Einstein's Genius Club (23 page)

There is no evidence that anyone shared Einstein's views concerning the limitations imposed by gravitation on special relativity, nor that anyone was ready to follow his program for a tensor theory of gravitation. Only Lorentz had given him some encouragement.
⁴³

Despite the doubts of others, Einstein constructed his theory of general relativity. The self-confidence it gave him can hardly be overestimated. He expected to prevail again in his quest for a unified theory. In 1949, though stymied for a quarter century, he still evoked the heady experience that culminated in general relativity. After cataloguing the “impossibles” evoked by the quantum partisans—that is, the numerous ways in which Einstein's search for unity could not reconcile with the evidences of quantum mechanics—Einstein stubbornly returned to his thesis:

All these remarks [i.e., against a unified field theory built on relativity] seem to me to be quite impressive. However, the question which is really determinative appears to me to be as follows: What can be attempted with some hope of success in view of the present situation of physical theory? At this point it is the experiences with the theory of gravitation which determine my expectations. These equations give, from my point of view, more warrant for the expectation to assert something
precise
than all the other equations of physics.
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Yet it was a false hope, or so it now seems. Einstein wanted to ground his unified theory upon general relativity—that is, his explanation of the force of gravity. Yet in recent history, it has become clear that the ground floor must be quantum physics, not gravity.

As he kept trying, he reversed a bedrock assumption that governed the first half of his career. Before he took up unified theory, Einstein was an empiricist who trusted only his intuition about physical reality, not the beauty or inner consistency of equations. His 1905 paper on special relativity contained very little mathematics—and simple mathematics, at that. Indeed, when a small academic industry soon began to formalize and refine the mathematics of special relativity, the young Einstein mocked the efforts as “superfluous learnedness.”
⁴⁵
In 1918, his mathematical friend Besso apparently suggested that, in the discovery of general relativity,
mathematics had been more important than empiric knowledge. Einstein was irked and flatly disagreed:

You allude to the development of relativity theory. But I think that this development teaches us nearly the opposite: if a theory is to inspire confidence, it must be founded on
facts
susceptible of being generalized…. Neverhasa useful and fertile theory been found by purely speculative means.
⁴⁶

In 1918, the mathematician Hermann Weyl made a try at unifying gravity and electromagnetism, and amazingly found apparently successful equations. Einstein crushingly replied: “Your argument has a wonderful homogeneity. Except for not agreeing with reality, it is certainly a magnificent achievement of pure thought.”
⁴⁷
Again and again, Einstein championed “reality,” “facts,” and “experience.”

But as his search for a unified theory dragged on, his views changed. He began to speak of the “pure thought” of mathematical formalism as a uniquely privileged approach to the reality of physics. Here is the former empiricist preaching the new message in a 1933 lecture at Oxford:

I am convinced that we can discover by means of purely mathematical constructions the concepts and laws connecting them with each other, which furnish the key to the understanding of natural phenomena…. Experience remains, of course, the sole criterion of the physical utility of a mathematical construction. But the creative principle resides in mathematics. In a certain sense, therefore, I hold it true that pure thought can grasp reality, as the ancients dreamed.
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The phrase “purely mathematical constructions” comes as a shock. In 1921, still skeptical, he had put the matter with his customary lucidity: “[A]s far as the propositions of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.”
⁴⁹
Now, twelve years later, he had come to saying the opposite: The more certain the equations, the more they refer
to reality. Reversing the view he had expressed to Besso in 1918, he claimed that general relativity did spring mainly from its formalisms: “Coming as I did from skeptical empiricism of [Mach's] type… the gravity problem turned me into a believing rationalist, i.e., into a person who seeks the only reliable source of truth in mathematical simplicity.”
⁵⁰

Einstein had not turned into a mathematician. He had changed his method, not his goal. Mathematics for him was never the point, only a tool for doing physics. When the French mathematician Elie Cartan suggested a promising but complex theory, Einstein replied with his inimitable humor:

For the moment, the theory seems to me to be like a starved ape who, after a long search, has found an amazing coconut, but cannot open it; so he doesn't know whether there is anything inside.
⁵¹

Still, the popular cartoon image of Einstein as a wild-eyed scientist standing before a blackboard crammed with incomprehensible equations springs from his work on general relativity. Such an image was not possible before Einstein. General relativity required such new and rarefied mathematics that in 1914, the great German mathematician David Hilbert said half-jokingly that “physics has become too difficult for the physicists.” After general relativity, theoretical physics and abstruse mathematics were ever more closely wedded.

In 1919, when proof came that the sun's field curved light, Einstein entered the pantheon alongside Newton. Satisfying enough for anyone else, but not for Einstein. He was unhappy that general relativity had produced another dualism at the center of physics—this time, matter versus field. Einstein found such incoherence in the structure of physics “intolerable.”

Could we not reject the concept of matter and build a pure field physics? What impresses our senses as matter is really a
great concentration of energy into a comparatively small space. We could regard matter as the regions in space where the field is extremely strong.
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He thus sought an even more heroic theory, one able to dissolve matter into pure field laws. To do this, he had to enlarge general relativity, just as he had generalized special relativity.

Einstein's effort to find a unified “theory of everything” so clearly mirrors his earlier work that a brief look back at a few points is indispensable:

The famous perplexities of special relativity (1905)—peculiar clocks, shrinking distances—arise from a situation we do not encounter in our commonsense world. If we drive our car from New York, we know how many miles we are from that city, where it is, and how long it will take to drive back. We move about; New York is fixed in place.

But what if New York were also moving, as well as all the landmarks in between? How would we know exactly where we are and when something happens? Or, put otherwise: How can we do the physics? Special relativity accepts that all matter is in constant motion: Galaxies, planets, and all observers thereon are moving relative to what they observe. In this universal flying circus, there is no privileged space from which to measure, and no “absolute” time from which to count. Since no one can freeze all motion to get things utterly straight, each observer inevitably sees “simultaneous” events differently. Einstein's genius was to understand how we can nonetheless get an accurate measurement of time and distance, without which physics is stymied. First, he proposed that differences can be aligned to ensure that the same laws of physics take the same form wherever observed.
⁵³
Second, he proposed that the speed of light does not change, allowing us to measure intervals between events reliably. From these postulates came an epochal redefining of time, space, and measurement, along with famously surprising insights into strangely behaving clocks, slowed time,
twins who live faster or slower, and the equivalence of mass and energy: e=mc
²
.

Special relativity, however, is limited to uniform speed, which is partly why railroad trains or spaceships are handy examples: They are man-made objects whose speed can be precisely controlled. But Einstein worried: “What has nature to do with
our
coordinate systems and their state of motion?”
⁵⁴
Indeed, as objects move through the universe, they “fall” and thus accelerate—and vice versa: The two motions are really equivalent. Once acceleration appears, so does gravity. Everything that falls also accelerates thirty-two feet per second during each second traversed. But since special relativity says nothing about acceleration, it also says nothing about gravity, and thus applies only when gravity is absent or negligible (as in subatomic dimensions, which is why atomic physics like Dirac's equation deals only with special relativity).

It is important to note that special relativity remains within the bounds of Euclidean geometry—as did all physics before Einstein. General relativity changed all that in 1915. Euclidean geometry is not only flat (recall high school math), it is also empty; it can hardly describe how monstrous caldrons like our sun pour such fiery energy around them that their gravitational fields skew nearby space. Einstein needed different geometry to describe a universe of energetic intensities and distended curvatures that seem positively surreal next to Newton's clockwork universe. Unlike Euclidean geometry's rigid structures, Einstein's geometry had to bend, flex, or “dimple” according to the energy or mass within it, a geometry not a backdrop for events, but actively part of the events it measures.

In Riemann's non-Euclidean geometry, Einstein found just what he needed. He adapted it to measure how huge masses mold curvatures in space through which lesser bodies “fall.” Here, bodies are not pushed or pulled by an outside force, as in Newtonian gravity; they simply “fall” in as straight a line as curved space-time allows—a geodesic, akin to a great circle drawn on the earth's globe.

But general relativity in turn was limited to bodies large enough to feel the power of gravitation. What of the subatomic world? Einstein's inevitable next move was to try joining gravity to the electromagnetic force which reigns in the subatomic dimension. Soon, he took his first stab at a unified field theory.

On July 15, 1925, the German quantum physicist Max Born wrote to Einstein: “I am tremendously pleased with your view that the unification of gravitation with electrodynamics has at long last been successful.”
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Decades later, Born mused: “In those days we all thought that his objective… was attainable.” Born soon came to believe that Einstein's search was “a tragic error.”
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Einstein's early attempt assumed that there were two fundamental forces: gravitation, which assemble the planets and galaxies, and electromagnetism, from which all matter is built. (Remember that we now know there are two additional forces.) How do these forces compare? One aspect is their relative strength. Gravity is a very weak force, but gathers strength as it deploys across the vastness of space.
⁵⁷
The more matter it attracts, the more cumulatively powerful it becomes—until finally it can gather together and swing around the very galaxies. The electromagnetic force is enormously stronger than gravity, by a factor of ten followed by forty-two zeros—luckily so, since the electromagnetic force binds electrons to the nucleus.
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If gravitational force were stronger in relation to electromagnetic force, matter might dissolve away, and us with it.
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Further, the strong electromagnetic force prevents negatively charged electrons from repelling each other so violently that they tear atoms and all matter to bits. The electromagnetic force subdues the anarchic tendencies of matter and brings stability to the atomic dimension. Thus can we bathe in waves and particles, light and radioactivity.

How these fields interact was a puzzle, but they must be related; it would be a strange universe otherwise, thought Einstein. If they differ in strength, they are similar in how they work. Both fields are generated by an excitation of matter: gravitation from
excited mass (or energy), the electromagnetic field from excited electric charges. It would make sense in the process of unifying if we were to fit such hints and patterns together, as when looking for family resemblances by a common bulk of chin or curve of lip. Einstein had to match mathematical shapes or quirks of matter suggesting kinship: The bones of an equation about gravity might resemble one about electromagnetism, a frequency in an equation about electromagnetism might seem like an oscillation in one about gravity.

Yet the clues led to more puzzles. Thus, the electron's charge might play the same role in electromagnetism that mass does in gravity. However, relativity proved that mass varies with velocity, whereas electromagnetic charge never changes (charge is “conserved”). Even Einstein's success with gravity hindered as much as it helped. Having geometrized gravitation, he now sought an even more general geometry that, while fitting gravity, would include electromagnetism as well. Riemann's geometry worked beautifully for enormous bodies, but could not be applied to atomic phenomena. The charged electron seemed to need a very different geometry than gravity's mutable, swaying geometry—but what sort? Electrons do not really “orbit” the nucleus, as in popular imagination: They move in no usual spatial sense, but rather “up” and “down” in energy levels (quantum “leaps”). They are at once particle and wave, they spin (but only at fixed, quantized levels) and have angular momentum—and this only begins to broach the difficulties.

Einstein had two choices. He could keep the Riemannian framework, but expand the number of dimensions to five or more. Or he could keep the four dimensions, but find a substitute for Riemann's geometry. At one time or another, decade after decade, he pursued both of these possibilities. He explored four- and five-dimensional continuums, differential geometries, gauge transformations, absolute parallelism. He took apart his final field equations for general relativity, assigning the symmetric part to gravitation
and the antisymmetric part to the electromagnetic field. He spent the years puzzling at chalk marks on the blackboard.