God In The Equation Page 6
Yet Einstein did not abandon religion. Rather, he made peace with God, albeit a very different kind of God from the one he heard about at the Luipold Gymnasium. Years later, when he met with the Jewish philosopher Martin Buber, Einstein told him, “I want to know how God created this world. . . I want to know His thoughts, the rest are details.” Sometimes, as with the whole story of Lambda, it seemed that Einstein chose to dictate God's thoughts and then step back and see if the Lord agreed with his decrees. When he famously insisted that “God does not play dice with the world”—a line that was repeated, discussed, and rephrased many times during his life—Einstein was not interpreting a religious text, he was writing one of his own. He once exposed this method explicitly: “When I am judging a theory, I ask myself whether, if I were God, I would have arranged the world in such a way.”
Einstein found his divine path through science and transformed science in the process. His journey down that path evidently began during his poorly documented teenage years. By 1895 he had completed his secondary education (leaving without a degree), applied to the Swiss Federal Polytechnic School, and sent his uncle Caesar a remarkable letter. In it, he included a handwritten draft of a paper entitled “Concerning the Investigation of the State of Ether in the Magnetic Field.” The title refers to the then widespread theory of how waves of light move through empty space. The teen Einstein already exhibited a keen interest in understanding the propagation of light, a fascination that would later show up both in his theories of relativity and in his formulation of quantum physics. A decade later, Einstein's new physics put the ether theory to rest. Even as a brash eighteen-year-old, he felt the stirrings that would make him a great scientist and a great religious leader. “Strenuous labor and the contemplation of God's nature are the angels which. . . will guide me through the tumult of life,” he declared.
While young Einstein was pondering how to carry out this project, a number of scientists were smugly speculating that there might not be too much left to contemplate, now that their studies had succeeded so well in describing the mechanics of the world. The eminent American physicist A. A. Michelson summed up the spirit of the times: “The most important fundamental laws and facts of physical science have all been discovered, and these are now so firmly established that the possibility of their ever being supplemented in consequence of new discoveries is exceedingly remote.” This was by no means a universal view, but many otherwise sensible people believed there was little need for new theories, because the old ones were doing the job quite well. Science always moves forward when challenged. At the end of the nineteenth century, however, the prevailing feeling was one of intellectual and spiritual stagnation. The gaps in understanding hardly seemed sufficient to spark a fundamental realignment between science and religion. As often happens, the magnitude of the problems became clear only in hindsight.
Newton's old cosmological predicaments remained. Olbers's paradox still had no satisfactory answer; the universe somehow managed not to come crashing down all around. There was also a more concrete, albeit much smaller, inconsistency in his theory of gravity. Newton's equations implied a clockwork universe that operated with unerring mathematical precision. Yet Mercury, the planet closest to the sun, did not behave as expected. Its highly elliptical orbit does not stay put. The direction of the long axis of the orbit rotates gradually around the sun, so that the point where the planet is farthest from the sun sweeps out a huge circle. The pattern of successive orbits marks a kind of flower petal pattern, similar to the lines produced by a spirograph set. Newtonian gravitation could account for most, but not all, of this motion. The error was so small that it would take 180 million years for it to produce one additional circuit of Mercury's orbit. But it was undeniably there, and none of the proposed fixes totally eliminated the problem. God's clockwork universe was not keeping perfect time.
Other pieces of Newton's physics, when scrutinized closely, seemed incomplete as well. He had never explained the fundamental nature of gravity and especially had never confronted the problem of how gravity propels itself through empty space. By the end of the nineteenth century, scientists thought they had a solution to this mystery of action at a distance, at least for the case of light and other forms of electromagnetic radiation. Their standard response was that an empty vacuum is never truly empty. All of space is permeated with an unseen and unfelt material, known as “the lumiferous ether,” that acted as a kind of cosmic signal relay. When light streaks across the seeming nothingness between the sun and the Earth, it is actually vibrating through the ether like waves traversing the ocean. Perhaps gravity could propagate through space in the same manner. Never mind that nobody could explain what ether consisted of or provide clear evidence that it existed. The modern ether, like the one invoked centuries earlier by Aristotle's, served a philosophically crucial purpose, giving form to the cosmic void.
Yet, also like Aristotle's ether, the updated version bore no resemblance to any known or imaginable earthly substance. It extended terrestrial logic into space but at the same time built a clear distinction between our world and the world above. The lumiferous ether needed to be stiffer than steel but completely invisible and imperceptible. Two physicists working together in the United States—first Michelson, the fellow who eventually declared science was petering out, and, later, Edward Morley—put the ether to a test. As the Earth moves through space, it must plow through the ether. Light should therefore appear to move at different speeds in different directions, faster in the direction where the ether is blowing into our faces and slower where the ether wind is at our backs. Michelson and Morley set up an experiment at Western Reserve University in Cleveland that split a beam of light into two, sent the halves in perpendicular directions, and then recombined them. One beam should have moved faster through the ether than the other, in which case the two beams would be visibly out of alignment when they came back together. In 1887, Michelson and Morley announced their results: They found nothing. Michelson repeated the experiment at different latitudes in case the ether was being dragged along by the body of the Earth. Still nothing.
This negative result was the first strong indication that the observed speed of light can never change, which Einstein later fashioned into a guiding principle of physics. It also cast a serious blow against Newton's belief in absolute space, an infinite, invisible universal reference grid that he referred to as “the Sensorium of God.” Ether theory attempted to reconceive this immovable backdrop as a material accessible to science, but the attempt to reach it by experimental means failed miserably. Einstein probably didn't learn the details of the Michelson-Morley experiment until years later, possibly not until after he had developed his basic ideas about relativity; his later comments are ambiguous and contradictory. But his studies at the Swiss Federal Polytechnic School certainly introduced him to the work of Scottish physicist James Clerk Maxwell and Austrian scientist and philosopher Ernst Mach, two brilliant minds whose work helped bring about Einstein's relativity theory and the death of the ether.
During the 1860s, Maxwell formulated a set of equations describing light as a wave in the form of an oscillating electromagnetic field. He also analyzed the flow of heat as a function of statistical changes in the motions of the molecules in a gas. Einstein's expansion of those ideas blossomed into a thoroughly new understanding of the nature of light and the rules that govern it. Mach's thinking had an even more profound effect on Einstein. Mach is best remembered for his research into the physics of supersonic motion, which is why faster-than-sound speeds are described on a Mach scale. But he was also a cunning philosopher of science who argued that our notions of space and time are fundamentally limited by the human senses we use to understand them, a line of reasoning that reappeared, wonderfully mutated, in the general theory of relativity. Mach was such an empirical purist that for years he refused to believe in the reality of atoms. In The Science of Mechanics he railed against Newton's “conceptual monstrosity of absolute space,” an att
ack that deeply influenced Einstein when he read it as a college student. Particularly in his early years, Einstein described himself as a devout Machist and cited Mach as the inspiration for his 1917 cosmology—even though, by introducing Lambda into the equations, Einstein defied his idol's warnings against any scientific idea that cannot be derived from experience. By the closing years of the nineteenth century, physics was astir with so many strange new discoveries that even the most sheltered thinkers could no longer cling to the notion that science had achieved a full explanation of the natural world. Wilhelm Roentgen encountered an unknown, penetrating kind of radiation he called “X rays.” Henri Becquerel discovered radioactive decay in uranium salts. J. J. Thomson uncovered evidence that the atom—assumed indivisible since it was first conceived in the philosophy of Leucippus and Democritus in the fifth century B.C.—contains a smaller particle, the electron.
Young Einstein started to develop the outlines of his cosmic religion amid this intellectual ferment. He graduated from the Polytechnic in 1900 and set out in search of an academic position. After months of fruitless searching, he landed a job at the Swiss Patent Office in June of 1902. The disciplined setting forced him to express himself clearly. More important, the rote nature of the work and the quiet evenings and Sundays it allowed gave him time to work out his ideas. Had he been in an academic setting, Einstein reflected some fifty years later, he would have felt pressure to churn out scientific work even if it was mediocre. In the shelter of the patent office, he could let his mind wander. He enjoyed the encouragement of a co-worker and former classmate, Michele Angelo Besso, who became a lifelong friend and confidant. This was also a time of tremendous personal change for Einstein: his father died in October 1902, and he married Mileva Marie in January of the following year.
Like Abraham, Einstein had heard the divine call, and now he was ready to proclaim his faith to the world. Historians call 1905 Einstein's “annus mirabilis,” his miracle year. This was his moment of greatest intellectual ferment, although the key insight that led him to the scientific promised land was still years away. In rapid succession he published four papers in Annalen der Physik—three of them in a single volume—that transformed the face of physics. He managed this feat even though he was then on the far fringes of academia. Einstein's access to current scientific debates came primarily through the physics journals. He was not in contact with the major researchers of his day, nor did he have access to the results from the newest experiments. What he did have was a keen sense that physics could be rebuilt in a way that was more harmonious, that looked better, and that he therefore felt must be true. In that sense he had access to the same tools that had aided Copernicus and Newton, a logical devotion to the principles of economy and unity in understanding the world.
One of the 1905 papers described the motions of molecules in statistical terms. A second worked out an explanation for the photoelectric effect, a phenomenon in which electricity flows from certain substances when they are exposed to light. Einstein found common ground in these two papers. He realized that the way light strikes a surface is analogous to how gas molecules hit the wall of a box, an idea that forms the foundation of quantum physics. But the main attraction of the 1905 papers was Einstein's formulation of his theory of relativity. More precisely, it was his special theory of relativity, so named to distinguish it from the general version he developed a dozen years later. “Special” in this context means that the theory applied only to restricted situations in which gravity and acceleration were not important factors.
The paper's title, “On the Electrodynamics of Moving Bodies,” hardly suggests its revolutionary content. In the span of nine thousand words, Einstein overturned three hundred years of wisdom regarding how to determine an object's motion or how to define the timing of an event. Much as Copernicus put the sun at the center of the solar system to simplify the motions of the heavens, Einstein set out to remove “asymmetries that do not appear to be inherent in the phenomena.” For instance, moving a magnet across a piece of wire generates current, but the equations describing the motion of a magnet past a wire were different from those describing the motion of a wire past a magnet. Einstein proposed a radical way to remove this arbitrary distinction: Abolish Newton's Sensorium and with it the entire notion of absolute motion and absolute space. The old universe and whatever we thought we knew about who oversaw it were dead. Hundreds of books and articles, including Einstein's own, have attempted to translate the concepts of relativity for the lay public, yet the theory remains stubbornly counterintuitive. A man is standing in a train car moving at ten miles per hour. Suddenly he starts to run ten miles per hour in the same direction as the train's motion. How fast is he moving? It seems like a trick question. Anyone trained in classical mechanics or everyday common sense knows the answer must be twenty miles per hour. Einstein too saw this as a trick question, but he perceived that the trick is to ask, “Moving relative to what?” Relative to the train, the man is running only ten miles per hour. But even relative to the ground, Einstein argued, he is actually traveling a bit less than twenty miles per hour. At such low speeds the effect is minute, but it becomes huge when the speeds approach the velocity of light. Assume now that the train is moving at nine-tenths light speed, and the runner sprints forward at another nine-tenths of light speed. From the ground, the combined motion still appears distinctly less than the speed of light.
The reason for this counterintuitive kind of addition is that the speed of light is a fundamental limit in the universe. Einstein realized that theory and observation alike declare the physics of light appears the same regardless of how the observer is moving. For this to be true, velocities cannot keep adding up they way we naively expect. A beam of light moves at the speed of light no matter what, even if it comes from a flashlight aboard that super-fast train. To the passenger aboard the train, the beam must recede at the familiar old speed of light. To a train spotter watching the cars whiz by, however, the passenger must nearly be keeping pace with the beam of light—because from the train spotter's vantage, that light still travels in its usual way, despite the added motion of the train. The only way both observers can be correct is if time and space are variable things that depend on whose perspective you choose.
Relativity expresses Einstein's faith that the universe is governed by inviolable laws and that these laws are accessible to human investigation. In 1906, Einstein wrote that “a theory is the more impressive the greater the simplicity of its premises is, the more different kinds of things it relates, and the more extended is its area of applicability.” The central premise of special relativity is indeed a remarkably simple one: that the perceived speed of light never changes. But like those of any great prophet, Einstein's words were open to misinterpretation. Some of Einstein's conservative critics, not to mention the racist ones, conflated the theory of relativity with moral relativism. In truth it was closer to absolutism, for it set inviolable standards regarding how the universe behaves. Einstein later scolded Newton for relying on the “shadowy concept” of absolute space. The source of ultimate truth lies not in an invisible world, Einstein argued, but entirely within what we can perceive. Relativity grew out of Mach's philosophy, which states that we can know only what we can perceive, and in fact Mach had attempted to develop a relativity theory of his own. But in Einstein's hands physics also took on an element of theology. Newton placed ultimate reality in the hands of an unfathomable God. Einstein pulled back the curtain and linked reality directly to perception, making science the hotline to heaven.
Special relativity also proposed a new kind of unity, one between energy and matter. As far back as the ancient Greeks, philosophers had wondered about the relationship between an object and the impulse that causes it to move. In his Optics, Newton had speculated about the possibility of converting “bodies into light, and light into bodies.” Einstein offered more than speculation. He explained how the conversion might work and gave an exact formula for the process, E=mc2. The
equation indicates that a minuscule amount of mass converts into a tremendous amount of energy—the source of power for deadly atomic bombs and for the life-giving radiance of the sun. It also shows that all forms of energy (heat, mechanical energy, and so on) are the same. When a burning log gives off heat, it looses a smidgen of mass in the form of energy; when a bowler sends a ball in motion down the lane, that kinetic energy slightly increases the ball's mass. Einstein's quantum physics created a related kind of unity by blurring the distinction between particles and waves.
At the same time, relativity theory dispensed with the nineteenth-century voodoo of the ether. To Einstein, the ether was as unnecessary and unknowable as its near twin, Newton's absolute space. “The introduction of a lumiferous ether will prove to be superfluous inasmuch as the view here to be developed will not require an 'absolutely stationary space,'” he wrote in his 1905 paper. One of the guiding principles of relativity is that all observers see the same thing, so the nature of light is the same to all observers at all times. No wonder Michelson could not find any effect of light blowing in the ether wind. The new theory also accounted for other unexplained physics phenomena, such as the way that the mass of the electron seemed to increase when it was accelerated to an extremely high velocity. One consequence of the equivalence of mass and energy is that an object appears weightier the faster it moves—again, the example of the bowling ball—because the energy of motion also expresses itself as mass. An interstellar traveler trying to accelerate his starship to the speed of light would find himself endlessly frustrated. Getting a little closer to the magic velocity would take a lot of energy, which would make his ship more massive, so accelerating it further would take still more energy and so on. Getting all the way to the speed of light would take an infinite amount of energy and so is impossible.