The Perfect Theory (2 page)

The general theory of relativity was also at the heart of some of the major intellectual battles of the twentieth century. It was the target of persecution in Hitler's Germany, hounded in Stalin's Russia, and disdained in 1950s America. It has pitted some of the biggest names in physics and astronomy against each other in a battle for the ultimate theory of the universe. They slugged it out over whether the universe started with a bang or has always been eternal and what the fundamental structure of space and time really is. The theory also brought distant communities together; in the midst of the Cold War, Soviet, British, and American scientists joined to solve the problem of the origin of black holes.

The story of general relativity is not all about the past. Over the past ten years, it has become apparent that if general relativity is correct, most of the universe is dark. It is full of stuff that not only doesn't emit light but doesn't even reflect or absorb it. The observational evidence is overwhelming. Almost a third of the universe seems to be made up of dark matter, heavy, invisible stuff that swarms around galaxies like a cloud of angry bees. The other two-thirds is in the form of an ethereal substance, dark energy, that pushes space apart. Only 4 percent of the universe is made of the stuff that we are familiar with: atoms. We are insignificant. That is,
if
Einstein's theory is correct. It may just be possible that we are reaching the limits of general relativity and that Einstein's theory is beginning to crack.

Einstein's theory is also essential to the new fundamental theory of nature that has theoretical physicists at each other's throats. String theory, which attempts to go even further than Newton and Einstein and unify
everything
in nature, relies on complicated spacetimes with strange geometrical properties in higher dimensions. Far more esoteric than Einstein's theory ever was, it is hailed by many as the final theory and railed against by others as romantic fiction, not even science. Like a breakaway cult, string theory wouldn't exist if not for the general theory of relativity, yet it is looked at with skepticism by many practicing relativists.

Dark matter, dark energy, black holes, and string theory are all progeny of Einstein's theory, and they dominate physics and astronomy. While giving talks at various universities, attending workshops, and participating in meetings of the European Space Agency, responsible for some of the world's most important scientific satellites, I have come to realize that we are in the midst of a momentous transformation in modern physics. We have talented young scientists looking at general relativity with an expertise that is built on a century of geniuses. They are mining Einstein's theory with unparalleled computational power, exploring alternative theories of gravity that might dethrone Einstein's, and looking for exotic objects in the cosmos that could confirm or refute the fundamental tenets of general relativity. The wider community of scientists is simultaneously being galvanized to build colossal machines to look farther and more clearly into space than we ever have done before, satellites that will set out to search for the outlandish predictions with which general relativity seems to have burdened us.

The story of general relativity is magnificent and overarching and needs to be told. For, well into the twenty-first century, we are facing up to many of its great discoveries and unanswered questions. Something important really is going to happen in the next few years, and we need to understand where it all comes from. My suspicion is that if the twentieth century was the century of quantum physics, the twenty-first will give full play to Einstein's general theory of relativity.

Chapter 1

D
URING THE
autumn of 1907, Albert Einstein worked under pressure. He had been invited to deliver the definitive review of his theory of relativity to the
Yearbook of Electronics and Radioactivity.
It was a tall order, to summarize such an important piece of work at such short notice, especially since he could do so only in his spare time. From 8:00 a.m. to 6:00 p.m. Monday through Saturday, Einstein could be found working at the Bern Federal Office for Intellectual Property in the newly built Postal and Telegraph Building, where he would meticulously pore over plans for newfangled electrical contraptions and figure out if there was any merit in them. Einstein's boss had advised him,
“When you pick up an application, think that everything the inventor says is wrong,” and he took his advice to heart. For much of the day, the notes and calculations for his own theories and discoveries had to be relegated to the second drawer of his desk, which he referred to as his “theoretical physics department.”

Einstein's review would recap his triumphant marriage of the old mechanics of Galileo Galilei and Isaac Newton with the new electricity and magnetism of Michael Faraday and James Clerk Maxwell. It would explain much of the weirdness that Einstein had uncovered a few years before, such as how clocks would run more slowly when moving, or how objects would shrink if they were speeding ahead. It would explain his strange and magical formula that showed how mass and energy were interchangeable, and that nothing could move faster than the speed of light. His review of his principle of relativity would describe how almost all of physics should be governed by a new common set of rules.

In 1905, over a period of just a few months, Einstein had written a string of papers that were already transforming physics. In that inspired burst he had pointed out that light behaves like bundles of energy, much like particles of matter. He had also shown that the jittery, chaotic paths of pollen and dust careening through a dish of water could arise from the turmoil of water molecules, vibrating and bouncing off one another. And he had tackled a problem that had been plaguing physicists for almost half a century: how the laws of physics seem to behave differently depending on how you look at them. He had brought them together with his principle of relativity.

All these discoveries were a staggering achievement, and Einstein had made them all while working as a lowly patent expert at the Swiss patent office in Bern, sifting through the scientific and technological developments of the day. In 1907, he was still there, having yet to move into the august academic world that seemed to elude him. In fact, for someone who had just rewritten some of the fundamental rules of physics, Einstein was thoroughly undistinguished. Throughout his unimpressive academic studies at the Polytechnic Institute in Zurich, Einstein skipped classes that didn't interest him and antagonized the very people who could nurture his genius. One of his professors told him,
“You are a very clever boy . . . But you have one great fault: you'll never let yourself be told anything.” When Einstein's supervisor prevented him from working on a topic of his own choice, Einstein handed in a lackluster final essay, lowering his grade to a point where he was unable to secure a post as an assistant at any of the universities to which he had applied.

From his graduation in 1900 until he finally landed his job in the patent office in 1902, Einstein's career was a sequence of failures. To compound his frustration, the doctoral thesis he submitted to the University of Zurich in 1901 was rejected a year later. In his submission, Einstein had set about to demolish some of the ideas put forward by Ludwig Boltzmann, one of the great theoretical physicists of the end of the nineteenth century. Einstein's iconoclasm had not gone over well. It wasn't until 1905, when he submitted one of his magical papers, “A New Determination of Molecular Dimensions,” that he finally obtained his doctorate. The degree, a newly diplomatic Einstein discovered,
“considerably facilitates relations with people.”

While Einstein struggled, his friend Marcel Grossmann was on the fast track to becoming an august professor. Well organized, studious, and beloved by his teachers, it was Grossmann who had saved Einstein from going off the rails by keeping detailed, immaculate notebooks of the lecture courses. Grossmann became close friends with Einstein and Einstein's future wife, Mileva Marić, while they studied together in Zurich, and all three graduated in the same year. Unlike Einstein's, Grossmann's career had progressed smoothly from then on. He had been appointed as an assistant in Zurich and in 1902 had obtained his doctorate. After a short stint teaching in high schools, Grossmann had become a professor of descriptive geometry at the Eidgenössische Technische Hochschule, known as the ETH, in Zurich. Einstein had failed to even get an appointment as a schoolteacher. It was only through the recommendation of Grossmann's father to an acquaintance, the head of the patent office in Bern, that Einstein had finally secured a job as a patent expert.

Einstein's job in the patent office was a blessing. After years of financial instability and depending on his father for an income, he was finally able to marry Mileva and begin to raise a family in Bern. The relative monotony of the patent office, with its clearly defined tasks and lack of distractions, seemed to be an ideal setting for Einstein to think things through. His assigned work took only a few hours to complete each day, leaving him time to focus on his puzzles. Sitting at his small wooden desk with only a few books and the papers from his “theoretical physics department,” he would perform experiments in his head. In these thought experiments (
gedankenexperimenten
as he called them in German) he would imagine situations and constructions in which he could explore physical laws to find out what they might do to the real world. In the absence of a real lab, he would play out carefully crafted games in his head, enacting events that he would scrutinize in detail. With the results of these experiments, Einstein knew just enough mathematics to be able to put his ideas to paper, creating exquisitely crafted jewels that would ultimately change the direction of physics.

His employers at the patent office were pleased with Einstein's work and promoted him to Expert II Class, yet they remained oblivious to his growing reputation. Einstein was still working on a daily quota of patents in 1907 when the German physicist Johannes Stark commissioned Einstein to write his review “On the Relativity Principle and the Conclusions Drawn From It.” He was given two months to write it, and in those two months Einstein realized that his principle of relativity was incomplete. It would need a thorough overhaul if it was to be
truly
general.

 

The article in the
Yearbook
was to be a summary of Einstein's original principle of relativity. This principle states that the laws of physics should look the same in any inertial frame of reference. The basic idea behind the principle was not new and had been around for centuries.

The laws of physics and mechanics are rules for how things move, speed up, or slow down when subjected to forces. In the seventeenth century, the English physicist and mathematician Isaac Newton laid out a set of laws for how objects respond to mechanical forces. His laws of motion consistently explain what happens when two billiard balls collide, or when a bullet is fired out of a gun, or when a ball is thrown up in the air.

An inertial frame of reference is one that moves at a constant velocity. If you're reading this in a stationary spot, like a cozy chair in your den or a table in a café, you're in an inertial frame. Another classic example is a smoothly moving fast train with the windows closed. If you're sitting inside it, once the train gets up to speed there's no way to know you're moving. In principle, it should be impossible to tell the difference between two inertial frames even if one is moving at a high speed and the other is at rest. If you do an experiment in one inertial frame measuring the forces acting on an object, you should get the same result as in any other inertial frame. The laws of physics are identical, regardless of the frame.

The nineteenth century brought a completely new set of laws that wove together two fundamental forces: electricity and magnetism. At first glance, electricity and magnetism appear to be two separate phenomena. We see electricity in the lights in our home or lightning in the sky, and magnetism in the magnets stuck to our fridge or the way the North Pole draws a compass. The Scottish physicist James Clerk Maxwell showed that these two forces could be seen as different manifestations of one underlying force, electromagnetism, and that how they are perceived depends on how an observer is moving. A person sitting next to a bar magnet would experience magnetism but no electricity. But a person whizzing by would experience not only the magnetism but also a modicum of electricity. Maxwell unified the two forces into one that remains equivalent regardless of an observer's position or speed.

If you try to combine Newton's laws of motion with Maxwell's laws for electromagnetism, troubles arise. If the world indeed obeys both of these sets of laws, it is possible, in principle, to construct an instrument out of magnets, wires, and pulleys that will not sense any force in one inertial frame but can register a force in another inertial frame, violating the rule that inertial frames should be indistinguishable from one another. Newton's laws and Maxwell's laws thus appear inconsistent with each other. Einstein wanted to fix these
“asymmetries” in the laws of physics.

In the years leading up to his 1905 papers, Einstein devised his concise principle of relativity through a series of thought experiments aimed at solving this problem. His mental tinkering culminated in two postulates. The first was simply a restatement of the principle: The laws of physics must look the same in any inertial frame. The second postulate was more radical: In
any
inertial frame, the speed of light always has the same value and is 299,792 kilometers per second. These postulates could be used to adjust Newton's laws of motion and mechanics so that when they were combined with Maxwell's laws of electromagnetism, inertial frames remained completely indistinguishable. Einstein's new principle of relativity also led to some startling results.