The Most Beautiful theory Part I
A century ago Albert Einstein changed the way humans saw the universe. His work is still offering new insights today
“ALFRED, it’s spinning.” Roy Kerr, a New Zealand-born physicist in his late 20s, had, for half an hour, been chain-smoking his way through some fiendish mathematics. Alfred Schild, his boss at the newly built Centre for Relativity at the University of Texas, had sat and watched. Now, having broken the silence, Kerr put down his pencil. He had been searching for a new solution to Albert Einstein’s equations of general relativity, and at last he could see in his numbers and symbols a precise description of how space-time—the four-dimensional universal fabric those equations describe—could be wrapped into a spinning ball. He had found what he was looking for.
When this happened, in 1962, the general theory of relativity had been around for almost half a century. It was customarily held up as one of the highest intellectual achievements of humanity. And it was also something of an intellectual backwater. It was mathematically taxing and mostly applied to simple models with little resemblance to the real world, and thus not widely worked on. Kerr’s spinning solution changed that. Given that pretty much everything in the universe is part of a system that spins at some rate or other, the new solution had a relevance to real-world possibilities—or, rather, out-of-this-world ones—that previous work in the field had lacked. It provided science with a theoretical basis for understanding a bizarre object that would soon bewitch the public imagination: the black hole.
General relativity was presented to the Prussian Academy of Sciences over the course of four lectures in November 1915; it was published on December 2nd that year. The theory explained, to begin with, remarkably little, and unlike quantum theory, the only comparable revolution in 20th-century physics, it offered no insights into the issues that physicists of the time cared about most. Yet it was quickly and widely accepted, not least thanks to the sheer beauty of its mathematical expression; a hundred years on, no discussion of the role of aesthetics in scientific theory seems complete without its inclusion.
When gravity fails
Today its appeal goes beyond its elegance. It provides a theoretical underpinning to the wonders of modern cosmology, from black holes to the Big Bang itself. Its equations have recently turned out to be useful in describing the physics of earthly stuff too. And it may still have secrets to give up: enormous experiments are under way to see how the theory holds in the most extreme physical environments that the universe has to offer.
The theory built on the insights of Einstein’s first theory of relativity, the “special theory”, one of a trio of breakthroughs that made his reputation in 1905. That theory dramatically abandoned the time-honoured description of the world in terms of absolute space and time in favour of a four dimensional space-time (three spatial dimensions, one temporal one). In this new space-time observers moving at different speeds got different answers when measuring lengths and durations; for example, a clock moving quickly with respect to a stationary observer would tell the time more slowly than one sitting still. The only thing that remained fixed was the speed of light, c, which all observers had to agree on (and which also got a starring role in the signature equation with which the theory related matter to energy, E=mc2).
Special relativity applied only to special cases: those of observers moving at constant speeds in a straight line. Einstein knew that a general theory would need to deal with accelerations. It would also have to be reconciled with Isaac Newton’s theory of gravity, which relied on absolute space, made no explicit mention of time at all, and was believed to act not at the speed of light but instantaneously.
Einstein developed all his ideas about relativity with “thought experiments”: careful imaginary assessments of highly stylised states of affairs. In 1907 one of these provided him with what he would later refer to as his “happiest thought”: that someone falling off a roof would not feel his own weight. Objects in free-fall, he realised, do not experience gravity. But the curved trajectories produced by gravity—be they the courses of golf balls or planets—seemed to imply some sort of pushing or pulling. If golf balls and planets, like people falling off roofs, felt no sort of push or pull, why then did they not fall in straight lines?
The central brilliance of general relativity lay in Einstein’s subsequent assertion that they did. Objects falling free, like rays of light, follow straight lines through space-time. But that space-time itself is curved. And the thing that made it curve was mass. Gravity is not a force; it is a distortion of space-time. As John Wheeler, a physicist given to pithy dictums about tricky physics, put it decades later: “Space-time tells matter how to move; matter tells space-time how to curve.”
The problem was that, in order to build a theory on this insight, Einstein needed to be able to create those descriptions in warped four-dimensional space-time. The Euclidean geometry used by Newton and everyone else was not up to this job; fundamentally different and much more challenging mathematics were required. Max Planck, the physicist who set off the revolution in quantum mechanics, thought this presented Einstein with an insurmountable problem. “I must advise you against it,” he wrote to Einstein in 1913, “for in the first place you will not succeed, and even if you succeed no one will believe you.”
Handily for Einstein, though, an old university chum, Marcel Grossmann, was an expert in Riemannian geometry, a piece of previously pure mathematics created to describe curved multi-dimensional surfaces. By the time of his lectures in 1915 Einstein had, by making use of this unorthodox geometry, boiled his grand idea down to the elegant but taxing equations through which it would become known.
Just before the fourth lecture was to be delivered on November 25th, he realised he might have a bit more to offer than thought experiments and equations. Astronomers had long known that the point in Mercury’s orbit closest to the sun changed over time in a way Newton’s gravity could not explain. In the 1840s oddities in the orbit of Uranus had been explained in terms of the gravity of a more distant planet; the subsequent discovery of that planet, Neptune, had been hailed as a great confirmation of Newton’s law. Attempts to explain Mercury’s misbehaviour in terms of an undiscovered planet, though, had come to naught.
Famous long ago
Einstein found that the curvature of space-time near the sun explained Mercury’s behaviour very nicely. At the time of the lectures it was the only thing he could point to that general relativity explained and previous science did not. Martin Rees, Britain’s Astronomer Royal, is one of those who sees the nugatory role played by evidence in the development of the theory as one of the things “that makes Einstein seem even more remarkable: he wasn’t motivated by any mysterious phenomena he couldn’t explain.” He depended simply on his insight into what sort of thing gravity must be, and the beauty of the mathematics required to describe it.
After the theory was published, Einstein started to look for ways to test it through observation. One of them was to compare the apparent positions of stars that were in the same part of the sky as the sun during a solar eclipse with their apparent positions at other times. Rays of light, like free-falling objects, trace straight lines in space-time. Because the sun’s mass warps that space-time, the positions of the stars would seem to change when the rays skirted the sun