Hiding in the Mirror: The Quest for Alternate Realities, From Plato to String Theory (By Way of Alicein Wonderland, Einstein, and the Twilight Zone)

by Lawrence M. Krauss

  One of the people whose critical examination helped Ampère ultimately refine his theory was the budding physicist Faraday. The year after Oersted made his discovery, in fact, Faraday published his own first significant discovery regarding electricity and magnetism. (Essentially all of his previous work had been on chemical analysis.) He discovered that small magnets would rotate around a wire with a current flowing through it, or alternatively, that a wire with a current flowing in it could be made to rotate about a fixed magnet. This established the peculiar nature of the magnetic force that was produced by moving electric charges, and ultimately verified key aspects of Ampère’s ideas. The fact that the resulting force between the magnet and the wire was not merely attractive or repulsive, like the electric force between charges, but rather, pointed perpendicularly to an imaginary line joining the two objects (which would make one rotate around the other) was the first hint that the relationship between electricity and magnetism would require a completely new way of thinking. The simple, intuitive world that Newton unveiled with his brilliance was about to reveal its hidden underbelly.

  It is interesting to note that in a letter written at the time to a friend in Geneva, Faraday talked about his early reticence in working on the subject associated with Ampère’s “wild” theories: Theory makes up the great part of what M. Ampère has published, and theory in a great many points unsupported by experiments when they ought to have been adduced . . . [F]or myself, I had thought very little about it before your letter came, simply because, being naturally skeptical on philosophical theories, I thought there was a great want of experimental evidence. Faraday went on to spend the next forty years of his life providing that evidence, and in what is perhaps one of the more profound ironies of physics, he ultimately provided the key theoretical idea that would reveal the true relationship between electricity and magnetism. While Oersted had shown that the former could create the latter, as early as 1822 Faraday wrote in his experimental notebook, where he recorded all his thoughts and ideas, the suggestion “convert magnetism into electricity.”

  Nine years later, on August 30, 1831, Faraday achieved the longsought goal by means of his most famous experiment, described at the beginning of this chapter. But while Faraday demonstrated that magnetism could create electricity, it did so in a way that no one had suspected. A normal magnet, no matter how strong, could not generate an electric current. However, a magnet whose strength changed could produce a current in a nearby wire. In his initial experiment Faraday created such a changing magnet simply by turning on and off a current in the first wire. As Oersted had already established, once a current was flowing in a wire, that wire acted like a magnet. Thus, during the brief period that the strength of the current rose from zero to its ultimate value, the corresponding strength of the magnet that it generated varied accordingly. It was only on the short interval surrounding the times that the circuit was either opened or closed in the first wire that Faraday noticed a current flowing in the second wire.

  Faraday verified his idea that it was actually the changing strength of the magnet that caused a current to flow in the second wire by conducting a different experiment. Instead of turning a current on and off in the first wire, he simply moved a magnet closer and then farther away from the second. A current flowed as the magnet approached and again as it was withdrawn.

  We now call Faraday’s discovery induction, because one can induce currents to flow in wires exposed to magnets whose magnetic strength, relative to the wire, is changing. Faraday was justified in the promise he made Gladstone quoted in the epigraph to this chapter, because today we do tax this phenomenon, which has made possible most modern technology, as it allows us to produce electric power from sources such as falling water. If the water can be channeled through a tunnel, and made to spin a turbine holding several magnets within it, as the turbine spins around currents will be induced to flow in wires surrounding it. This is how we generate most of the electricity in the area of the United States where I currently live.

  While Faraday’s experimental discoveries therefore changed the face of modern society, they also changed our picture of nature. With his highly intuitive sense of nature, Faraday distrusted simple mathematical descriptions of phenomena, such as the force of attraction between two magnets. He preferred instead to formulate a physical “picture” of this force, so as a visual aid he suggested that throughout the space surrounding the magnets, one could imagine “lines of force.” The direction of the force that would be experienced by another magnet that one might locate at any position would follow along the lines of force passing nearby. Similarly, the total number of field lines located near this point would signify the strength of the force. Ultimately Faraday used the same kind of visualization to describe the electric forces between charged particles, again without resort to mathematical equations. Had Faraday been more comfortable with mathematics, he would have recognized that these “field lines” themselves had a simple mathematical description in terms that we now describe as a “magnetic field.” A field is simply a function that assigns to each point in space some quantity. This quantity can be something as simple as a single number, or it can be something more complicated, such as a vector, which is a number plus a direction, appropriate to describe a force, for example. The idea that magnets and charges might give rise to magnetic and electric fields, respectively, represented a major conceptual advance. From the time of Newton onward the question of how forces such as gravity actually act on distant objects had been a complete mystery. So-called instantaneous action at a distance seemed physically implausible—how did the earth know where the sun was in order to be attracted to it?—but a necessary, if unpleasant, fact of life. Faraday’s fields solved this problem, at least in principle. If electric or magnetic fields exist throughout all of space, surrounding every charged object or magnet respectively (and for the moment one could ignore the question of how long it would take for such fields to develop around each such object), then a charged object or magnet located at a remote distance from another such object could experience a force due indirectly to that distant charge or magnet, but manifested directly via an interaction with the electric or magnetic field present in its own immediate vicinity. No direct action at a distance would be required! Faraday reasoned that gravity, too, could be described in terms of lines of force, thus avoiding Newton’s conundrum.

  By the time that Faraday introduced these ideas in print, he was a wellestablished scientific figure, so his colleagues certainly took note of them. However, his descriptions were sufficiently vague that it is fair to say that most others were not convinced by them. For the case to become truly compelling it would require a physicist whose talents as a theorist were a match for those of Faraday as an experimentalist. Fortunately, such a theoretician had just moved to England at around the time Faraday was proposing his ideas. The nineteenth century was full of towering mathematical geniuses, a number of whom pushed forward the frontiers of accepted knowledge, such as Newtonian mechanics. James Clerk Maxwell, however, in his short lifetime, left a legacy that is unmatched by any of them. He not only originated what is now the modern theory of gases, and the basis for the theory of statistical mechanics, which Boltzmann, Einstein, and Gibbs would later place firmly at the center of modern physics, but also completed the theoretical formulation of electromagnetism, the model prototype for the theories of all the known forces in nature. So complete and beautiful was his formulation that his equations for electrodynamics, now called “Maxwell’s Equations,” are emblazoned on the T-shirts of physics students and teachers throughout the world, who rely on them for much of what they do on a daily basis (the equations, not the T-shirts).

  All these were conceived by a man who, before he died at the tender age of forty-eight, established the reputation of the Cavendish Laboratory at Cambridge, whose first director he was, as the major experimental physics laboratory in the world. Born and raised in Scotland, Maxwell did not have an auspicious youth. A private t
utor who had been employed to teach him was not optimistic, reporting that he was a slow learner. Later Maxwell got the nickname “Dafty” from his schoolmates. By his teens he began to show mathematical promise, and studied at Edinburgh University and then Cambridge, where he ultimately received a fellowship. Nevertheless, he longed for his native Scotland and returned to Aberdeen to teach.

  His treatment there, however, does not suggest that he gave any indication that he would eventually become known as perhaps the greatest theoretical physicist of the century. When Marischal College, where he was professor of natural philosophy, was merged with King’s College to form Aberdeen University, two professorships were merged into one, and his post was given to the professor at King’s, forcing Maxwell to seek another position. He applied for the professorship at Edinburgh University, which had become vacant, but it was given to one of his friends and former classmates instead. Maxwell was once again driven back down to England, where he accepted a post at King’s College London, which he occupied until he was ultimately offered his position as Cavendish Professor at Cambridge. While in London, Maxwell got to know Faraday, for whom he had immense respect. Both physicists thought in terms of physical pictures, although Maxwell’s mathematical talent was sufficient to allow him to translate his ideas into precise mathematical formulations. In 1856, while still in studying in Cambridge, Maxwell wrote a lengthy paper entitled “On Faraday’s Lines of Force,” in which he attempted to put Faraday’s idea on a solid mathematical footing. This was the first step in his attempts to determine and formulate the laws of electrodynamics in a mathematically consistent fashion, which would culminate in his Treatise on Electricity and Magnetism (1873). By the time his work was completed, he had taken the geometric crutch of Faraday—the electric and magnetic lines of force, and the “fields” they represented—and turned them into entities as real as you or I.

  As it was originally discovered, through the experiments of Oersted, Faraday, and their colleagues, the theory of electromagnetism was framed completely in terms of measurable physical entities (charges, currents, and magnets) and how they interact with one another. By trying to picture how these interactions operated, Faraday imagined space as full of electric and magnetic fields. Who would have guessed that the fields themselves could produce physical effects even if there were no charges, currents, or magnets nearby to respond to them? It would be disingenuous to say that the answer was as clear as the nose on your face, except that it is: The nose on your face is clear precisely because of these fields. It is these very fields that allow you to see.

  Let’s recap the rules of electromagnetism up until Maxwell. Oersted had discovered that currents (i.e., moving charges) could produce a force on magnets. Ampère had shown that these currents were in themselves magnets. Faraday discovered that changing the strength of a magnet put near a charge could produce a force on the charge.

  What concerned Maxwell (as it had Faraday) was trying to find a unified understanding of these effects. What happened in the empty space between charges and magnets that could convey these forces? Both scientists, as they flailed about trying to understand the nature of the electromagnetic interaction, imagined this empty space as being filled with a remarkable amount of paraphernalia (invisible vortices, ball bearings, etc.) that might implement the action of Faraday’s imaginary field lines. Ultimately Maxwell realized that the magnetic and electric fields that Faraday envisaged throughout space might have a reality beyond their mere mathematical convenience, even if Maxwell himself probably still personally retained a physical picture of some “fluid” medium that permeated space, like the classical aether of Aristotle, with currents flowing within it. But the mathematical discovery that Maxwell made that changed everything was simply the following: One could frame the laws of electromagnetism in terms of these electric and magnetic fields as fundamentals and not derived quantities. If moving charges would produce an everchanging electric field and also a constant magnetic field, then perhaps the observation about currents and magnets could instead be framed as this: Changing electric fields can produce magnetic fields. And the observation about forces on charges being produced by moving magnets (which would produce changing magnetic fields) could be rephrased: Changing magnetic fields produce electric fields. This subtle revision, with the fields taking center stage, could only truly have physical meaning if, in empty space, devoid of charges and currents, a measurable magnetic field could be produced purely by a changing electric field, and vice versa. Again, Maxwell led the way by showing that the mathematical description of electromagnetism was not consistent unless this phenomenon—occurring in empty space without physical changes and currents—could also occur, and he described precisely an experiment that would demonstrate just this effect.

  But the biggest prediction—one of my favorite ones in all of physics—was yet to come. If I take a charge and move it, the electric field around it changes. That changing electric field in turn produces a changing magnetic field. But that changing magnetic field in turn produces a changing electric field. And so on, and so on, and before you know it an “electromagnetic disturbance” will propagate out into space. Maxwell could use the equations of electromagnetism he had derived to calculate the velocity of this disturbance in terms of two fundamental constants in nature: the strength of the electric force between charged particles, and the strength of the magnetic force between magnets. When he did this calculation, he found that this disturbance would have the character of a wave, like a water wave, with crests and troughs not of water, but of the fields itself. Moreover, the speed that he calculated for this “electromagnetic wave” was familiar. It turned out to be the speed of light. This suggested, and it was later confirmed by experiments, that light itself might be waves of electromagnetic fields.

  Maxwell’s remarkable proposal—that light itself is an electromagnetic wave—occurred a full decade before Edwin Abbott wrote Flatland, and it would be over twenty more years before a young physicist working as a patent clerk in Switzerland would realize the full implication of this insight. Nevertheless, nature was competing with the literary imagination. Within less than seventy-five years of the discovery of the electromagnetic phenomena that power our modern civilization today, Faraday’s imaginary crutches had become real, and they would ultimately force us to change the way we conceive of such fundamental concepts as space and time.

  C H A P T E R 3

  THE ROAD TO RELATIVITY

  We have no direct intuition about the equality of two time intervals. People who believe they have this intuition are the dupes of an illusion.

  —Henri Poincaré, La Mesure du Temps

  The eighth edition of the Encyclopedia Britannica appeared in 1878, just a year before James Clerk Maxwell’s untimely demise. In that edition Maxwell penned an article entitled “Ether,” in which he sardonically commented, “Space has been filled three or four times over with ethers.” His critique was based on the fact that scientists had, over the years, proposed separate, distinguishable, but invisible media permeating all space, in which either light, heat, electricity, or magnetism might be conveyed. Maxwell felt that one of his great contributions, by demonstrating that light was an electromagnetic wave, was to reduce all of these separate “ethers” to a single medium, in which such waves might propagate. Maxwell was so convinced that such a medium must exist that he actually set out to measure its effect on the propagation of light rays from the moons of Jupiter when the gas giant eclipses them, as seen from Earth, when our planet is moving at different speeds relative to Jupiter. In 1879 he wrote a letter acknowledging the receipt of data on Jupiter and its moons from the Nautical Almanac Office in Washington, D.C.

  Maxwell reasoned that if one measured the apparent velocity of light at different times relative to Earth by measuring the time it took light to traverse the distance from Jupiter to Earth when Earth was moving in different directions in its orbit through the fixed ether in which the light rays presumably propagated, one could meas
ure Earth’s motion relative to this ether. Whether Maxwell had sufficient time to adequately analyze the Nautical Almanac data before his death, or whether the data was good enough to even discern such a possible effect in principle, is now immaterial. The truth is, his proposal was doomed to fail, for reasons even he probably never imagined.

  The first empirical evidence that the velocity of light did not obey the expected dependence on Earth’s motion appeared less than two years after Maxwell’s letter to Washington, in an experiment performed by the man who would eventually become America’s first Nobel laureate in science, Albert A. Michelson. Michelson was on leave from the navy at the time, doing what all good would-be scientists living in the United States who wanted to get ahead then did—namely, spending time in the superior laboratories in Europe. In this case, he chose to work in Helmholtz’s laboratory in Berlin. Michelson, an experimental genius, had designed an apparatus that could detect a far smaller effect caused by the Earth’s motion through the ether than Maxwell had proposed looking for. Instead of relying on data from observations of the Jovian system, Michelson could compare the round-trip travel time of two light rays traveling at the earth’s surface in different directions with respect to the earth’s motion around the sun—and thus also, presumably, with respect to the ether background. (Light rays traveling through the ether would presumably travel more slowly relative to the earth if they were battling an “aether headwind” as opposed to being propelled along by it, just as a golf ball hit into a headwind will travel more slowly, and hence cover less distance, than a ball hit into a tailwind. As a result, the round-trip travel time of a light ray should depend on its direction of motion relative to an ether headwind.) Even though the predicted effect of the earth’s motion through the ether was minute, Michelson’s apparatus should have been able to discern it, but in 1881 he reported that his attempt to do so was unsuccessful. He was unequivocal in his conclusion: “The result of the hypothesis of a stationary aether is thus shown to be incorrect, and the necessary conclusion follows that the hypothesis is erroneous.”