Maxwell’s Theory of Relativity

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    To a Chinese painter the voids on his paper have as much importance to the meaning of the picture he paints as does the imagery that envelopes and penetrates them. As in the Map of Physics, what-is-not is necessary to the existence of what-is: the voids provide a contrastive context against which the imagery stands manifest. But we do not understand those voids as pure emptiness: the image of a fisherman poling his raft floats on an unbroken expanse of pure white, but we see the river nonetheless.

    Like a Chinese painting, the picture that scholars have drawn of History has its voids among the imagery, voids that show us not merely gaps in our collective knowledge but also show us the might-have-beens, the what-was-not that, by its contrast, enables us to better comprehend the what-was and the what-is. We contemplate the images of past events and imagine also the river of possibility on which they float, a swift current of what-ifs, sometimes turbulent and muddy, othertimes calm and clear.

    What would have happened (or not happened) if Benjamin Franklin had not suspected that storm clouds carry electricity and had not confirmed that suspicion through his famous kite experiment? If Franklin (or someone else) had not discovered that the tiny sparks appearing in electrical experiments were merely miniature versions of Zeus’s thunderbolts, one of the most fruitful branches of physics would have remained barren for a very long time. In particular, the connection between electricity and magnetism would have remained hidden, possibly as far as well into the Twentieth Century. Moreover, Franklin’s popularity, especially among Europeans, came largely from his discovery of atmospheric electricity. If he had not made that discovery, could he have functioned as effectively, if at all, as he did as America’s ambassador to France?

    Or how would history have gone if Luigi Galvani had not kept an electrostatic generator on his dissecting table and thus had not discovered that electricity makes animal muscles twitch? Without that discovery to inspire and guide him, Alessandro Volta would not have invented the electric pile, which led to the discoveries made by Ørsted and Ampere.

    (Contrary to what many believe, that what-if likely would not have erased from History one of the greatest exercises in literature in the Nineteenth Century. Although the movies made from the book give the impression that Mary Shelley gained inspiration from Galvani’s discovery (some Hollywood writer took her characterization of Viktor Frankenstein as "the new Prometheus" a little too literally), the fact remains that she did not mention the use of lightning in the creation of the monster. While Frankenstein brought his creation to life on a cold, rainy night, he did so, insofar as Shelley describes it, purely as an act of chemistry. So we would still have Frankenstein in this alternate history, but we might not have movies).

    Or what would it mean to us if James Clerk Maxwell had discovered the Special Theory of Relativity in 1861, forty-four years before Einstein did in Real History? Of course, we say, such a thing couldn’t have possibly happened. After all, wasn’t it Maxwell who hypothesized the luminiferous æther, whose motion relative to Earth the Michelson-Morley and Trouton-Noble experiments were specifically designed to detect and measure? And wasn’t it the failure of those experiments to find any hint of an ætherial effect that led George FitzGerald and Hendrik Lorentz to propose the contraction of lengths, one of the conceptual stepping stones that supported Einstein when he made his great intuitive leap into Relativity? Therefore, wasn’t it Maxwell’s theory that had to be overcome before Relativity could be discovered and thus wasn’t it effectively impossible for Maxwell to discover Relativity? Well, not exactly.

    The best event with which to start explaining that remark happened in July and September of 1820. In that July Hans Christian Ørsted followed up a demonstration experiment that he had performed earlier for his physics class at the University of Copenhagen. Possibly predisposed toward the idea by the monotheism of western religion, Ørsted harbored, by his own account, a nebulous intuition that the forces in Nature all exist as manifestations of one fundamental phenomenon, a belief that now serves us as the heart that pumps the lifeblood of modern physics. In particular, Ørsted believed that electricity and magnetism are related to each other in some fundamental way and in his lecture prior to his demonstration he buttressed his belief with comments on the variations that travelers had noticed in the behavior of compass needles in the presence of thunderstorms, whose electrical nature Benjamin Franklin had proven and verified roughly seventy years before. Ørsted’s demonstration consisted of mounting a thin platinum wire over a magnetic compass, passing the electric current from a voltaic pile through the wire, and pointing out the consequent movement of the compass needle. Although he originally believed that the magnetic effect had its cause in the incandescence induced in the wire by the electric current, Ørsted found in his follow-up experiments that the electric current alone deflected the compass needle.

    The following September Andre Marie Ampere conducted his own versions of Ørsted’s experiments and from the results deduced the mathematical form of the relation between an electric current and the magnetic force it exerts. With the fact that electricity can have a magnetic effect thus firmly established, physicists naturally speculated that magnetism, considered at the time to be every bit as fundamental as electricity, might have an electric effect. In 1831 Michael Faraday paid off the speculators.

    At first physicists believed that the reciprocal relation between electricity and magnetism has this form: as an electric current creates a magnetic force, so a magnet creates an electric force. That relation, of course, stands false to Reality and we should take interest in the fact that the people who conceived it should have known better: they knew that an electric current consists of electric charge in motion. No one at the time knew how the charge was manifested (they didn’t know about electrons) but the concept of electric current as a motion of electric charge had been known since the first half of the previous century. In light of that fact we have the correct reciprocity relation as this: as motion of electric charges creates a magnetic force, so motion of magnetic charges (poles) creates an electric force. If anyone had seen that relation, they could have confirmed it easily enough. The experiment consists of making a coil of wire and attaching the wire’s ends to a galvanometer, ramming a bar magnet through the center of the coil, and watching the galvanometer’s needle jump. That experiment is still performed today to illustrate Faraday’s principle of electromagnetic induction. But for all our association of his name with it, Faraday didn’t use that particular experiment in his discovery.

    It may stand out in the history of physics as a powerful stroke of cultural luck that Michael Faraday was not an able mathematician. Unable to think in terms of sophisticated mathematical representations of physical processes, he organized his understanding of his work by way of some rather fantastic "aids to the imagination". One of those was his concept of "lines of force", a concept in which we can easily see the reflection of Faraday more as an artist than as a scientist. He had noticed that iron filings scattered on a piece of paper placed over a bar magnet formed patterns that suggested lines emanating from one pole of the magnet and looping around the magnet to plunge into the opposite pole. When he scattered iron filings on a paper that had a current-carrying wire running up through it, he saw a pattern that suggested concentric circles with the wire at their common center. Like the river in a Chinese painting, the lines existed only in the observer’s mind and not on the paper.

    Faraday conceived a bar magnet as a material anchor surrounded by lines of force that invisibly filled the space around and beyond the bar. In modern parlance, a magnetic forcefield envelopes the bar. When the bar moves, the lines move with it, so when the bar passes through a coil of wire, some of the lines will cross the wire. We understand that crossing of the wire by the magnetic lines of force as the phenomenon that generates an electric potential in the wire and thus, if the wire forms part of a closed circuit, makes a current flow.

    We have another way in which we can make magnetic lines cross a wire, the one that Faraday followed when he discovered electromagnetic induction. If the current flowing in a wire increases or decreases, the change causes magnetic lines to expand away from the wire or to contract toward it. Those moving lines will cross any nearby wire and induce an electric potential in it. Faraday made an appropriate two-wire system when he wound two copper wires around opposite sides of an iron ring. He connected what we would call the secondary coil to a galvanometer, making a closed circuit through it, and connected the primary coil to a voltaic pile in the expectation that the current flowing in the primary would induce a current to flow in the secondary. Instead of what he expected, he discovered that the galvanometer needle jumped only when he opened and closed the primary circuit, indicating that it was the change in the current and not the current itself that caused the inductive effect. From that observation he deduced the form of the law that now bears his name, the law that we use as the foundation of the modern electrical industry.

    Taking up where Faraday left off, James Clerk Maxwell completed the description of the inter-relationship between electricity and magnetism. He provided the mathematical sophistication that Faraday lacked, doing for Faraday’s discoveries what Ampere had done for Ørsted’s. He presented his ideas on electromagnetism in three papers published in 1856 ("On Faraday’s Lines of Force"), 1861 ("On Physical Lines of Force"), and 1864 ("A Dynamical Theory of the Electromagnetic Field"). The first of those papers did little more that show how to convert Faraday’s discoveries into mathematical form.

    In his second paper Maxwell effectively completed the theory of electromagnetism, incidentally employing the æther that led physicists on a forty-four year wild goose chase. In essence Maxwell restated the reciprocity relation that underlay the discovery of Faraday’s law, replacing the Newtonian concepts of centers of force exerting actions at a distance with Faraday’s notion of forcefields permeating all space. In its new form the relation stands before us as this: as motion of electric lines generates magnetic lines of force, so motion of magnetic lines generates electric lines of force. Expressed in that way the relation requires a change in the statement of Ampere’s law. Ideally, Maxwell would have restated Ampere’s law to describe the generation of magnetic fields entirely in terms of moving electric fields. However, Maxwell instead modified Ampere’s law by adding to the term representing electric currents a term that he called the electric displacement current. That term represents the overt manifestations of moving electric fields while the conventional electric-current term represents covertly manifested moving electric fields, the fields of moving charges whose electric effect gets cancelled by the fields of stationary charges (just the kind of thing that happens in the case of a current-carrying wire).

    As an immediate consequence of his modifying Ampere’s law Maxwell discovered a mathematical theory of electromagnetic waves. By combining his version of Ampere’s law with Faraday’s law, Maxwell deduced an equation perfectly analogous to the equation describing the propagation of the pressure waves called sound. The solution to his wave equation, he found, showed him the mathematical form of an electromagnetic-field wave propagating through space at a speed that he could calculate from the electric and magnetic proportionality constants that had been measured in the laboratories of Wilhelm Weber and Rudolf Kohlrausch. His calculation gave the speed as 193,088 miles per second, a number close enough to the 195,868 miles per second derived from Armand Fizeau’s 1849 measurement of the speed of light to make him believe "that we can scarcely avoid the inference that light consists in the transverse undulations of the same medium which is the cause of electric and magnetic phenomena."

    The medium to which Maxwell referred is the infamous æther. Though Maxwell didn’t invent the concept, we associate him with it because he gave it a special plausibility. The æther concept became entrenched in the mythology of physics when Thomas Young demonstrated in 1802 that light is a wave phenomenon beyond any reasonable doubt. As a wave, like sound or the motion of the ocean’s surface, light must therefore manifest the vibration of some medium, which the physicists of the time called æther, using the word the Greeks had applied to the transparent-blue substance they believed filled the upper atmosphere. Maxwell devised his own invisible medium as an aid to his imagination, but he conceived its manifestations as nothing more than the electric and magnetic lines of force. Only the discovery of how fast electromagnetic waves move led Maxwell to identify his medium with the luminiferous æther. By deducing the fundamental property of the æther, the speed of light, from considerations outside the study of light, Maxwell confirmed for many people the existence of the medium.

    Though he gave it a special plausibility, we have little doubt that Maxwell did not take the æther as seriously as others did. He abandoned the concept altogether in his 1864 paper, in which he first presented the famous eight equations (condensed to four in modern textbooks) that sum up all of electromagnetic theory. We can even conceive the possibility that he regarded the æther as something of a joke, a kind of electromagnetic farcefield: he was known among his contemporaries for a sense of humor of sublime whimsy. But if Maxwell conceived the æther as a joke, Einstein got to deliver the punchline and some people regard that as entirely appropriate, seeing a Jungian synchronicity connecting the two men through the fact that Einstein was born the same year, 1879, that Maxwell died (though I must point out that Einstein was born the fourteenth of March and Maxwell died the fifth of November).

    However useful or funny he may have found it, Maxwell most likely employed the æther for Michael Faraday’s sake. The two men were good friends and Maxwell had a knack for converting the most sophisticated mathematical ideas of physics into concepts that Faraday could think with comfortably. In a letter that he wrote to Maxwell in 1857 Faraday reminded him of that special ability and urged him to use it, when he had completed his works, to translate the "hieroglyphics" of higher mathematics into imagery more easily accessible to minds unskilled in mathematics. If, indeed, such urgings prompted Maxwell to employ the æther concept, then History might easily have followed a different path.

    One of the tasks that Maxwell had accomplished early on was a demonstration that theories based on mathematical descriptions of Faraday’s lines of force are fully equivalent to theories drawn from Newtonian concepts of centers of force exerting actions at a distance. He thus used the older concepts as a test to confirm the validity of the newer concepts, thereby providing us an example of what we now call the correspondence principle. In the light of that effort, his failure to make a similar confirmatory test of his theory of electromagnetic waves looks strange. The test is easy to make and if Maxwell had made it, he would have run into an intriguing problem.

    After deducing the existence and properties of electromagnetic waves from manipulation of his equations of abstract mathematics, Maxwell could have confirmed his discovery by direct application of the lines-of-force model. Mathematically the test would have involved translating Maxwell’s Equations from their conventional form as a set of differential equations into an equivalent set of integral equations, a minor exercise for Maxwell. Conceptually the test consists of imagining an experimenter observing a field of magnetic lines passing through a series of galvanometers. The lines move in a direction perpendicular to the direction in which they point, so, in accordance with Faraday’s law, they will generate an electric field whose intensity stands in proportion to both the magnetic field’s intensity and its velocity. That electric field will be manifested in all of the galvanometers as the magnetic field passes through them, leading the experimenter to conclude that the electric field travels with the magnetic field. But Maxwell’s version of Ampere’s law says that a moving electric field will generate a magnetic field, one that, in this case, will act to support the original magnetic field.

    At speeds achievable in a Nineteenth Century laboratory the amount of support that a magnetic field would obtain from its induced electric field is insignificant. Thus the field must gain support from a material source, such as a bar magnet or a current-carrying wire. But of course we know a speed, the speed of light, at which the induced electric field has sufficient strength and moves fast enough to generate full support for its magnetic field. Fields traveling past the experimenter at that speed can fly free of all material sources. In fact, according to Maxwell’s theory, free-flying fields can travel only at the speed of light. If they travel slower, they will undersupport each other and decay and if they travel faster, they will oversupport each other and grow: in either case they would violate the conservation of energy theorem.

    When Maxwell deduced the electromagnetic wave equation from combining the differential equations of Faraday’s law and Ampere’s law, the speed at which the waves propagate appeared as a mathematical abstraction that then needed an associated physical interpretation. More psychology than physics, the free association of mathematical results with real or imagined features of Reality tells more about what physicists believe than it does about the workings of Nature. The river we see in the painting doesn’t always coincide with the river the artist depicted and the "c" in Maxwell’s wave equation does not represent velocity relative to a medium, as many physicists believed at the time. The lines-of-force derivation outlined above removes the ambiguity from the interpretation: in it the speed has been specifically described as the speed at which the fields move past an experimental apparatus. Maxwell would have understood that the fields must conform to the requirement that they fly at the same constant speed past any apparatus and that understanding seems to lead directly to a logical contradiction.

    (Further, the constancy of the speed of light follows from the fact that the speed of light must necessarily display perfect isotropy. If we try to invoke an æther wind to make light pass different observers at different speeds, then we must assert that the speed of light can display anisotropy, having different values in different directions, which necessitates that in some inertial frames of reference the electric and magnetic force constants must be anisotropic. But that makes the forces themselves anisotropic, which sets up violations of the conservation laws.)

    Imagine, as Maxwell would have done, that two experimenters have set up arrays of galvanometers to measure the field of a free-flying electromagnetic wave. One experimenter has set up his apparatus on a flatcar that workers have integrated into an express train and the other has set up his apparatus on the platform of a small station, a minor whistle stop for which the express won’t even slow down. An assistant so generates the wave that it flies along the track without spreading; thus, when it passes through the station experimenter’s apparatus at the speed of light, all of the galvanometers in the array will measure the same value for the amplitude of the induced electric field. Given that fact and the knowledge that the train moves away from the wave’s source, we can form a preliminary expectation that the wave will fly through the train experimenter’s apparatus at a speed slightly less than the speed of light and that, therefore, the fields in the wave won’t fully support each other: we should expect the wave to display a progressively diminishing electric field on successive galvanometers in the array. Fulfillment of that expectation would create a contradiction in which the train experimenter reports that the wave faded as it flew, being extinguished by the defect in its velocity, while the station experimenter maintains that the wave flew along the track without diminution.

    Confronted with that dilemma and unable to deny the validity of the laws that create it, Maxwell would have to question his interpretation of the laws. He would almost certainly begin by reaffirming Formal Logic’s law of the excluded middle, which stands as the basis for our belief in the non-contrariness of Nature’s laws. That reaffirmation might take the form of an axiom worded to have obvious application to the two railroad experimenters:

    1. The character of any phenomenon has the same form for all observers, regardless of how the traits of that character may be distorted by the uniform motion of the observers relative to each other and relative to the objects associated with the phenomenon.

    We can sum up the character of the phenomenon under consideration as "an electromagnetic field flying free of any entanglement in material sources, the fields so supporting each other that they can travel together without diminution". Having reaffirmed that proposition, Maxwell would then proceed to resolve the contradiction between the railroad experimenters by stating a second axiom:

    2. Any electromagnetic wave will always pass observers at the same speed, regardless of how the observers move relative to each other and relative to the source of the wave.

We recognize those axioms simply as reworded versions of the two postulates that Einstein presented as the foundations of Special Relativity in his 1905 paper "On the Electrodynamics of Moving Bodies":

    "1. The laws by which the states of physical systems undergo change are not affected, whether these changes of state be referred to the one or the other of two systems of co-ordinates in uniform translatory motion.

    2. Any ray of light moves in the ‘stationary’ system of co-ordinates with the determined velocity c, whether the ray be emitted by a stationary or by a moving body."

Thus Maxwell could have come to the foundations of Special Relativity, though at the expense of exchanging one contradiction for another. He would now have two observers in relative motion seeing the same thing, the electromagnetic wave, pass each of them at the same speed. But even that contradiction has a resolution, albeit a strange one.

    Translated into mathematical form (via the wave equation), Maxwell’s second axiom looks like a misshapened version of Pythagoras’ Theorem. Following Einstein, we deduce from that expression the bizarre effects of Special Relativity, collectively known as the Lorentz Transformation. Happily for our speculation, Maxwell, educated in the classics, had available to him an easy way to understand the meaning of the expression in a way that would lead him to the Lorentz Transformation. Further, it was a way that would have held a strong appeal for a Victorian thinker: it led through Ancient Greece.

    In "The Republic" Plato presents an allegory that illustrates his belief that Reality consists of fleeting, shifting Appearance that takes its shape from eternal, perfect, and changeless Forms that we can never apprehend directly. He describes a deep cave with a large chamber in which people sit chained to positions before a wall on which the shadows of an unseen puppet play appear, shadows cast by the light from a fire burning behind the puppets. The puppets represent the Forms and their shadows on the wall represent the illusions of Appearance. We assume that Maxwell would notice that confusion would reign in the cave until someone made an unusual application of Plane Geometry.

    Though the chained spectators would agree that they all see the shadows on the wall, they would disagree over what the shadows look like. A shadow that appeared square to one spectator would look trapezoidal to another; one spectator might see as circular a shadow that others see as elliptical; and so on. Unable to move, to share each other’s points of view, the spectators would seem to have no way to reach an agreement. Eventually the spectators would learn to measure the shadows, but their enchainment would restrict them to using instruments, such as the sextant, that measure the angles subtended by the distant figures. At first the measurements would only add to the confusion: neighbors who thought they were in agreement would find that their measurements disagree. Finally, one clever fellow, well skilled in Plane Geometry, would develop a technique through which he would use the knowledge of his neighbor’s position relative to himself to translate his own measurements of shadows into measurements identical to the ones his neighbor makes of the same shadows. Mathematicians call the technique a transformation and the clever fellow will have deduced it from the classical Pythagorean Theorem.

    Seeing an analogy between the spectators occupying fixed positions in Plato’s cave and his own imaginary experimenters traveling at different fixed velocities, Maxwell would have seen his way clear to interpret his second axiom as analogous to the Pythagorean Theorem. Like the clever fellow in the cave, he would have deduced the appropriate transformation and reconciled his two observers, thereby creating the theory of Special Relativity much as we know it. In doing that, Maxwell would have at least implied that material Reality is a mere shadow play, but that would not have been seen as a radically new idea. Indeed, Maxwell’s Theory of Relativity would certainly have inspired a powerful upsurge of interest in the beliefs of Bishop George Berkeley, the Irish immaterialist philosopher who did believe that Reality is a shadow play and that perception stands as the sole criterion of existence.

    Once established, Maxwell’s Theory of Relativity would have exerted an influence far outside physics and philosophy. In this Age of Reason, science has replaced religion as the source of ultimate truth and in a kind of modern animism scientists’ ways of thinking about the world get transposed onto people’s ways of feeling about the world as the spirit of this or that theory appears to inhabit and control more phenomena than the theory was originally meant to describe. A prime example of that process comes from a theory that was published about the time that Maxwell was completing electromagnetism, Charles Darwin’s theory of evolution via natural selection. Conceived as an organizing principle for the facts of biology and geology, Darwin’s theory, often summed up in the catchphrase "survival of the fittest", has been used (illegitimately, of course) to justify things ranging from the hereditary class structure of Victorian England to modern street thuggery to the megacrimes of the Nazis.

    Unlike Darwin’s theory, which had its profoundest side effect on politics, Maxwell’s theory would have made its deepest and most obvious impression on art. In particular, it would have supplied a much needed validation for the artistic style called Impressionism.

    Though we can find examples of the style originating as far back as the late 1830's, Impressionism was first seriously applied as a way of experiencing the visual world in the 1860's. Today it stands as one of the best loved styles of art, but from its inception it was mercilessly derided and vilified by art critics and rejected by the established salons. Only in the late 1880's did Impressionism gain any acceptability, though as late as 1900 at the Universal Exposition in Paris an art critic could still, with some dignity, stand in the doorway to a room full of Impressionist paintings and implore President Loubet not to gaze upon "the shame of France".

    The Impressionist style, so-named in derision at Claude Monet’s 1872 painting "Impression, Sunrise", is typified by the visibility of the artist’s brushstrokes. From Paul Cezanne’s broad splashes to Georges Seurat’s pointlike dabs, Impressionist paintings display images made up of discrete areas of color whose borders the artist has not worked out and obscured as in conventional Realist painting. The artist makes no effort to create a photographic reproduction of Reality, but rather the artist presents a dappled vision of the world, a vision that plays on the human mind’s tendency to see patterns even in phenomena that have no patterns: the artist needs only imply a vision and the viewer makes it real.

    Such a view makes Impressionism seem to prefigure the modern quantum theory with its observer-created Reality, but we see Maxwell’s relativity axiom as the statement that the Impressionists would have taken to heart. The basic principle of Impressionism tells the artist to paint the essential and to leave the obvious implied, somewhat in the manner of the traditional Chinese style. That statement is equivalent to saying that the artist is to paint in a way that preserves the character of his subject, however much he may distort the traits manifesting that character. Like Relativity, Impressionism emphasizes the subjectivity of observation by denying the possibility of objective observation.

    The Relativists, as people would likely have called the Impressionists in this alternate history, would still have to endure derision and rejection, but with the support of the relativity axiom they would have faced a shorter and less intense battle to invade the "legitimate" salons. Thus not only would the originators of the style – Monet, Renoir, Cezanne, et al. – have gained the ability to paint more canvases, but more artists would have adopted the style to express their own interpretations of life and the style would have spread faster than it did in Real History.

    So advancing the discovery of Special Relativity by forty-four years gives the world more weird paintings. That may be good news for art lovers, but it does not represent a significant change in the course of History. Or does it?

    Twentieth-Century artists have pretty much given up on the idea that their craft can exert any meaningful influence on the collective behavior of Humanity. They certainly seem to have plenty of reason for pessimism, but in that impression we have only an illusion. The pessimism simply manifests the letdown from expectations that should never have been raised, expectations that people set up on beliefs that did not include knowledge of the unconscious mind and its workings. Now modern psychology tells us (and experiments with pornographic movies confirm) that any phenomenon that touches our feelings will change our attitudes, however subtly, and will thereby reshape our behavior. So Impressionism, with its joyous celebration of the mundane world of the common people, would certainly have pushed Humanity into a history different from the one it actually experienced, the one guided in part by an art that somberly glorified ancient mythologies and the hereditary aristocracy that identified with the ancient heroes. (The Great Humanistic Liberation, marked by the growth of the democratic ideal, would be enhanced just as the reactionary [retrograde] attitudes of hereditary oligarchy were bolstered by Darwinianism (however wrongly). We find in the celebration of the ordinary mundane scenes of life among the common people that which makes Impressionism so distinct from the traditional form that glorifies the oligarchies and the ancient myths that give form to their hierarchical ideals.) We must thus ask the question: how would the two histories have differed one from the other?

    Today we can’t answer such a question. We might guess that a Humanity that preferred soft-focus pictures of the simple pleasures of life to razor-sharp pictures of imperial splendor would have had the good sense not to create the First World War and its sequel, but that would only be a guess. (As a political metaphor Maxwell’s axiom would likely be seen as a more accurate version of what Jefferson intended with his social algebra [all men are created equal] and thus a more effective argument for achieving the perfection of the democratic vision.) For now the discipline of psychohistory, which could answer the question accurately, exists only in imagination as a bare possibility. But someday psychohistorians, like Hari Seldon in Isaac Asimov’s "Foundation" stories, will have a clear and sufficient knowledge of individual and collective psychology adequate to plot alternative histories accurately. They will have the ability to provide unambiguous answers to the questions posed at the beginning of this essay. They will use those answers and others like them in a technique similar to the Lagrangian method of classical physics, in which we deduce the path a body actually follows from an analysis of all possible paths available to it. Then, like the Chinese fisherman poling his raft on the unpainted, yet nonetheless visible, river, they will guide Humanity as it floats on and drifts down the river of possible histories, exploiting its currents, avoiding its dangers, and fishing up nutrition from its depths to sustain Humanity on its endless journey toward the non-existent End of Time.

Appendix:

The Apocalypse of the Physicists

    To anyone who speaks Greek, apocalypse means an unveiling. The word takes it negative connotations, especially in the English-speaking part of the world, from one particular apocalypse, the one written by Saint John of Patmos, also known as the Book of Revelations. But an apocalypse can have positive implications, as we shall see.

    Beginning around A.D. 1600 the group of people that we call physicists began an apocalypse of their own. At their instigation, Nature began to perform for Humanity a kind of Dance of the Seven Veils. That dance continues today and may never end, simply because the removal of each veil obliges us to create concepts through which we discover the next veil.

    Consider Newtonian dynamics. In establishing his dynamic geometry, Isaac Newton gave mathematical definition to the concept of force. In order to do that he also had to offer mathematically suitable definitions of quantity of motion (momentum) and inertial mass. With those mathematized concepts and the laws associated with them, Newton worked out a mathematical description of the action of gravity and laid the foundation of much of the physics used today, especially in engineering.

    As the Eighteenth Century shaded into the Nineteenth physicists found it convenient to define a quantity that we now call energy and began to work out the mathematical relations among the various forms in which it manifested itself in their experiments and theories. Energy defined led to Hamiltonian mechanics and the concept of action. It also led to the study of heat and light.

    At the beginning of the Twentieth Century radiation thermodynamics, especially in the minds of Max Planck, Albert Einstein, and Niels Bohr, offered clues to yet another veil. In the 1920's physicists began pulling away that veil to reveal the quantum-mechanical nature of Reality. Also near the turn of the century Einstein introduced the concept of invariance as a touchstone against which theories could be tested. His theory of Relativity, a prime example of the application of invariance, refined our concepts of space and time from that of a single entity, as Newton had assumed, to an infinite set of inertial reference frames, some of them warped out of true by gravity and other phenomena. Combining that theory with the quantum theory led physicists even deeper into the nature of matter, led them to discern the fundamental constituents of all that exists.

    Now, at the beginning of the Twenty-First Century, the dance seems close to coming to an end. But physicists had entertained just such an illusion at the end of the Nineteenth Century only to have that illusion shattered by the discoveries of radioactivity, Relativity, and the quantum theory. Nonetheless, in the Map of Physics we seem to see the hazy outline of the much desired Theory of Everything. We now conceive space as a thing whose boundary moves away from all observers at the fixed speed of light, moving with the elapse of time. We conceive space as a thing filled with waves that all move at the speed of light and understand that the phenomenon that we call matter consists solely of interference patterns in those waves. Have we finally discerned the puppet play whose shadow constitutes the Reality that we perceive? Or will we encounter more veils? Only time and further study will tell.

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