The Perfect Theory (3 page)

The latter postulate required some adjustments to Newton's laws. In the classic Newtonian universe, speed is additive. Light emitted from the front of a speeding train moves faster than light coming from a stationary source. In Einstein's universe, this is no longer the case. Instead, there is a cosmic speed limit set at 299,792 kilometers per second. Even the most powerful rocket would be unable to break that speed barrier. But then odd things happen. So, for example, someone traveling on a train moving at close to the speed of light will age more slowly when observed by someone sitting at a station platform, watching the train go by. And the train itself will look shorter when it is moving than when it is sitting still. Time dilates and space contracts. These strange phenomena are signs that something much deeper is going on: in the world of relativity, time and space are intertwined and interchangeable.

With his principle of relativity, Einstein seemed to have simplified physics, albeit with strange consequences. But in the autumn of 1907, as Einstein set out to write the review, he had to admit that while his theory seemed to work well, it wasn't yet complete. Newton's theory of gravity didn't fit into his picture of relativity.

 

Before Albert Einstein came along, Isaac Newton was like a god in the world of physics. Newton's work was held up as the most stunning success of modern thought. In the late seventeenth century, he had unified the force of gravity acting on the very small and the very large alike in one simple equation. It could explain the cosmos as well as everyday life.

Newton's law of universal attraction, or the “inverse square law,” is as simple as they come. It says that the gravitational pull between two objects is directly proportional to the mass of each object and inversely proportional to the square of their distance. So if you double the mass of one of the objects, the gravitational pull also doubles. And if you double the distance between the two objects, the pull
decreases
by a factor of four. Over two centuries, Newton's law kept on giving, explaining any number of physical phenomena. It proved itself most spectacularly not only in explaining the orbits of the known planets but also in predicting the existence of new ones.

Beginning in the late eighteenth century, there was evidence that the planet Uranus's orbit had a mysterious wobble. As astronomers amassed observations of Uranus's orbit, they could slowly map out its path in space with ever more precision. Predicting Uranus's orbit was not a straightforward exercise. It involved taking Newton's law of gravity and working out how the other planets influenced Uranus's motion, nudging it here and there, making its orbit ever so slightly more complicated. Astronomers and mathematicians would publish the orbits in the form of tables that would, for different days and years, predict where Uranus or any other planet should be in the sky. And when they compared their predictions with subsequent observations of Uranus's actual position, there was always a discrepancy they couldn't explain.

The French astronomer and mathematician Urbain Le Verrier was particularly skilled at working out the celestial orbits and producing orbits for various planets in the solar system. When he focused his attention on Uranus, he assumed from the start that Newton's theory
was
perfect, given how well it worked for the other planets. If Newton's theory was correct, he surmised, the only other possibility was that there had to be something out there that hadn't been accounted for. And so Le Verrier took the bold step of predicting the existence of a new, fictitious planet and producing its very own astronomical table. To his delight, a German astronomer in Berlin, Gottfried Galle, pointed his telescope in the direction that Le Verrier's table indicated and found a big, undiscovered planet shimmering in his field of view. As Galle put it in a letter to Le Verrier, “Monsieur, the planet of which you indicated the position really exists.”

Le Verrier had taken Newton's theory a step further than anyone before and was rewarded for his audacity. For decades, Neptune was known as “Le Verrier's planet.” Marcel Proust
used Le Verrier's discovery as an analogy for ferreting out corruption in his
Remembrance of Things Past,
and Charles Dickens referred to it when describing hard-boiled detective work in his short piece “The Detective Police.” It was a beautiful example of using the fundamental rules of scientific deduction. Le Verrier, basking in the glory of his discovery, then turned his attention to Mercury. It too seemed to have a strange, unexpected orbit.

In Newtonian gravity, an isolated planet orbiting the sun follows a simple, closed orbit with the shape of a squashed circle, known as an ellipse. A planet will go around and around, endlessly following the same path, periodically getting closer to and then more distant from the sun. The point in its orbit at which the planet is closest to the sun—called its perihelion—remains constant over time. Some planets, like the Earth, have almost circular orbits—the ellipse is barely squashed—while others, like Mercury, follow much more elliptical paths.

Even accounting for all the other planets' effects on Mercury's orbit, Le Verrier found that Mercury's actual orbit was at odds with the predictions of Newtonian gravity; the planet's perihelion shifted by approximately 40 arcseconds per century. (An arcsecond is a unit of angular measurement; the entire dome of the sky is made up of about 1.3 million arcseconds, or 360 degrees.) This anomaly, known as the precession of the perihelion of Mercury, could not be explained by Le Verrier's deployment of Newton's rules. Something else was going on.

Once again, Le Verrier assumed that Newton had to be right, and so, in 1859, he conjectured that a new planet, Vulcan, about the same size as Mercury had to exist very close to the sun. It was a bold, outlandish conjecture. As he put it,
“How could a planet, extremely bright and always near the Sun, fail to have been recognized during a total eclipse?”

Le Verrier's conjecture set off a race to discover the new planet Vulcan. Over the following decades, there were occasional reported sightings of an object nearer the sun, but none of them stood up to scrutiny. Although the search for Vulcan didn't end with Le Verrier's death, the precession of the perihelion of Mercury remained firmly entrenched in astronomical lore. Something other than an invisible planet would have to explain the 40-arcsecond anomaly.

When Einstein sat down to worry about gravity in 1907, he had to reconcile Newton's theory with his principle of relativity. In the back of his mind, he knew that he also had to explain Mercury's anomalous orbit. It was a tall order.

 

Gravity as explained by Newton violates both of the postulates in Einstein's beautiful and concise principle of relativity. For a start, in Newton's theory, the effect of gravity is instantaneous. If two objects are suddenly situated near each other, the force of gravity between them would be in effect immediately—it would require no time to travel from one object to the other. But how could this be if, according to Einstein's new principle of relativity, nothing, no signal, no effect, can move faster than the speed of light? Just as crucial and as vexing was the fact that, while Einstein's principle of relativity harmonized mechanics and electromagnetism, it left out Newton's law of gravity. Newtonian gravity looked different in different inertial frames.

Einstein's first step on his long trek to fix gravity and generalize his theory of relativity came one day as he sat at his chair at the patent office in Bern, lost in his world of thought. Years later he recalled the idea that came to him and led him toward his theory for gravity:
“If a person falls freely he will not feel his own weight.”

Imagine yourself as Alice in the rabbit hole, falling freely with nothing to stop you. As you fall under the pull of gravity, the speed at which you fall increases at a constant rate. The acceleration will exactly match the gravitational pull, and as a result your fall will feel effortless—you won't feel any force to pull or push against—although it will be undoubtedly terrifying as you hurtle through space. Now imagine a bunch of stuff falling with you: a book, a cup of tea, a similarly panicked white rabbit. All the other objects will accelerate at the same rate to compensate for the pull of gravity, and as a result they will hover around you as you all fall together. If you try to set up an experiment with these objects to measure how they move relative to you so as to determine the gravitational force, you will fail. You will feel weightless and the objects will look weightless. All of this seems to indicate that there is an intimate relationship between accelerated motion and the pull of gravity—in this case one is exactly compensating for the other.

Maybe falling freely is a step too far. There is too much going on around you: the air is rushing by, and the fear that you'll eventually hit the bottom makes clear thinking a challenge. Let's try something slightly simpler, and a little more sedate. Imagine that you have just entered an elevator on the ground floor of a tall building. The elevator starts to go up, and in those first few seconds, as it accelerates, you feel just a little bit heavier. Conversely, suppose you are now at the top of the building and the elevator starts to go down. During those initial moments when the elevator picks up speed, you feel lighter. Of course, once the elevator reaches its maximum speed, you don't feel any heavier or lighter. But during those moments in which the elevator accelerates or decelerates, your sense of your own weight, and hence of gravity, is skewed. In other words, what you sense of gravity is completely dependent on whether you are speeding up or slowing down.

On that day in 1907 when Einstein conjured up his falling man, he realized that there must be some deep connection between gravity and acceleration that would be the key to bringing gravity into his theory of relativity. If he could change his principle of relativity so that the laws of physics remained the same not only in frames moving at constant speed but also in frames that were speeding up or slowing down, he just might be able to bring gravity into the mix with electromagnetism and mechanics. He wasn't sure how, but this brilliant insight was the initial step toward making relativity more general.

Under pressure from his German editor, Einstein wrote up his review, “On the Relativity Principle and the Conclusions Drawn From It.” He included a section on what would happen if he generalized his principle to include gravity. He summarily noted a few consequences: The presence of gravity would alter the speed of light and cause clocks to run more slowly. The effects of his generalized principle of relativity might even explain the minute drift in Mercury's orbit. These effects, tossed in at the end of the paper, could eventually be used to test his idea, but they would need to be worked out in more detail and with more care at a later time. They would have to wait. For a few years, Einstein wouldn't work on his theory at all.

By the end of 1907, Einstein's brilliant obscurity was coming to an end. Slowly but surely, his 1905 papers had begun to make an impact. He started receiving a trickle of letters from distinguished physicists asking for his offprints and discussing his ideas. Einstein was excited by the developments, telling a friend,
“My papers are meeting with much acknowledgement and are giving rise to further investigation.” One of his admirers quipped, “I must confess to you that I was amazed to read that you have to sit in an office for eight hours of the day. But history is full of bad jokes!” It wasn't that he had a bad life. His job in Bern had allowed him to begin a family with Mileva. In 1904 they had a son they named Hans Albert. Einstein's regular hours at the patent office allowed him to spend time at home building toys for his young son, but he was ready to enter the world of academia.

In 1908, Einstein was finally made a private lecturer at the University of Bern, a position that allowed him to give lectures to paying students. He found teaching incredibly burdensome and earned a terrible reputation as a lecturer. Still, in 1909 he was lured over to the University of Zurich as an associate professor. Einstein remained in Zurich for just over a year. In 1911, he was offered a professorship at the German University in Prague. This time he would have no teaching obligations. Without the bustle of his academic teaching duties, he returned to a state of mind much like that enabled by the ordered and isolated environment of the patent office. He could think about generalizing relativity once again.

Chapter 2

A
LBERT EINSTEIN
once confided to his friend and colleague the physicist Otto Stern,
“You know, once you start calculating you shit yourself up before you know it.” It is not that he didn't know his fair share of mathematics. Indeed, he had excelled at math in school and knew enough to put across his ideas. His papers were a perfect balance of physical reasoning and just enough mathematics to lay his ideas on a firm setting. But his 1907 predictions from his generalized theory had been done on a mathematical shoestring—one of his Zurich professors described the presentation of his work as “mathematically cumbersome.” Einstein disdained mathematics, which he called a “superfluous erudition,” sniping, “Since the mathematicians pounced on the relativity theory I no longer understand it myself.” But in 1911, when he looked at the ideas he had written up in his review, he realized that math could help him push them a bit further.

Einstein looked at his principle of relativity and thought about light, once again. Imagine yourself riding in a spaceship far from any planets and stars. Now imagine that a ray of light from a distant star enters through a small window directly to your right, cuts across the inside of your ship, and exits through a window to your left. If your spaceship is standing still, and the light hits the window straight on, it will exit through the window directly to your left. If, however, the spaceship is moving at a very fast but constant velocity when the light ray enters, by the time the light hits the far side of the spaceship, the ship will have moved forward and the ray will exit through a window farther back on the ship. From your point of view, the light ray enters at an angle and cuts across in a straight line. If the ship is
accelerating,
things will look quite different: the light ray will
curve
through the ship and exit farther back.