without reducing them to imaginary mechanisms or kinetic quanti ties." They condemned such conceptions as the ether, with proper ties not accessible to direct observation, and they issued a call "to consider anew the ultimate principles of all physical reasoning, notably the scope and validity of the Newtonian laws of motion and of the conceptions of force and action, of absolute and relative motion."5 All these iconoclastic demands?except anti-atomism?must have been congenial to the young Einstein who, according to his colleague Joseph Sauter, was fond of calling himself "a heretic."6 Thus, we may well suspect that Einstein felt sympathetic to Ost wald who denied in the Allgemeine Chemie1 that "the assumption of that medium, the ether, is unavoidable. To me it does not seem to be so. . . . There is no need to inquire for a carrier of it when we find it anywhere. This enables us to look upon radiant energy as independently existing in space." It is a position quite consistent with that shown later in Einstein s papers of 1905 on photon theory and relativity theory.
In addition, it is worth noting that Einstein, in applying to Ostwald's laboratory, seemed to conceive of himself as an experi mentalist. We know from many sources that in his student years in Z?rich Einstein's earlier childhood interest in mathematics had slackened considerably. In the Autobiographical Notes, 6 Einstein reported: "I really could have gotten a sound mathematical edu cation. However, I worked most of the time in the physical labora tory, fascinated by the direct contact with experience" (p. 15). To this, one of his few reliable biographers adds: "No one could stir him to visit the mathematical seminars. . . . He did not yet see the possibility of seizing that formative power resident in mathe matics, which later became the guide of his work. ... He wanted to proceed quite empirically, to suit his scientific feeling of the time. ... As a natural scientist, he was a pure empiricist" (Anton Reiser, Albert Einstein [New York, 1930], pp. 51-52.) Ostwald's main philosophical ally was the prolific and versatile Austrian physicist and philosopher Ernst Mach (1838Mach ( -1916, whose main work Einstein had read avidly in his student years and with whom he was destined to have later the encounters that form a main concern of this paper. Mach's major book, The Science of Mechanics,9 first published in 1883, is perhaps most widely known for its discussion of Newton's Principia, in particular for its dev astating critique of what Mach called the "conceptual monstrosity of absolute space" (Preface, 7th Edition, 1912)?a conceptual mon strosity because it is "purely a thought-thing which cannot be pointed to in experience." Starting from his analysis of Newtonian presuppositions, Mach proceeded in his announced program of eliminating all metaphysical ideas from science. As Mach said quite bluntly in the preface to the first edition of The Science of Me chanics: "This work is not a text to drill theorems of mechanics. when going from the field of physics to that of physiology or psychol ogy. Such a firm point of view he reached by going back to that which is given before all scientific research: namely, the world of sensations. . . . Since all our testimony concerning the so-called external world rely only on sensations, Mach held that we can and must take these sensations and complexes of sensations to be the sole contents [Gegenst?nde] of those testimonies, and, therefore, that there is no need to assume in addition an unknown reality hidden behind the sensations. With that, the existence der Dinge an sich is removed as an unjustified and unnecessary assump tion. A body, a physical object, is nothing else than a complex, a more or less firm [we would say, invariant] pattern of sensations, i.e., of colors, sounds, sensations of heat and pressure, etc.
There exists in this world nothing whatever other than sensations and their connections. In place of the word "sensations," Mach liked to use rather the more neutral word "elements." . . . [As is particularly clear in Mach's book Erkenntnis und Irrtum,] scientific knowledge of the world consists, according to Mach, in nothing else than the simplest possible description of the connections between the elements, and it has as its only aim the intellectual mastery of those facts by means of the least possible effort of thought This aim is reached by means of a more and more complete "accommodation of the thoughts to one another." This is the formulation by Mach of his famous "principle of the economy of thought."11 The influence of Mach's point of view, particularly in the Ger man-speaking countries, was enormous?on physics, on physiology, on psychology, and on the fields of the history and the philosophy of science12 (not to mention Mach's profound effect on the young Lenin, Hofmannstal, Musils, among many others outside the sci ences). Strangely neglected by recent scholarship?there is not even a major biography?Mach has in the last two or three years again become the subject of a number of promising studies. To be sure, Mach himself always liked to insist that he was beleaguered and neglected, and that he did not have, or wish to have, a philo sophical system; yet his philosophical ideas and attitudes had be come so widely a part of the intellectual equipment of the period from the 1880's on that Einstein was quite right in saying later that "even those who think of themselves as Mach's opponents hardly know how much of Mach's views they have, as it were, imbibed with their mother's milk. "13 The problems of physics themselves at that time helped to reinforce the appeal of the new philosophical attitude urged by Mach. The great program of nineteenth-century physics, the rec onciliation of the notions of ether, matter, and electricity by means of mechanistic pictures and hypotheses, had led to enormities?for 639 example, Larmor's proposal that the electron is a permanent but movable state of twist or strain in the ether, forming discontinuous particles of electricity and possibly of all ponderable matter. To many of the younger physicists of the time, attacking the problems of physics with conceptions inherited from classical nineteenth century physics did not seem to lead anywhere. And here Mach 1897. The book exerted a deep and persisting impression upon me . . ., owing to its physical orientation toward fundamental concepts and fundamental laws." As Einstein noted in his Auto biographical Notes8 written in 1946, Ernst Mach's The Science of Mechanics "shook this dogmatic faith" in "mechanics as the final basis of all physical thinking. . . . This book exercised a profound influence upon me in this regard while I was a student. I see Mach's greatness in his incorruptible skepticism and independence; in my younger years, however, Mach's epistemological position also influenced me very greatly ( p. 21 )." As the long correspondence between those old friends shows, Besso remained a loyal Machist to the end. Thus, writing to Ein stein on 8 December 1947, he still said: "As far as the history of science is concerned, it appears to me that Mach stands at the center of the development of the last 50 or 70 years." Is it not true, Besso also asked, "that this introduction [to Mach] fell into a phase of development of the young physicist [Einstein]  cation of reality with what is given by sensations, the "events," rather than putting reality on a plane beyond or behind sense experience. From the outset, the instrumentalist, and hence sensationist, views of measurement and of the concepts of space and time are strikingly evident The key concept in the early part of the 1905 paper is introduced at the top of the third page in a straight forward way. Indeed, Leopold Infeld in his biography of Einstein called them "the simplest sentence[s] I have ever encountered in a scientific paper." Einstein wrote: "We have to take into account that all our judgments in which time plays a part are always judg ments of simultaneous events. If for instance I say, 'that train arrived here at seven o'clock/ I mean something like this: 'The pointing of the small hand of my watch to seven and the arrival of the train are simultaneous events/ "1T The basic concept introduced here, one that overlaps almost entirely Mach's basic "elements," is Einstein's concept of events (Ereignisse)?a word that recurs in Einstein's paper about a dozen times immediately following this citation. Transposed into Minkow ski's later formulation of relativity, Einstein's "events" are the inter sections of particular "word lines," say that of the train and that clock located at the place of the event" (p. 894). We can say that just as the time of an event assumes meaning only when it connects with our consciousness through sense experience (that is, when it is subjected to measurement-in-principle by means of a clock pres ent at the same place), so also is the place, or space coordinate, of an event meaningful only if it enters our sensory experience while being subjected to measurement-in-principle (that is, by means of meter sticks present on that occasion at the same time ) .18 This was the kind of operationalist message which, for most of his readers, overshadowed all other philosophical aspects in Einstein's paper. His work was enthusiastically embraced by the groups who saw themselves as philosophical heirs of Mach, the Vienna Circle of neopositivists and its predecessors and related followers,19 providing a tremendous boost for the philosophy that had initially helped to nurture it. A typical response welcoming the relativity theory as "the victory over the metaphysics of absolutes in the conceptions of space and time ... a mighty impulse for the development of the philosophical point of view of our time," was extended by J. Petzoldt in the inaugural session of the Gesell schaft f?r Positivistische Philosophie in Berlin, 11 November 1912.20 Mich?le Besso, who had heard the message from Einstein before anyone else, had exclaimed: "In the setting of Minkowski's space time framework, it was now first possible to carry through the thought which the great mathematician, Bernhard Riemann, had grasped: 'The space-time framework itself is formed by the events in it.'"21 To be sure, re-reading Einstein's paper with the wisdom of hindsight, as we shall do presently, we can find in it also very different trends, warning of the possibility that "reality" in the end is not going to be left identical with "events." There are premoni tions that sensory experiences, in Einstein's later work, will not be regarded as the chief building blocks of the "world," that the laws of physics themselves will be seen to be built into the event-world as the undergirding structure "governing" the pattern of events.
Such precursors appear even earlier, in one of Einstein's early letters in the Archives. Addressed to his friend Marcel Grossmann, it is dated 14 April 1901, when Einstein believed he had found a connection between Newtonian forces and the forces of attraction between molecules: "It is a wonderful feeling to recognize the unity of a complex of appearances which, to direct sense experience, seem to be separate things." Already there is a hint here of the 642 high value that will be placed on intuited unity and the limited role seen for evident sense experience.
But all this was not yet ready to come into full view, even to the author. Taking the early papers as a whole, and in the context of the physics of the day, we find that Einstein's philosophical pilgrimage did start on the historic ground of positivism. Moreover, Einstein thought so himself, and confessed as much in letters to Ernst Mach.

The Einstein-Mach Letters
In the history of recent science, the relation between Einstein and Mach is an important topic that has begun to interest a number of scholars. Indeed, it is a drama of which we can sketch here four stages: Einstein Happily, the correspondence is preserved at least in part. A few letters have been found, all from Einstein to Mach. Those of concern here are part of an exchange between 1909 and 1913, and they testify to Einstein's deeply felt attraction to Mach's viewpoint, just at a time when the mighty Mach himself?forty years senior to the young Einstein whose work was just becoming widely known?had for his part embraced the relativity theory publicly by writing in the second (1909) edition of Conservation of Energy: "I subscribe, then, to the principle of relativity, which is also firmly upheld in my Mechanics and W?rmelehre."22 In the first letter, Einstein writes from Berne on 9 August 1909. Having thanked Mach for sending him the book on the law of conservation of energy, he adds: "I know, of course, your main publications very well, of which I most admire your book on Mechanics. You have had such a strong influ ence upon the epistemological conceptions of the younger genera tion of physicists that even your opponents today, such as Planck, undoubtedly would have been called Mach followers by physicists of the kind that was typical a few decades ago." It will be important for our analysis to remember that Planck was Einstein's earliest patron in scientific circles. It was Planck who, in 1905, as editor of the Annalen der Physik, received Einstein's first relativity paper and thereupon held a review seminar on the paper in Berlin. Planck defended Einstein's work on relativity in public meetings from the beginning, and by 1913 had succeeded in persuading his German colleagues to invite Einstein to the Kaiser Wilhelm-Gesellschaft in Berlin. With a polemical essay "Against the New Energetics" in 1896, he had made clear his position, and by 1909 Planck was one of the few opponents of Mach, and scientifi cally the most prominent one. He had just written a famous attack, Die Einheit des physikalischen Weltbildes. Far from accept ing Mach's view that, as he put it, "Nothing is real except the per ceptions, and all natural science is ultimately an economic adapta tion of our ideas to our perceptions," Planck held to the entirely antithetical position that a basic aim of science is "the finding of a fixed world picture independent of the variation of time and peo ple," or, more generally, "the complete liberation of the physical picture from the individuality of the separate intellects."23 At least by implication in Einstein's remarks to Mach, he dissociated himself from allegiance to Planck's view. It may also not be irrelevant that just at that time Einstein, who since 1906 had been objecting to inconsistencies in Planck's quantum theory, was preparing his first major invited paper before a scientific congress, the eighty-first meeting of the Naturforscherversammlung, announced for Septem ber, 1909, in Salzburg. Einstein Here, Einstein is referring delicately to the Mach Principle, which he had been putting at the center of the developing theory.24 Mach responded by sending Einstein a copy of one of his books, probably the Analysis of Sensations.
In the last of these letters to Mach (who was now seventy-five years old, and for some years had been paralyzed), Einstein writes from Z?rich on 25 June 1913: Recently you have probably received my new publication on Relativity and Gravitation which I have at last finished after unending labor and painful doubt. [This must have been the "Entwurf einer verallgemein erten Relativit?tstheorie und einer Theorie der Gravitation/' written with Marcel Grossmann.25] Next year at the solar eclipse it will turn out whether the light rays are bent by the sun, in other words whether the basic and fundamental assumption of the equivalence of the acceleration of the reference frame and of the gravitational field really holds. If so, then your inspired investigations into the foundations of mechanics? despite Planck's unjust criticism?will receive a splendid confirmation.
For it is a necessary consequence that inertia has its origin in a kind of mutual interaction of bodies, fully in the sense of your critique of New ton's bucket experiment.26 The Paths Diverge In your last letter I find, on re-reading, something which makes me angry: That speculation has proved itself to be superior to empiricism. You are thinking here about the development of relativity theory. How ever, I find that this development teaches something else, that it is prac tically the opposite, namely that a theory which wishes to deserve trust must be built upon generalizable facts. Careful reading of this letter shows us that already here there is evidence of divergence between the conception of "fact" as under stood by Einstein and "fact" as understood by a true Machist. The impossibility of the perpetuum mobile, the first law of Newton, the constancy of light velocity, the validity of Maxwell's equations, the equivalence of inertial and gravitational mass?none of these would have been called "facts of experience" by Mach. Indeed, Mach might have insisted that?to use one of his favorite battle words?it is evidence of "dogmatism" not to regard all these conceptual con structs as continually in need of probing re-examination; thus, Mach had written:27 ... for me, matter, time and space are still problems, to which, inci dentally, the physicists (Lorentz, Einstein, Minkowski) are also slowly approaching.
Similar evidence of Einstein's gradual apostasy appears in a Mach would have applauded Einstein's life-long suspicion of formal epistemological systems, but how strange would he have found this use of the word empirical to characterize the hypothesis of the equivalence of all inertial systems with respect to light! What we see forming slowly here is Einstein's view that the fundamental role played by experience in the construction of fundamental physi cal theory is, after all, not through the "atom" of experience, not through the individual sensation or the protocol sentence, but through some creative digest or synthesis of "die gesammten Er fahrungstatsachen," the totality of physical experience.28 But all this was still hidden. Until Mach's death, and for several years after, Einstein considered and declared himself a disciple of Mach.
In the meantime, however, unknown to Einstein and everyone else, a time bomb had been ticking away. Set in 1913, it went oflF in 1921, five years after Mach's death, when Mach's The Principles of Physical Optics was published at last. Mach's preface was dated July, 1913?perhaps a few days or, at most, a few weeks after Mach had received Einstein's last, enthusiastic letter and the article on general relativity theory. In a well-known passage in the preface (but one usually found in an inaccurate translation), Mach had written: It was to be expected that philosophers and physicists should carry on a crusade against me, for, as I have repeatedly observed, I was merely an unprejudiced rambler endowed with original ideas, in varied fields of knowledge. I must, however, as assuredly disclaim to be a forerunner of the relativists as I personally reject the atomistic doctrine of the present day school, or church. The reason why, and the extent to which, I reject [ablehne] the present-day relativity theory, which I find to be growing more and more dogmatical, together with the particular reasons which have led me to such a view?considerations based on the physiology of the senses, epistemological doubts, and above all the insight resulting from my experiments?must remain to be treated in the sequel [a sequel which was never published].
Certainly, Einstein was deeply disappointed by this belated dis^ closure of Mach's sudden dismissal of the relativity theory. Some months later, during a lecture on 6 April 1922 in Paris, in a discus sion with the anti-Machist philosopher Emile Meyersori, Einstein allowed in a widely reported remark that Mach was "un bon m?chaniden," but a "deplorable philosophe." 29 We can well understand that Mach's rejection was at heart very painful, the more so as it was somehow Einstein's tragic fate to have the contribution he most cared about rejected by the very men whose approval and understanding he would have most gladly had ?a situation not unknown in the history of science. In addition to Mach I see his weakness in this, that he more or less believed science to consist in a mere ordering of empirical material; that is to say, he did not recog nize the freely constructive element in formation of concepts. In a way he thought that theories arise through discoveries and not through inven tions. He even went so far that he regarded "sensations" not only as ma terial which has to be investigated, but, as it were, as the building blocks of the real world; thereby, he believed, he could overcome the difference between psychology and physics. If he had drawn the full consequences, he would have had to reject not only atomism but also the idea of a physical reality. The list of evidences is long. Here only a few examples can be given, the first from the 1905 relativity paper itself: What had made it really work was that it contained and combined elements based on two entirely different philosophies of science?not merely the empiricist-operationist component, but the courageous initial pos tulation, in the second paragraph, of two thematic hypotheses ( one on the constancy of light velocity and the other on the extension of the principle of relativity to all branches of physics), two postulates for which there was and can be no direct empirical confirmation.
For a long time, Einstein did not draw attention to this feature.
In a lecture at King's College, London, in 1921, just before the posthumous publication of Mach's attack, Einstein still was protest ing that the origin of relativity theory lay in the facts of direct experience: ... I am anxious to draw attention to the fact that this theory is not spec ulative in origin; it owes its invention entirely to the desire to make physical theory fit observed fact as well as possible. We have here no revolutionary act, but the natural continuation of a line that can be traced through centuries. The abandonment of certain notions connected with space, time, and motion, hitherto treated as fundamentals, must not be regarded as arbitrary, but only as conditioned by observed facts. 34 give the Herbert Spencer Lecture at Oxford entitled "On the Method of Theoretical Physics," the more complex epistemology that was in fact inherent in his work from the beginning had begun to be expressed. He opened this lecture with the significant sen tence: "If you want to find out anything from the theoretical physi cists about the methods they use, I advise you to stick closely to one principle: Don't listen to their words, fix your attention on their deeds." He went on to divide the tasks of experience and reason in a very different way from that advocated in his earlier visit to England: We are concerned with the eternal antithesis between the two insepar able components of our knowledge, the empirical and the rational. . . .
The structure of the system is the work of reason; the empirical contents and their mutual relations must find their representation in the conclu sions of the theory. In the possibility of such a representation lie the sole value and justification of the whole system, and especially the concepts and fundamental principles which underlie it. Apart from that, these latter are free inventions of the human intellect, which cannot be justi fied either by the nature of that intellect or in any other fashion a priori.
In the summary of this section, he draws attention to the "purely fictitious character of the fundamentals of scientific theory." It is this penetrating insight which Mach must have smelled out much earlier and dismissed as "dogmatism." Indeed, Einstein, in his 1933 Spencer Lecture?widely read, as were and still are so many of his essays?castigates the old view that "the fundamental concepts and postulates of physics were not in the logical sense inventions of the human mind but could be de duced from experience by 'abstraction'?that is to say, by logical means. A clear recognition of the erroneousness of this notion really only came with the general theory of relativity." Einstein ends this discussion with the enunciation of his cur rent credo, so far from that he had expressed earlier: Technically, Einstein was now at?or rather just past?the mid stage of his pilgrimage. He had long ago abandoned his youthful allegiance to a primitive phenomenalism that Mach would have commended. In the first of the two passages just cited and others like it, he had gone on to a more refined form of phenomenalism which many of the logical positivists could still accept. He has, however, gone beyond it in the second passage, turning toward in terests that we shall see later to have matured into clearly meta physical conceptions.
Later, Einstein himself stressed the key role of what we have called thematic rather than phenomenic elements36?and thereby he fixed the early date at which, in retrospect, he found this need to arise in his earliest work. Thus he wrote in his Autobiographical Notes of 1946 that "shortly after 1900 ... I despaired of the possi bility of discovering the true laws by means of constructive efforts based on known facts. The longer and the more despairingly I tried, the more I came to the conviction that only the discovery of a uni versal formal principle could lead us to assured results."37 Another example of evidence of the undercurrent of disen gagement from a Machist position is an early one: It comes from Einstein  This is the characteristic position?the crucial difference be tween Einstein and those who make the correspondence with ex perimental fact the chief deciding factor for or against a theory: Even though the "experimental facts" at that time very clearly seemed to favor the theory of his opponents rather than his own, he finds the ad hoc character of their theories more significant and objectionable than an apparent disagreement between his theory and their "facts."40 So already in this 1907 article?which, incidentally, Einstein men tions in his postcard of 17 August 1909 to Ernst Mach, with a re* mark regretting that he has no more reprints for distribution?we have explicit evidence of a hardening of Einstein against the epistemological priority of experiment, not to speak of sensory ex perience. In the years that followed, Einstein more and more openly put the consistency of a simple and convincing theory or of a thematic conception higher in importance than the latest news from the laboratory?and again and again he turned out to be right.
Thus, only a few months after Einstein had written in his fourth letter to Mach that the solar eclipse experiment will decide "whether the basic and fundamental assumption of the equivalence of the acceleration of the reference frame and of the gravitational field really holds," Einstein writes to Besso in a very different vein (in March 1914), before the first, ill-fated eclipse expedition was scheduled to test the conclusions of the preliminary version of the general relativity theory: "Now I am fully satisfied, and I do not doubt any more the correctness of the whole system, may the ob servation of the eclipse succeed or not. The sense of the thing [die Vernunft der Sache] is too evident." And later, commenting on the fact that there remains up to 10 per cent discrepancy between the measured deviation of light owing to the sun's field and the calcu lated effect based on the general relativity theory: wFor the expert, this thing is not particularly important, because the main signifi cance of the theory does not lie in the verification of little effects, but rather in the great simplification of the theoretical basis of physics as a whole."41 Or again, in Einstein's "Notes on the Origin of the General Theory of Relativity,"42 he reports that he "was in the highest degree amazed" by the existence of the equivalence be tween inertial and gravitational mass, but that he "had no serious doubts about its strict validity, even without knowing the results of the admirable experiment of E?tv?s." The same point is made again in a revealing account given by Minkowskts "World9 and the World of Sensations The third major point at which Mach, if not Einstein himself, must have seen that their paths were diverging is the development of relativity theory into the geometry of the four-dimensional space time continuum, begun in 1907 by the mathematician H. Minkow ski (who, incidentally, had had Einstein as a student in Z?rich). In deed, it was through Minkowski's semipopular lecture, "Space and Time," on 21 September 1908 at the eightieth meeting of the Natur forscherversammlung,44 that a number of scientists first became in trigued with relativity theory. We have several indications that Mach, too, was both interested in and concerned about the intro duction of four-dimensional geometry into physics (in Mach's cor respondence around 1910, for example, with A. F?ppl); according to F. Herneck,4* Ernst Mach specially invited the young Viennese physicist Philipp Frank to visit him "in order to find out more about the relativity theory, above all about the use of four-dimensional geometry." As a result, Frank, who had recently finished his studies under Ludwig Boltzmann and had begun to publish noteworthy contributions to relativity, published the "presentation of Einstein's theory to which Mach gave his assent" under the title "Das Rela tivit?tsprinzip und die Darstellung der physikalischen Erschein ungen im vierdimensionalen Raum."46 It is an attempt, addressed to readers "who do not master modern mathematical methods," to show that Minkowski's work brings out the "empirical facts far more clearly by the use of four-dimensional world lines." The essay ends with the reassuring conclusion: "In this four-dimensional world the facts of experience can be presented more adequately than in three-dimensional space, where always only an arbitrary and one-sided projection is pictured." Following Minkowski's own papers on the whole, Frank's treat ment can make it nevertheless still appear that in most respects the time dimension is equivalent to the space dimensions. Thereby one could think that Minkowski's treatment based itself not only on a functional and operational interconnection of space and time, but also?fully in accord with Mach's own views?on the primacy of ordinary, "experienced" space and time in the relativistic descrip tion of phenomena.
Perhaps as a result of this presentation, Mach invoked the names of Lorentz, Einstein, and Minkowski in his reply of 1910 to Planck's first attack, citing them as physicists "who are moving closer to the problems of matter, space, and time." Already a year earlier, Mach seems to have been hospitable to Minkowski's presentation, al though not without reservations. Mach wrote in the 1909 edition of Conservation of Energy22: "Space and time are here conceived not as independent entities, but as forms of the dependence of the phenomena on one another"; he also added a reference to Minkow ski's lecture of 1908.44 But a few lines earlier, Mach had written: "Spaces of many dimensions seem to me not so essential for physics. I would only uphold them if things of thought [Gedunkendinge] like atoms are maintained to be indispensable, and if, then, also the freedom of working hypotheses is upheld." It was correcdy pointed out by C. B. Weinberg47 that Mach may eventually have had two sources of suspicion against the Minkow skian form of relativity theory. As was noted above, Mach re garded the fundamental notions of mechanics as problems to be continually discussed with maximum openness within the frame of empiricism, rather than as questions that can be solved and settled ?as the relativists, seemingly dogmatic and sure of themselves, were in his opinion more and more inclined to do. In addition, Mach held that the questions of physics were to be studied in a broader setting, encompassing biology and psychophysiology. Thus Mach wrote: "Physics is not the entire world; biology is there too, and belongs essentially to the world picture. "48 But I see also a third reason for Mach's eventual antagonism against such conceptions as Minkowski's ( unless one restricted their application to "mere things of thought like atoms and mole cules, which by their very nature can never be made the objects of sensuous contemplations"49). If one takes Minkowski's essay seri ously?for example, the abandonment of space and time separately, with identity granted only to "a kind of union of the two"?one must recognize that it entails the abandonment of the conceptions of experiential space and experiential time; and that is an attack on the very roots of sensations-physics, on the meaning of actual measurements. If identity, meaning, or "reality" lies in the four dimensional space-time interval ds, one is dealing with a quantity which is hardly denk?konomisch, nor one that preserves the pri macy of measurements in "real" space and time. Mach may well have seen the warning flag; and worse was soon to come, as we shall see at once.
In his exuberant lecture of 1908 (see Ref. 44), Minkowski had announced that "three-dimensional geometry becomes a chapter in four-dimensional physics. . . . Space and time are to fade away into the shadows, and only eine Welt an sich will subsist." In this "world" the crucial innovation is the conception of the "zettartige Vektorelement," ds, defined as (1/c) V c2dt2-dx2-dy2-dzl with imaginary components. To Mach, the word Element had a crucial and very different meaning. As we saw in Schlick's summary, elements were nothing less than the sensations and complexes of sensations of which the world consists and which completely define the world. Minkowski's rendition of relativity theory was now revealing the need to move the ground of basic, elemental truths from the plane of direct experience in ordinary space and time to a mathemati cized, formalistic model of the world in a union of space and time that is not directly accessible to sensation?and, in this respect, is reminiscent of absolute space and time concepts that Mach had called "metaphysical monsters." 50 Here, then, is an issue which, from the beginning, had separated Einstein and Mach even before they realized it. To the latter, the fundamental task of science was economic and descriptive; to the former, it was speculative-constructive and intuitive. Mach had once written: *If all the individual facts?all the individual phe nomena, knowledge of which we desire?were immediately acces sible to us, science would never have arisen."51 To this, with the forthrightness caused perhaps by his recent discovery of Mach's op position, Einstein countered during his lecture in Paris of 6 April 1922: "Mach's system studies the existing relations between data of experience: for Mach, science is the totality of these relations. That point of view is wrong, and in fact what Mach has done is to make a catalog, not a system." 52 We are witnessing here an old conflict, one that has continued throughout the development of the sciences. Mach's phenomenal ism brandished an undeniable and irresistible weapon for the critical re-evaluation of classical physics, and in this it seems to hark back to an ancient position that looked upon sensuous appear ances as the beginning and end of scientific achievement. One can read Galileo in this light, when he urges the primary need of de scription for the fall of bodies, leaving "the causes" to be found out later. So one can understand (or rather, misunderstand) Newton, with his too-well-remembered remark: "I feign no hypotheses."53 Kirchhoff is in this tradition. Boltzmann wrote of him in 1888: The aim is not to produce bold hypotheses as to the essence of matter, or to explain the movement of a body from that of molecules, but to present equations which, free from hypotheses, are as far as possible true and quantitatively correct correspondents of the phenomenal world, careless of the essence of things and forces. In his book on mechanics, Kirchhoff will ban all metaphysical concepts, such as forces, the cause of a motion; he seeks only the equations which correspond so far as possible to de served motions. 54 And so could, and did, Einstein himself understand the Machist component of his own early work.
Phenomenalistic positivism in science has always been victori ous, but only up to a very definite limit. It is the necessary sword fo? destroying old error, but it makes an inadequate plowshare for cultivating a new harvest. I find it exceedingly significant that Einstein saw this during the transition phase of partial disengage 656 ment from the Machist philosophy. In the spring of 1917 Einstein wrote to Besso and mentioned a manuscript which Friedrich Adler had sent him. Einstein commented: "He rides Mach's poor horse to exhaustion." To this, Besso?the loyal Machist?responds on 5 May 1917: "As to Mach's little horse, we should not insult it; did it not make possible the infernal journey through the relativities? And who knows?in the case of the nasty quanta, it may also carry Don Quixote de la Einsta through it alll" Einstein's answer of 13 May 1917 is revealing: "I do not inveigh against Mach's little horse; but you know what I think about it. It cannot give birth to anything living, it can only exterminate harm ful vermin."

Toward a Rationalistic Realism
The rest of the pilgrimage is easy to reconstruct, as Einstein more and more openly and consciously turned Mach's doctrine up side down?minimizing rather than maximizing the role of actual details of experience, both at the beginning and at the end of sci entific theory, and opting for a rationalism that almost inevitably would lead him to the conception of an objective, "real" world be hind the phenomena to which our senses are exposed.
In the essay, "Maxwell's Influence on the Evolution of the Idea of Physical Reality" (1931), Einstein began with a sentence that could have been taken almost verbatim from Max Planck's attack on Mach in 1909, cited above: "The belief in an external world in dependent of the perceiving subject is the basis of all natural sci ence." Again and again, in the period beginning with his work on the general relativity theory, Einstein insisted that between experi ence and reason, as well as between the world of sensory percep tion and the objective world, there are logically unbridgeable chasms. He characterized the efficacy of reason to grasp reality by the word miraculous; the very terminology in these statements would have been anathema to Mach.
We may well ask when and under what circumstances Einstein himself became aware of his change. Here again, we may turn for illumination to one of the hitherto unpublished letters, one written to his old friend, C. Lanczos, on 24 January 1938: Coming from sceptical empiricism of somewhat the land of Mach's, I was made, by the problem of gravitation, into a believing rationalist, that is, one who seeks the only trustworthy source of truth in mathematical simplicity. The logically simple does not, of course, have to be physically true; but the physically true is logically simple, that is, it has unity at the foundation.
Indeed, all evidence points to the conclusion that Einstein's work on general relativity theory was crucial in his epistemological development. As he wrote later in "Physics and Reality" (1936): "the first aim of the general theory of relativity was the prelim inary version which, while not meeting the requirements for con stituting a closed system, could be connected in as simple a manner as possible with /directly observed facts.'" But the aim, still ap Physical Theory has two ardent desires, to gather up as far as possible all pertinent phenomena and their connections, and to help us not only to know how Nature is and how her transactions are carried through, but also to reach as far as possible the perhaps Utopian and seemingly arro gant aim of knowing why Nature is thus and not otherwise. Here lies the highest satisfaction of a scientific person. . . . [On making deductions from a "fundamental hypothesis" such as that of the kinetic-molecular theory,] one experiences, so to speak, that God Himself could not have arranged those connections [between, for example, pressure, volume, and temperature] in any other way than that which factually exists, any more than it would be in His power to make the number 4 into a prime number. This is the promethean element of the scientific experience. . . . Here has always been for me the particular magic of scientific consider ations; that is, as it were, the religious basis of scientific effort.
This fervor is indeed far from the kind of analysis which Ein stein had made only a few years earlier. It is doubly far from the asceticism of his first philosophic mentor, Mach, who had written in his day book: "Colors, space, tones, etc. These are the only realities. Others do not exist."00 It is, on the contrary, far closer to the rational realism of his first scientific mentor Planck, who had written: "The disjointed data of experience can never furnish a veritable science without the intelligent interference of a spirit actuated by faith. . . .
We have a right to feel secure in surrendering to our belief in a philosophy of the world based upon a faith in the rational ordering of this world."61 Indeed, we note the philosophical kinship of Ein stein's position with seventeenth-century natural philosophers?for example, with Johannes Kepler who, in the preface of the Myste rium Cosmographicum, announced that he wanted to find out con cerning the number, positions, and motions of the planets, "why they are as they are, and not otherwise," and who wrote to Herwart in April, 1599, that, with regard to numbers and quantity, "our knowledge is of the same kind as God's, at least insofar as we can understand something of it in this mortal fife." Not unexpectedly, we find that during this period (around 1930) Einstein's non-scientific writings began to refer to religious questions much more frequently than before. There is a close rela tion between his epistemology, in which reality does not need to be validated by the individual's sensorium, and what he called "Cosmic religion,"62 defined as follows: "The individual feels the vanity of human desires and aims, and the nobility and marvelous order which are revealed in nature and in the world of thought. He feels the individual destiny as an imprisonment and seeks to ex perience the totality of existence as a unity full of significance." Needless to say, Einstein's friends from earlier days sometimes had to be informed of his change of outlook in a blunt way. For ex ample, Einstein wrote to Moritz Schlick on 28 November 1930: In general your presentation fails to correspond to my conceptual style insofar as I find your whole orientation so to speak too positivistic. ... I tell you straight out: Physics is the attempt at the conceptual construc tion of a model of the real world and of its lawful structure. To be sure, it The very next speaker disagreed and showed Frank that he had been mistaken still to associate Einstein's views with that of Mach and himself. "He added that Einstein was entirely in accord with Planck's view that physical laws describe a reality in space and time that is independent of ourselves. At that time," Frank com The essential point of the positivist theory is that there is no other source of knowledge except the straight and snort way of perception through the senses. Positivism always holds strictly to that Now, the two sen tences: (1) there is a real outer world which exists independently of our act of knowing and (2) the real outer world is not directly knowable form together the cardinal hinge on which the whole structure of physi cal science turns. And yet there is a certain degree of contradiction be tween those two sentences. This fact discloses the presence of the irra tional, or mystic, element which adheres to physical science as to every other branch of human knowledge. The effect of this is that a science is never in a position completely and exhaustively to solve the problem it has to face. We must accept that as a hard and fast, irrefutable fact, and this fact cannot be removed by a theory which restricts the scope of science at its very start. Therefore, we see the task of science arising be fore us as an incessant struggle toward a goal which will never be reached, because by its very nature it is unreachable. It is of a meta physical character, and, as such, is always again and again beyond our achievement.67 From then on, Einstein's and Planck's writings on these matters are often almost indistinguishable from each other. Thus, in an essay in honor of Bertrand Russell,68 Einstein warns that the "fateful 'fear of metaphysics'. . .has come to be a malady of contemporary empiricistic philosophizing." On the other hand, in the numerous letters between the two old friends, Einstein and Besso, each to the very end touchingly and patiently tries to explain his position, and perhaps to change the others. Thus, on 28 February 1952, Besso once more presents a way of making Mach's views again acceptable to Einstein. The latter, in answering on 20 March 1952, once more responds that the facts cannot lead to a deductive theory and, at most, can set the stage "for intuiting a general principle" as the ba sis of a deductive theory. A little later, Besso is gently scolded (in Einstein's letter of 13 July 1952): "It appears that you do not take the four-dimensionality of reality seriously, but that instead you take the present to be the only reality. What you call 'world' is in physical terminology 'spacelike sections' for which the relativity theory?already the special theory?denies objective reality." In the end, Einstein came to embrace the view which many, and perhaps he himself, thought earlier he had eliminated from physics in his basic 1905 paper on relativity theory: that there exists an ex ternal, objective, physical reality which we may hope to grasp?not directly, empirically, or logically, or with fullest certainty, but at least by an intuitive leap, one that is only guided by experience of the totality of sensible "facts." Events take place in a "real world," of which the space-time world of sensory experience, and even the world of multidimensional continua, are useful conceptions, but no more than that. For a scientist to change his philosophical beliefs so fundamentally is rare, but not unprecedented. Mach  In an unpublished fragment apparently intended as an addi tional critical reply to one of the essays in the collection Albert Einstein, Philosopher-Scientist (1949), Einstein returned once more?and quite scathingly?to deal with the opposition. The very words he used showed how complete was the change in his episte mology. Perhaps even without consciously remembering Planck's words in the attack on Mach of 1909 cited earlier?that a basic aim of science is "the complete liberation of the physical world picture from the individuality of the separate intellects"23?Einstein refers to a "basic axiom" in his own thinking: It is the postulation of a "real world" which so-to-speak liberates the "world" from the thinking and experiencing subject The extreme posi tivists think that they can do without it; this seems to me to be an illu sion, if they are not willing to renounce thought itself.
Einstein's final epistemological message was that the world of mere experience must be subjugated by and based in fundamental thought so general that it may be called cosmological in character. To be sure, modern philosophy did not gain thereby a major novel and finished corpus. Physicists the world over generally feel that today one must steer more or less a middle course in the area be tween, on the one hand, the Machist attachment to empirical data or heuristic proposals as the sole source of theory and, on the other, the aesthetic-mathematical attachment to persuasive internal har mony as the warrant of truth. Moreover, the old dichotomy be tween rationalism and empiricism is slowly being dissolved in new approaches. experiment, to undertake a complete reconstruction. The Michelson ex periment is the cause and chief support of this reconstruction, namely, the electrodynamic theory of relativity. To do justice to this experiment one has no scruples to submit the foundations of theoretical physics as it has hitherto existed, namely, Newtonian mechanics, to a pro found transformation.
In his interesting essay "Das Verh?ltnis der Machschen Gedankenwelt zur Relativit?tstheorie," published as an appendix in the eighth German edition of Mach's The Science of Mechanics in the year 1921, Petzoldt faithfully attempts to identify and discuss several Machist aspects of Einstein's relativity theory: ( 1 ) The theory "in the end is based on the recognition of the coincidence of sensations; and therefore it is fully in accord with Mach's worldview, which may be best characterized as a relativistic positivism" (p. 516).
(2) Mach's works "produced the atmosphere without which Einstein's work was influenced thereby is impossible for me to find out. Mach occupied himself in his last years with the relativity theory, and in a preface to a late edition of one of his works even spoke out in rather sharp refusal against the relativity theory. However, there can be no doubt that this was a consequence of a lessening ability to take up [new ideas] owing to his age, for the whole direction of thought of this theory conforms with Mach's, so that Mach quite rightly is con sidered as a forerunner of general relativity theory.... I thank Colonel Bern Dibner for making a copy of the letter available to me from the Archives of the Burndy Library in Norwalk, Connecticut Among other hitherto unpublished letters in which Einstein indicated his indebted ness to Mach, we may cite one to A. Lampa, 9 December 1935: ... You speak about Mach as about a man who has gone into oblivion.
I cannot believe that this corresponds to the facts since the philosophical orientation of the physicists today is rather close to that of Mach [46][47]: Schr?dinger worked from a more mathematical point of view, trying to find a beautiful theory for describing atomic events, and was helped by deBroglie's ideas of waves associated with particles. He was able to extend deBroglie's ideas and to get a very beautiful equation, known as Schr?dinger's wave equation, for describing atomic processes.
Schr?dinger got this equation by pure thought, looking for some beau tiful generalization of deBroglie's ideas, and not by keeping close to the experimental development of the subject in the way Heisenberg did. I might tell you the story I heard from Schr?dinger of how, when he first got the idea for this equation, he immediately applied it to the behavior of the electron in the hydrogen atom, and then he got results that did not agree with experiment. The disagreement arose because at that time it was not known that the electron has a spin. That, of course, was a great disappointment to Schr?dinger, and it caused him to abandon the work for some months. Then he noticed that if he applied the theory in a more approximate way, not taking into account the refinements required by relativity, to this rough approximation his work was in agreement with observation. He published his first paper with only this rough approximation, and in this way Schr?dinger's wave equation was presented to the world. Afterward, of course, when people found out how to take into account correctly the spin of the electron the discrepancy between the results of applying Schr?dinger's relativistic equation and the experiments was completely cleared up.
I think there is a moral to this story, namely, that it is more im portant to have beauty in one's equations than to have them fit ex periment. If Schr?dinger had been more confident of his work, he could have published it some months earlier, and he could have pub lished a more accurate equation. That equation is now known as the Klein-Gordon equation, although it was really discovered by Schr?dinger, and in fact was discovered by Schr?dinger before he discovered his non relativistic treatment of the hydrogen atom. It seems that if one is work ing from the point of view of getting beauty in one's equations, and if one has really a sound insight, one is on a sure line of progress. If there is not complete agreement between the results of one's work and experi ment, one should not allow oneself to be too discouraged, because the discrepancy may well be due to minor features that are not properly taken into account and that will get cleared up with further develop ments of the theory. That is how quantum mechanics was discovered ....