EPILOGUE
IN 1885 HEINRICH HERTZ devised an electrical oscillator in his laboratory at Karlsruhe and set up certain vibrations which were not visible, but which did exhibit the other properties of light as to frequency, refrangibility, interference, polarization, and so on, and which were later found to travel at the same velocity. Radio waves, therefore, passed Maxwell’s prediction of the identity of light and electromagnetism triumphantly through the trial by which a theory stands or falls. It was as decisive an experimental victory as any in the history of science, and more strategic than most, for it forced physics to assume a new and different posture and to confront seriously the preoccupations with space and aether which Faraday had initiated and Maxwell had formulated. Hitherto, indeed, physicists had adopted an attitude to field theory compounded of bewilderment at the turns taken by Maxwell’s imagination and disdain of the detailed naïveté exhibited in the models created and destroyed in his imagination. Disdain was the response of the French school. Pierre Duhem wrote an entire treatise on Maxwell’s theories of light and electro-magnetism wherein the reader may learn (as Duhem says in The Aim and Structure of Physical Theory), “to what degree the lack of concern for all logic and even for any mathematical exactitude went in Maxwell’s mind….” And Duhem quotes Poincaré’s Science and Hypothesis on how it was that, “The first time a French reader opens Maxwell’s book a feeling of discomfort, and often even of distrust, is at first mingled with his admiration… And it may have been the penalty attaching to the perpetual Cartesianism of French science in its critical provincialism that it thus rose above the battle of the laboratory, and looked down in diminishing vigor upon Anglo-Saxon handiness, of the earth earthy.
It is rather German taste which relishes bewilderment and builds upon it. The very obscurities of Maxwell’s views drew Hertz and Boltzmann into their confirmation. Hertz was twenty-eight when he succeeded in detecting radio waves. Because of his early death, his was the last great career to transpire entirely within the confines of classical thought. Of the same generation, Boltzmann resolved the difficulties in Maxwell’s kinetic approach to gases, and deduced the laws of thermodynamics by means of a statistical method. To carry the stories of fields and particles beyond Maxwell would require either a higher mathematical competence than this history has so far exacted of the reader (and the author), or else a wider departure from the texts than has been the policy by which the book has been composed. Nevertheless, a history of the ideas of classical science would be incomplete without an epilogue to indicate how the great themes had in Maxwell not only their climax but their turning; how when the last knots were pulled tight, the great web of Newtonian realism all unexpectedly unravelled; what it was (in short) that Albert Einstein had in mind when he recalled that during his student days Maxwell’s theory had been the most fascinating subject in physics.
No doubt this second scientific revolution, which like other revolutions of our time begins to seem open-ended in its permanence, has been technical as well as intellectual and philosophical in genesis and content. Technical triumphs forced the pace: Willard Gibbs’s reformation of physical chemistry in the guise of mechanistic thermodynamics, H. A. Lorentz’s capture by prediction of the individual electron, Konrad Roentgen’s recognition of X-rays, the Curies’ laborious isolation of radium, Max Planck’s deduction of a discontinuous element in the radiation of energy and his calculation of the constant of action, the creation by all hands of an anatomy (if not yet a physiology) of the atom itself. And it is with no wish to undervalue these fundamental factors that attention is here directed instead to the sector of general ideas and assumptions about the relation of science to the way the world is made, and specifically to the renaissance of positivism at the end of the nineteenth century. For certainly the criticism which its leading adepts among scientists—Pierre Duhem in France, Wilhelm Ostwald in Germany, and most notably, Ernst Mach in Vienna—directed, first against domination by mechanics, and then against fundamental Newtonian assumptions about the structure of reality, this above all was what nourished the transformation of classical science with ideas.
Positivism was an essential element, moreover, destructively at least. Constructively it did not quite suffice, in its phenomenalism and radical despair of approaching theory to reality. Indeed, in no episode in intellectual history does the errancy of philosophy mingle more intimately with its indispensability. For at the start of the century the positivists repudiated with a certain violence the physics of particles—precisely that physics in which their doctrine has since gone from strength to strength, what with quantum mechanics, probability, and uncertainty. And on the other hand, positivism inspired the train of thought which led Einstein to the special theory of relativity—that same epistemology which he for his part repudiated in later life as the besetting abdication of reason in his science. To reach the general theory, Einstein went beyond Mach into an ontology of his own creation, rising into higher regions where the real merged with the ideal in the bracing atmosphere of (non-Euclidean) geometry.
What is less clear is the philosophical situation in which positivism itself revived. Auguste Comte coined the word early in the nineteenth century. Comte retrieved the essential elements of Condillac’s philosophy of science from the somewhat sterile verbalism of the idéologues, those last spokesmen of the Enlightenment who, having outlived it, continued to write of reason amid the vast unreason of revolutionary and Napoleonic Europe. Merging Condillac’s educationism into historicism, Comte converted sociology from the science to the engineering of humanity. Since history then replaced nature as the norm, Comte had to do what no Condillacian had done and repudiate not only metaphysics but also ontology. Thus would he deprive science of any and every claim to deal with objective reality or with any truth deeper than consistency or efficacy. He would know in order to predict, and predict in order to control, and such was the program of positivism. In Comte it became a social gospel. For all his extravagances Comte was the founder of his school, and it is extraordinary that he is held in so little honor among his successors, however repellent the secular religiosity of his later years, however alarming the authoritarianism of his technocracy, and however tedious the prolixity of his literary style. But it must be left to the historians of philosophy to identify the missing links between Paris and Vienna, between Comte and Mach, across the middle decades of the century when Hegel, Spencer, and the great spinners of systems enjoyed the renaissance of metaphysics.
The problem invites inquiry, for it appears that the relation between the protagonists who revived positivism in the decades before 1900 was rather one of resonance than derivation. And the historian of science is likely to experience a fellow feeling for this generation which is denied him in the work of their successors, the logical positivists among his own contemporaries. For unlike these latter, who ignore the development of science in favor of its method and logic, Duhem, Ostwald, and Mach were historically minded. Not perhaps in quite the historian’s own sense—they would study the history of scientific doctrine not for its own sake, as a record of culture and creation, but rather didactically, in order to forge of it an instrument of criticism of current science (or perhaps of current scientific error, since there lived on in them something of the attitude to history of the Enlightenment which was their ultimate philosophical inspiration). Mach’s Science of Mechanics in Its Historical Development remains a classic to be reckoned with by every student of the history or philosophy of science. That book, said Einstein of his own youth, first shook him in the “dogmatic faith” of physicists in mechanics as the foundation of their science.
Duhem, for his part, belongs not only to the philosophy, but perhaps primarily to the history of science, and indeed to science itself for his work in thermodynamics. His multi-volume history of cosmology from Thales to Kepler inaugurated the modern historiography of science, and his three volumes of essays on the predecessors of Leonardo da Vinci in mechanics established the vitality of medieval thought on that subject by tracing the tradition which Galileo consummated back to the fourteenth-century school of Paris. In contrast to Mach, Duhem’s scholarship appears to better advantage in his truly imposing erudition, which was often proof against his philosophy, than in his criticism, where parti pris too often got the better of judgment. Ostwald, finally, interested himself more in the intellectual personalities and thought processes of the great moderns of science than in the remote reaches of culture. His set of biographical essays, Grosse Männer, is a kind of Plutarch’s Lives of Modern Science. The collection of great texts which he edited under the rubric Ostwalds Klassiker still serves the scholar and the student very well. In short, the historian of science is bound to appreciate the service which the positivists rendered in this, their heroic generation, through their perception of current science as the surface of its past—even though he may feel equally bound to deliver Galileo and Newton from the hands of Mach, who would turn everyone into a positivist insofar as he was a scientist at all, or to retrieve the Platonic realism of Copernicus and Kepler from Duhem’s passion for downgrading all of physics into a likely story.
What the most dispassionate historian will have no wish to do is to underestimate the degree of Ostwald’s enthusiasm for the movement in physics started by Robert Mayer. Indeed, a positivist in philosophy at the end of the century was almost certain to be an energeticist in physics. Heat itself occupied those who, following first Clausius and Maxwell, and then Gibbs and Boltzmann, would reduce it to a problem in dynamics (hence the term thermodynamics), and their dissenting colleagues who, in the manner of Duhem and Ostwald, and after Mayer, would transcend mechanics in the study of energy—and hence the implication of energetics as the phase of science that would supersede the Newtonian. For these latter did mean to make a revolution in physics. And it was their misfortune that they stormed the wrong door—the atom instead of the laws themselves.
Seldom has history so rapidly and so drastically undone a scientific crusade led by men who were themselves responsible and eminent scientists. It is easy to sympathize with the discontent that mechanism aroused. Certain temperaments still glory in a kind of emancipation from some classical tyranny, though it is now as dead as slavery. The formulation of conservation of energy, of electrodynamics, of optics, ultimately of all science, in the language of Newton’s laws could be seen as a triumph. On the other hand, it could be seen—and the positivists did so see it—as a foreing of language and a straining of definitions. Energy had to be arbitrarily divided between potential and kinetic to fit the equations. A universal body had to be admitted rigid enough to bear shear waves and rare enough to pass detectable bodies undetectably through its subtlety. Electricity had to be resolved into mass-points (for the equations of ordinary dynamics) or into a hypothetical but incompressible fluid (for the equations of hydrodynamics). In either case something imponderable had to be given substance in order to be set in motion. Everywhere, outside of the domain of mechanics proper, it was not the observations but the laws of motion which prescribed these propositions. Everywhere, it seemed to those who felt the structure of classical science rather as a prison-house than a house built upon the rocks, everywhere the extension of mechanics committed the fallacy which invests the formulations of theory (or the conventions of language) with the attributes of reality.
And everywhere false problems sprang up to obstruct the path. Since atomism, the subsistence of reality in ultimate particles whose motions the laws describe, had provided classical physics with its ontology ever since the seventeenth century, it is obvious why the atom appeared to the critics of mechanics as the villain of the piece. And it must be admitted that the atom which offended them was not the rich and complicated structure, full of interest, promise, and threat, which emerged to refute them in the twentieth century. The object of their scorn was rather that atom which was a minute ball-bearing in dynamics, a carrier for valence (which would be the same without it) in chemistry, an infinitesimal concretization of energy in electricity, a population of the unobservable in the statistical mechanics of gases, and everywhere the postulation as an image of reality of what was properly only an analytical technique. Such atoms were easy targets. And perhaps there lay the trouble. Perhaps they were too easy. Perhaps they were straw atoms.
For the rub was less in the content of these criticisms, which were obvious enough and which may be repeated against the reality of strange particles in contemporary physics, than in the mood in which the campaign was conducted and the purpose that it served. Reading Duhem and Ostwald on (or rather contra) atoms, one is struck by the sense of having been here before and found it a blind alley. In The Aim and Structure of Physical Theory Duhem feels compelled to qualify phenomenalism, in which no physicist can quite content his intuition that a real world exists outside his science. To be sure, mathematical laws are in themselves only economical statements of experience. Nevertheless, they chime so beautifully together, they give so persuasive a suggestion of transcendent order, that they must echo some harmony subsisting out there in reality. It is not given to mechanical models, or to pictorial images, or indeed to any form of hypothesis, truly to represent that harmony. Our access to it is indirect, to be worked toward by discerning natural classifications among the laws of nature. And by “natural” Duhem means such a one as will reflect the relations of things in the natural order, though not their actual structure. We are, indeed, assured that proper classification does hold such a promise by the very capacity of theory to guide experiment in the prediction of phenomena not yet observed and in the formulation of laws not yet expressed. This, of course, was simply the difficulty with which the fact of discovery and the aim of innovation always confronts a phenomenalistic logic. It was no new problem, and the resort to classification was no new answer.
But Ostwald’s general treatise, Energy, remains the most characteristic statement of the position. The argument is congruent with the contemporary biological retreat from the theory of natural selection into Lamarckism. Ostwald was a chemist, and it makes a curious reprise that once again an indictment of the sterility of physics should proceed from one whose own outlook was formed in the science of palpable matter rather than matter in motion, and who would yearn to re-invest science with a sense of biological subjectivity and process. Thus, Ostwald objects against mechanism that it deprives bodies of the properties in which alone they do have reality for a science of perceived phenomena. Precisely because manifestations of energy are what we do perceive, and all we perceive, energy is the only concept which can express reality for a phenomenalistic science. Energy is that which does act, and whatever its transformations in an event are the content of the event. It is absurd, therefore, to consider energy changes as an extension of mechanics. The practice requires us (to choose the most radical example) to take inertial motion as a fundamental occurrence, although no one has ever observed it, and to dismiss friction as an accident, although nothing ever transpires without it. And instead of this, Ostwald would have us penetrate beyond Newton in the direction marked out by Mayer. Nature is to be numbered in the intensive magnitudes of energy, rather than the extensive magnitudes of geometry. Then mechanical problems might themselves become special cases of exchange of energy.
Not all ad hominem arguments are to be avoided, not at least when historical judgment is in play rather than logical analysis, and in the perspective of the history of science it will appear more evident than it could to the protagonists—all men of good will—that energetics confronts us with a phenomenon by now familiar: a dissatisfaction with science ever latent among scientists themselves who would serve some grateful purpose. Thus, Duhem plays the pundit as well as the philosopher in his preachments on abstracting in theory and ordering by natural classifications. His implication was ever that the future for France in science lay in strict, uncompromising adherence to the “deep and narrow” way of her own national style, not to be adulterated by the “weak and ample” thinking of the Anglo-Saxon. It was natural and worthy in Duhem to wish to rehabilitate the scientific merit of those medieval centuries which were the great ones for his church. But his reader may feel reservations about his enthusiasm for reducing physics to the status of a useful fiction, in the reflection that a religious metaphysics might then monopolize the realm of truth.
Extremes of fidelity and agnosticism could touch in positivism. The religion which fired Ostwald’s fervor was Comte’s godless sociology revived. Ostwald thought to serve humanity by refounding all of physics in energetics. Indeed, the intractability of the propositions of mechanics offended him more deeply than their implausibility. Mechanics impoverished science by refusing any handle to psychology. A new phenomenalism, on the other hand, built upon our intensive perceptions of energy, would return us a psychology continuous with physics, correspondingly certain and enlightened, and applicable to the reformation of society. Ostwald was as uncompromising as Condillac on theory as the syntax of experience, as definite as Comte on prediction as the verification of theory, and as utilitarian as Bacon on application as the justification for science. And the advantage of considering science first as language and then as act was that it might then become subjective in the proper, the operational or inter-subjective sense, rather than in the metaphysical.
No such overtones accompany the work of Ernst Mach, who could make, therefore, a cleaner, straighter thrust toward a science which would be the purest rationalization of experience. His was a conscious debt to the Enlightenment—only to its skepticism, however, and never to its sentimentality. “I see Mach’s greatness,” wrote Einstein, “in his incorruptible skepticism and independence …”—in Mach’s daring, Einstein might well have added, and in his radicalism. The mood of lesser positivists partook, after all, of petulance. Theirs was less a criticism than a dismissal of mechanics. No more than they did Mach have patience with the reality of atoms, but instead of simply waving away the entities that figured in the equations of mechanics, he attacked its fundamental assumptions about absolute space, time, and motion. He went right to the heart of Newtonian doctrine, and called the principle of inertia itself to account before the bar of empiricism.
Mach inherited his discontent with existential space and time from an early phase of idealism in his personal development, first Kantian and then Berkeleyan. He was prepared, therefore, to consider space and time rather as categories of experience than attributes of reality. Mach’s own development, indeed, recapitulated the evolutionary contribution of idealism as the subjective component in positivist phenomenalism, for which the ego and its sensations constitute reality. And in execution of his own epistemological program, that we make knowledge only of observed phenomena, he turned his criticism of Newtonian inertia on points which Berkeley had already handled metaphysically.
By Newton’s second law of motion, force is measured as the product of mass times acceleration. Acceleration relative to what, however? Had Newton allowed himself to be deterred by this difficulty, he might never have founded classical physics. In effect, he simply passed around it. Not without qualms, one suspects—Newton’s language is labored in the distinction which he introduced into the definitions of the Principia between the absolute space and time of physics and reality on the one hand, and on the other the relative space and time wherein the vulgar live and have their being and awareness. All he can say in justification is that “the thing is not altogether desperate,” in virtue of a famous thought experiment. A bucket of water hangs upon a twisted rope. The physicist releases the bucket so that the untwisting rope may spin it. Gradually the water picks up rotation and climbs along the side. Now the pail is suddenly stopped—and for a time the motion of the water and the concavity of its surface persist. Since that concavity obtained both when the water was at rest relative to the pail and when it was moving within it, its form must be the consequence of a (circular but no matter) acceleration relative to absolute space, and an instance, therefore, of absolute motion.
It is far from obvious why this is unconvincing, and Berkeley’s refutation seemed even farther fetched. Newton’s experiment loses its point unless taken to mean that the water curved its surface independently, not just of the matter in the bucket, but of all other matter whatsoever. Only so could motion be abstracted into a purely relational state between a body and space. But this is meaningless, Berkeley had objected. Matter can displace only relative to matter, and not to extension. The water is affected by nothing less than all the matter in the universe, and its apparent inertia is only motion relative to the fixed stars which, speaking strictly, cause the curvature of the surface. In their absence it would remain flat. But this means in the absence of all other matter. Thus, if there were only one body in the universe, it would have no inertia.
In appreciating the appeal which this extremely metaphysical proposition held for Mach, himself the scourge of metaphysics, one must remember that it was not the laws of Newtonian physics which he questioned, but their existential value; not the principle of inertia, the citadel of classical physics, but its attribution to matter as an intrinsic property independent of measurement and specifications of reference. His criticism in mechanics constantly aimed to expose the delusions which had led a Lagrange, a Galileo, an Archimedes to claim for their reason what they had learned from experience. Thus, Archimedes had really exploited his sense of the symmetry of his own body in his appeal to considerations of equilibrium. The question is not one of the utility of the law of the lever, but of rightly understanding it. Similarly, a propos of interpreting Foucault’s pendulum (in principle the same experiment as Newton’s bucket), Mach agrees that we must admit either to absolute motion in the earth (and in general), or to a fallacy in the expression of the law of inertia. And he differed from all other serious physical thinkers—it is the mark of his radicalism—in so posing the problem that he must dispute what no physicist had found wanting: the validity of the principle of inertia as a local law. What can it mean for a body to persist in the same direction if we do not specify what direction? We cannot attribute inertia to this or that body, held Mach. We must restate the law so that it contains the full indifference of nature to the false problem of whether the earth or heavens revolve daily. It must make no difference to what our law predicts of the surface, whether we spin the bucket or the fixed stars.
Bodies are not indifferent to their motion, therefore. They are affected in their inertia by the distance and disposition of all other masses. Deep ideas, these—the relativity of motion; the re-definition of its parameters, time and space, as orders of functional dependence observed among events; the principle that statements about inertia and therefore gravity and acceleration are about nothing if not about the interaction of all the matter in the universe—these very difficult but highly logical consequences of complete empiricism moved physics as close to its revolution into relativity as philosophy alone could carry it. It could go no further unnourished by consideration of what Mach’s principles forbade him to take seriously, the reality of the electromagnetic field and the constitution of the aether that seemed increasingly to fill the universe, or at least the universe of discourse. For the Michelson-Morley experiment did not concern Mach. He did not see that the undetectability of the aether (at which any positivist might have said, “But of courser!”) posed as a real problem the status of the field.
H. A. Lorentz was to Einstein in physics what Mach was in philosophy, the mentor who had half the story. “For me personally,” wrote Einstein in the centennial tribute to this John-the-Baptist of relativity, “he meant more than all the others I have met on my life’s journey.” Einstein was then looking back from near the journey’s end, and though the tribute is personal, it might equally well have been scientific, for he came after Lorentz in equations as in spirit. And Lorentz lacked only that ultimate quality of something like divinity in Einstein’s mind, which would take the same evidence and quite transform the shape of the world that physics sees in nature.
Lorentz had the advantage forced upon many Dutchmen of being equally conversant with the languages and scientific traditions of England, France, and Germany. Sympathetic to and detached from all three styles, he worked in the finest tradition of European scholarship. His own exemplar was Fresnel. The doctoral dissertation which Lorentz defended at Leyden considered the wave theory of light in relation to Maxwell’s fields, and showed that certain anomalies in Fresnel’s formulations—the most serious was the absence of longitudinal vibrations accompanying the transverse—disappeared in the electromagnetic theory of light. A more troubling complexity remained in field theory itself. Maxwell had established the field to obviate action at a distance. Nevertheless, his equations did not liberate it from association with ordinary matter. A boundary rather than a continuum obtained between aether in free space and aether in (say) glass. In order to describe the whole field, therefore, one had to combine its strength with the dielectric displacement by means of a specific constant, the dielectric constant for glass.
Lorentz came to this unhappy situation by way of Fresnel’s investigation of a coefficient of aether drag. Fresnel’s theory too had predicted that a specific portion of the aether coincident with a body in space is captive, so to say. And though Lorentz took all physics for his province with a more serene catholicity than was usual even then, rendering a consistent and rational account of the aether always did attract him more winningly than any other problem. It appeared to him early in his career that field theory might be straitened in the unity of light and electromagnetism and further simplified by liberating aether from this partial but rather vague and arbitrary association with ponderable matter. He tried as a hypothesis, therefore, that the seat of the field precisely is the aether, imponderable, omnipresent, and stationary. He divorced it, indeed, as sharply from ordinary matter as Newton had done in his day in distinguishing between matter and extension. Thus, he eliminated the distinction in terms between field strength and dielectric displacement. Elementary electric charges on the atomic constituents of matter are what create the field. They remain distinct from the field, however, and it exerts forces on the charges in accord with Newton’s laws. That is to say, the field interacts with matter as physics knows it, not by mechanical linkages, but only through the intimate association of atoms with electrons (if in using that word one may presume on the discovery to which Lorentz’s particularization of charge did actually lead).
Worked out in detail, the theory gave a beautifully simplified account of all the phenomena of electrodynamics and exacted as the price of simplicity only a single, essential condition: that the aether remain stationary with respect to matter in motion, and that the two be kept distinct. Maxwell’s laws, in other words, were about one thing: the field; and Newton’s laws, about another: bodies in motion; and Lorentz would save both sets by arraying them against the aether. If this were so, the earth and all bodies move through aether. Maxwell had himself suggested the design of an experiment to detect that motion. Michelson first performed it in 1881, and together with Morley refined it in 1887. They sought to detect a difference in the apparent velocity of light, according to whether it be measured in the direction of the motion of the earth or at right angles. It was an interesting and famous question in its own right, of course, and not only as an arbiter of Lorentz’s uniform and stationary aether. Nor, though he accepted the verdict of the measurements which gave a final and a negative result, did Lorentz feel bound to interpret this experiment as crucially against his theory. What he modified were his equations.
In physical or mathematical problems it may often be convenient to convert the quantities from one set of coordinates to another. A problem may be stated in rectilinear co-ordinates. Its solution may be simpler in polar co-ordinates, or in some other set of rectilinear co-ordinates moving relative to the first—after which the results may be reduced to the initial system. Lorentz originated his transformations simply as such a mathematical device for relating the aether which carries the field to the inertial systems in which matter interacts with charge. Since classical mechanics treated time as a dimension of motion, his expressions were more complicated than simple spatial compositions in a plane or in three dimensions. Nevertheless, the handling of time did not differ in principle from the conversions worked (say) between the two systems of sidereal and solar time. In optics these transformations gave Lorentz the results with a stationary aether for which Fresnel had introduced his dragging coefficient. Their application to electrodynamics permitted description of the motion of a charge through a stationary field by the same formulae as through a second field in uniform linear motion relative to the first. And always it remained the postulate of Lorentz’s own world picture that the fundamental frame for inertial systems (including those of moving charges) is the aether at rest.
The Michelson-Morley experiment shook that cornerstone, for it seemed to show that the aether moves with the earth (and presumably with any body on which measurements might be made). There were two possibilities. Either Lorentz must abandon his stationary aether. Or he must extend his transformations. He chose the latter, and adapted his equations to the suggestion first advanced by an imaginative Irishman, G. F. Fitzgerald, in 1892. Lorentz himself had established that an electrostatic charge in motion is equivalent in its effects—that is, in setting up a magnetic field—to an ordinary current of electricity in a wire. For a physicist here on the earth, Fitzgerald argued, a charge of statical electricity will generate only an electrostatic but not a magnetic field. If he were on the sun, however, he would find the charge to be in motion, and he ought to detect a magnetic field. In rigid bodies the atoms bear just such charges; the form of an object depends upon the forces between its molecules; those forces will be affected by the state of electromagnetic fields; an object will or will not be accompanied by a magnetic field, according to whether it is in motion or at rest relative to electrical charges and vice versa; a body may be shorter, therefore, in the direction of its motion than it would be at rest or turned cross-wise; and that may be the explanation of the Michelson-Morley failure to observe motion through the aether—their instruments contracted in the direction of the earth’s motion through the aether by just that tiny amount which would necessarily compensate for the expected diminution which that motion should occasion in the apparent velocity of light.
It seemed a far-fetched notion. One must remember the alternative which Lorentz faced: to admit that Maxwell’s laws of the field, the laws of light and electromagnetism, do not hold in a world where matter in motion exhibits Newtonian inertia. By the Lorentz transformations, containing now the Fitzgerald contraction, the invariance of Maxwell’s laws was saved, and so too were Newton’s laws in their domain—provided it be allowed (as Lorentz said) that time and space be pulled askew a little in his equations. It must be remembered, too, that some phenomenalists in physics still regard what Einstein called the special theory of relativity as identical with the Lorentz transformations. In effect, it is identical. The difference is philosophical, not mathematical, and has to do with whether it is thought pleasing or physically important to discard the aether (now become undetectable in principle) as the locus of the field, and to treat as the foundation of the new physics the relativity of space and time.
It has become less clear than it once seemed in what sense Einstein went beyond Lorentz. And it may be that we should coin a new term, the Einsteinian synthesis, to suggest as does the phrase, Newtonian synthesis, a revolutionary combination of physics with philosophy in a new conception of natural reality. At the end of his life Einstein was asked to compose an intellectual autobiography to serve as preface to a symposium on the standing of his work. “Here I sit,” he began, “in order to write, at the age of sixty-seven, something like my own obituary.” And though no man’s reminiscences may do substitute for history, it may be helpful in the undeveloped state of scholarly criticism to respect Einstein’s recollections of the order in which his thoughts followed one upon another. He recalls his youthful sense of displeasure at a dogmatism there at the foundations of physics in mechanics: a displeasure not so much dispelled as repressed in the necessity to admire the achievements of mechanistic analysis in extraneous areas. Physics seemed only to spiral deeper into this awkwardness. Even Maxwell and Hertz adhered overtly to mechanistic thinking, though theirs was the thrust which had exposed the worm in the apple. For it cannot be too much emphasized that the identification of the laws of light and electro-magnetism is what opened the way to relativity, by rendering optical experiments relevant to the description of the field. But Einstein had to find grounds for his skepticism in Mach’s criticism of physics and not in the writings of physicists.
Physical theories may be criticized, Einstein thought, from two points of view. The first, which considers the fit with facts, is obvious in principle, though often ambiguous of application, since assumptions may and sometimes should be added to smooth the wrinkles. The second has to do rather with what Einstein called the “inner perfection” of the theory than with its “external confirmation.” He was unhappy with the vagueness of this characterization of theories—“naturalness,” he calls it elsewhere, admitting that exact formulation eludes him, or “the logical simplicity” of the premises. On the score of “inner perfection,” moreover, the laws of thermodynamics made a deeper impression than any other on Einstein in his youth. They were universal in their realm, and from this point of view, “We are confining ourselves to such theories whose object is the totality of physical appearances.” (Thus early does Einstein’s bent appear.) And even at the end of his life he wrote of classical thermodynamics: “It is the only physical theory of universal content concerning which I am convinced that, within the framework of the applicability of its basic concepts, it will never be overthrown.” And it is of crucial interest that thermodynamics should thus have stood before him as the exemplar of universal theory.
For it was not the main course of physical thinking at the turn of the century, nor even his own researches in that line, which issued into relativity. Quite independently of the embarrassments at the foundations of mechanics, Max Planck found in a function relating density of radiant energy to frequency and temperature the constant which argued the discontinuous transmission of “quanta” of energy. That occurred in 1900. The implications were grave indeed, as well for classical mechanics as for the school which would transcend its atomism in energetics. Einstein himself, if he were not the founder of relativity, would figure most honorably as a founder of quantum physics. He saw and investigated the consequences for the photo-electric effect, and in a paper of 1905 he identified the photon as the quantum of light.
Einstein must always have lived more to himself than most scientists do, whose ideas, less their own than his, are forged out of the dialogue of the laboratory amid the never-ending din of colloquia and shop-talk. Thus, he devised a statistical mechanics to express the laws of thermodynamics kinetically—without knowing that Boltzmann and Gibbs, who were anything but obscure, had already accomplished this. Thus, too, he found in his derivations the prediction that microscopic motes should dart about in suspensions accessible to the microscope—without knowing that the Brownian movement, of which he here gave the theory, had been a phenomenon well-known to physicists (though unexplained) for nearly a century. Critical though Einstein was of mechanics, moreover, he did not content himself with some facile philosophical victory over atoms. On the contrary: “My major aim in this was to find facts which would guarantee as much as possible the existence of atoms of definite finite size.” It is the signet of his genius. The appeal which energetics held for Einstein drew him deeper into science, not away from it, and it must be put down to the credit of Ostwald that Einstein’s paper convinced him of the futility of his own energeticist crusade against the atom.
Indeed, Einstein’s relation to particle physics begins in piquancy and ends in pathos. These papers appeared in 1905, as did that on special relativity. And thus at the very moment when he turned classical physics out of its Euclidean housing, he rehabilitated Newtonian views in subsidiary matters, restoring to light its element of corpuscularity and to mechanics its atom. For he was never insensible to the triumphs of particle physics in detail, but only in principle. That Bohr could build upon these shifting sands and relate chemical and spectral properties of matter to the number of electrons in the atomic shell seemed to him a miracle. “The highest form of musicality in the sphere of thought,” he called it, and for Einstein it was a pity that by the end of his life, an increasingly instrumental physics played rather that music than his own.
Instead, his early inability to draw a general theory out of experimental physics led him to abandon hope “of the possibility 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 universal formal principle could lead us to assured results. The example I saw before me was thermodynamics. The general principle was there given in the theorem: the laws of nature are such that it is impossible to construct a perpetuum mobile (of the first and second kind). How then could such a principle be found?” And Einstein turned for guidance from physics to positivism, from Lorentz to Mach and the philosophy which at last accounts would prefer quantum mechanics to the relativity it launched.
How could such a principle be found? For ten years Einstein thought on the matter. And like Descartes he found his insight in himself, in a paradox which had first come to mind when he was sixteen. Suppose he were able to travel with a beam of light at its own velocity. It would seem to be oscillating before his eyes, a standing electromagnetic field. Science knew no such field at rest, either in the laboratory or in Maxwell’s equations. And yet things should transpire for an observer, even rushing along at this extreme velocity, just as they do were he upon earth. How otherwise might he determine that he was in motion, except the laws of nature be the same from one system to another? It was a paradox first deepened and then resolved by consideration of the Michelson-Morley experiment, which established that whether the observer travel downstream with the light or upstream against it, its velocity appears to him to be the same. With sound waves things happen otherwise. Their behavior confirms the predictions of classical mechanics, in that their velocity appears augmented or diminished by one’s own according as one moves in the contrary or forward direction relative to their propagation. One may, perhaps, borrow a thought experiment from the popularization to which Einstein himself much later gave his name in collaboration with Leopold Infeld. They ask us to imagine a laboratory with transparent walls arranged on a truck. Observers stand ready inside and out—physicists with instruments. A device at the precise center of the laboratory emits flashes of light. Mounted on its truck, the laboratory rolls forward. The signal blinks. The physicists inside measure the velocity of light, find it to be 186,000 miles per second, and observe the front and rear walls illuminated simultaneously. Their colleagues outside on the ground measure the velocity of the same signal. Though its source is moving relative to them, they agree that its velocity is 186,000 miles per second, but they see it reach the rear wall an instant before it does the front.
What is simultaneous inside is not simultaneous outside. There is no reconciling these results with classical Newtonian physics, in which here is here, there is there, and now is now.
Einstein would, and often did, state in more sophisticated language the paradox that had occurred to him in germ as a boy. Two fundamental results of experience contradict each other in classical physics: the unchanging velocity of light and the invariance of the laws of nature in different inertial systems. Classical physics supposes that time and space are absolute, and transposes information from one system to another—ship to shore or earth to moon—by linear compositions of the quantity of length or duration. Galileo was quite capable of such compositions of motion. Just so might one move from one set of Cartesian co-ordinates to another by adding x’ to x and thereafter using the new abscissa X. But to save the Michelson-Morey experiment, a different method of getting from one inertial system to another must be employed. This is the Lorentz transformation. Now what remains constant is the velocity of light instead of the metrical meaning of the co-ordinates. Since the velocity of light does not change, then what measures it must. It was more than a mannerism, it was one legacy of his positivist phase, that Einstein preferred writing of clocks and measuring rods to time and space. Clocks in motion do slow down, rods in motion do contract—just enough so that the velocity of light does appear constant to all observers, regardless of their state of (uniform) motion relative to light.
Thus, the critique of simultaneity takes us to the heart of Einstein’s position on special relativity, and permits specifying what the elements were which he put together there. And clearly the first of these was his determination to refound theoretical physics in a universal principle like those of thermodynamics. He paid a price for his admiration for that science. The special theory of relativity was rather a restriction upon science than an induction from positive phenomena. In his taste for “inner perfection” in theory, Einstein answered to an aesthetic which logicians of science have not yet reduced to empirical terms, or to inter-subjective agreement. And certain very eminent physicists long felt uncomfortable about the physical reasoning in the special theory of relativity. In 1941, for example, Professor Bridgman in his book on Thermodynamics objected, in passing, that the special theory, like the second law, rests a general statement about the way the world works upon the physicist’s incapacity to perform certain operations, in the one case to construct a perpetuum mobile, in the other to detect the motion of the earth through aether. But what reason is there to think nature restricted by the disabilities of physicists? Statements about relativity and entropy, then, are really about science, not about nature, and since they say what science cannot do rather than what it can, they may scarcely take pride of place in a science which is nothing if not operational.
Einstein’s position before this criticism could scarcely have been altogether easy, since in the second place he had combined the mode of reasoning drawn from thermodynamics with a precept about physics itself drawn from positivism. The restriction on which the critique of simultaneity rests is that no signal may travel faster than the velocity of light. What gives that velocity its standing as a universal limiting constant is, therefore, rather a principle of communication than of nature. No one may say that nothing travels faster than light—it is only that we cannot be informed of it more rapidly. Information about measurements may be transmitted only by signals, light signals in the fastest case, and there is no significant statement in physics except about measurements. There is no measurement without an instrument, or ultimately without a physicist. And on the face of it, this might seem to have restored a species of subjectivism to science. Nevertheless, this must not be taken for a reversion to idealism—Einstein lapsing back into some Greek posture of humanism. It is all very well to say that there is no physics without a physicist—or perhaps two physicists, one to make a measurement and his colleague to be told of it. But it would, after all, be more accurate to say “without an instrument,” because for such purposes a physicist is an instrument. We are concerned, that is to say, not with a personal subjectivism, but with an instrumental subjectivism, the kind of which a computer is capable.
In the third place, in the principle that the laws of nature are the same in all co-ordinate systems, Einstein simply adhered to the assumption of the uniformity of nature, which is anterior to the very possibility of science. But what laws of nature? In posing that question, Einstein gave his measure as an innovator. Instead of seeking like Lorentz and the others to reconcile the laws of mechanics and of the field—Newton’s laws and Maxwell’s—he gave the precedence to Maxwell. It was a preference unheard of in itself, and full of consequence. The special theory did not involve Einstein in the non-Euclidean formalization of space, later worked for the general theory; and this, which is an epilogue to classical ideas about nature, will not attempt to follow his thoughts so far in verbal paraphrase. Suffice it to say that the general theory requires more complex transformations than Lorentz’s in order to save the invariance of the laws, regardless of whether or not systems were related in uniform motion. Therein he moved beyond positivism to geometrization, in a vein more suited to embracing nature in a single rationale. Already, however, the special theory bore witness to the appeal which the physics of the continuum had exerted over Einstein ever since he was first roused to admiration by Maxwell’s field theory. The original embarrassment of Newtonian physics, action-at-a-distance, disappeared in company with absolute simultaneity. Actions propagated with the speed of light might remain conceivable, but hardly plausible, for how might they be contained in statements about conservation of energy? Physical reality, therefore, would have to be described in continuous functions in space, and the material point would cease to figure as a fundamental entity in theory, along with the extended void across which Newton and classical mechanics had made it act.
Throughout, therefore, the main features of Einstein’s physics—unification, the continuum, and ultimately geometrization—renewed the tradition of rationalism in science, ever abstracting beyond common sense towards a more general formulation of the real in the ideal. It was not relativity of motion which administered the shock, nor even of space—the first is in Newton and the second imaginable enough, perhaps from awareness of perspective (though this is not the same thing). Rather, what wrenched the common consciousness was the relativity of time, and in this the common consciousness judged aright, for the critique of simultaneity lies deeper in Einstein’s physics than the redefinition of space. And thus, classical physics ended as it had begun in Galileo’s law of falling bodies—with a redefinition of the physical meaning of time. Time seems the intimate aspect of the continuum, and the consequence was to move science one stage further into the impersonal generality of things. There is no privilege left for quality in Galileo’s physics, no privilege left in circles by Kepler, no privilege left in life by Darwin, and now no privileged frame of reference or geometry left by Einstein.
Even if there were no other, this would be the decisive superiority of Einstein over Lorentz. Confronted with the inner demand for a consistent account, Lorentz identified the aether with Newtonian space as the absolute co-ordinate system which must still unify his science. Confronted with the same information, Einstein conjured the aether away, Since every effort to detect it ended in failure; since, indeed, it must possess just those properties which rendered its effects undetectable in principle; why then, the only necessity it served was intellectual, not physical, and Einstein would seek unity in the proper domain of the intellect: in the laws of nature rather than in an imaginary entity out in nature. And so disappeared the last of the imponderables, the last frontier of privilege in physics, and with it the space it had come to embody.
“Physics,” wrote Einstein at the end of his autobiography “is an attempt conceptually to grasp reality as it is thought independently of its being observed.” This, no doubt, is philosophically inconsistent with Einstein’s earlier, indeed his continuing instrumentalism. Nevertheless, the loftiness of his thought, as over against the brutality of the times and of its applications, was such that even the public obscurely sensed in him the symbol of the cultural predicament of physics: in the sad, sweet face; in that simplicity more suited to some other civilization, some gentler world; in the strange, the often inappropriate moments chosen for speech; in the great, the profound, the somehow altogether impersonal benevolence; in what shames the spotted adult as the innocence of a wise child.
A passage at the beginning of his Autobiography tells what it was he sought. He is writing of the shock of disillusionment he experienced at the age of twelve, when he found that the stories of the Bible could not be true, and of how he then decided that youth “is intentionally being deceived by the state through lies….”
It is quite clear to me that the religious paradise of youth, which was thus lost, was a first attempt to free myself from the chains of the “merely-personal,” from an existence which is dominated by wishes, hopes, and primitive feelings. Out yonder there was this huge world, which exists independently of us human beings and which stands before us like a great, eternal riddle, at least partially accessible to our inspection and thinking. The contemplation of this world beckoned like a liberation, and I soon noticed that many a man whom I had learned to esteem and to admire had found inner freedom and security in devoted occupation with it. The mental grasp of this extra-personal world within the frame of the given possibilities swam as highest aim half consciously and half unconsciously before my mind’s eye. Similarly motivated men of the present and of the past, as well as the insights which they had achieved, were the friends which could not be lost. The road to this paradise was not as comfortable and alluring as the road to the religious paradise; but it has proved itself as trustworthy, and I have never regretted having chosen it.
And surely the poignancy in Einstein’s destiny welled from disappointments deeper than the drawing off of physical interest from relativity into quanta? Surely the very generality of his liberation, rendering the perfectly benign perfectly irrelevant to the vast impersonality of nature, invested his inner freedom and security with the loneliness of a Greek tragedy, one inhering in the necessities of things rather than (like Galileo’s) in the characters of men.