Why Beauty is Truth (42 page)

All of which led up to the “golden year” of 1905, when the patent office clerk wrote a paper that eventually earned him the Nobel Prize. In the same year he obtained his PhD from the University of Zurich. He was also promoted to technical expert second class, with a raise of 1000 Swiss francs per year—it seems he had managed to master machine technology.

Even after he became famous, Albert always gave credit to Grossmann for paving the way to the job at the patent office. It was this, more than anything else, said Einstein, that had made his work in physics possible. It had been a stroke of genius, the perfect job, and he never forgot that.

In that most remarkable year in the history of physics, Einstein published three major research papers.

One was on Brownian motion, the random movements of very tiny particles suspended in a fluid. This phenomenon is named after its discoverer,
the botanist Robert Brown. In 1827, he was looking through his microscope at grains of pollen floating in water. Inside holes in the pollen he noticed even tinier particles jiggling about at random. The mathematics of this kind of motion was worked out by Thorvald Thiele in 1880, and independently by Louis Bachelier in 1900. Bachelier's inspiration was not Brownian motion as such, but the equally random fluctuations of the stock market—the mathematics proved identical.

The physical explanation was still up for grabs. Einstein, and independently the Polish scientist Marian Smoluchowski, realized that Brownian motion might be evidence for the then-unproved theory that matter was made of atoms, which combined to form molecules. According to the so-called “kinetic theory,” molecules in gases and liquids are constantly bouncing off each other, effectively moving at random. Einstein worked out enough of the mathematics of such a process to show that it matched the experimental observations of Brownian motion.

The second paper was on the photoelectric effect. Alexandre Becquerel, Willoughby Smith, Heinrich Hertz, and several others had observed that certain types of metal produce an electric current when exposed to light. Einstein started from the quantum-mechanical proposal that light is composed of tiny particles. His calculations showed that this assumption gives a very good fit to the experimental data. It was one of the first strong pieces of evidence in favor of quantum theory.

Either of these articles would have been a major breakthrough. But the third outclassed them all. It was on special relativity, the theory that went beyond Newton to revolutionize our views of space, time, and matter.

Our everyday view of space is the same as Euclid's and Newton's. Space has three dimensions, three independent directions at right angles to each other like the corner of a building—
north, east
, and
up.
The structure of space is the same at all points, though the matter that occupies space may vary. Objects in space can be moved in different ways: they can be rotated, reflected as if in a mirror, or “translated”—slid sideways without rotating. More abstractly, we can think of these transformations being applied to space itself (a change of the “frame of reference”). The structure of space, and the physical laws that express that structure and operate within it, are symmetric under these transformations. That is, the laws of physics are the same in all locations and at all times.

In a Newtonian view of physics, time forms another “dimension” that is independent of those of space. Time has a single dimension, and its symmetry transformations are simpler. It can be translated (add a fixed period of time to every observation) or reflected (run time in reverse—as a thought-experiment only). The physical laws do not depend on the starting date for your measurements, so they should be symmetric under translations of time. Most fundamental physical laws are also symmetric under time reversal, though not all, a fact that is rather mysterious.

But when mathematicians and physicists started to think about the newly discovered laws of electricity and magnetism, the Newtonian view seemed not to fit. The transformations of space and time that left the laws unchanged were not the simple “motions” of translation, rotation, and reflection; moreover, those transformations could not be applied to space or time independently. If you made a change in space alone, the equations got messed up. You had to change time in a compensating way.

To some extent this problem could be ignored, as long as the system under study was not moving. But the problem came to a head with the mathematics of a moving electric particle such as an electron—and this problem was central to the physics of the late nineteenth century. The associated worries about symmetry could no longer be ignored.

In the years leading up to 1905, a number of physicists and mathematicians had been puzzling about this strange feature of Maxwell's equations. If you performed an experiment involving electricity and magnetism in a laboratory or on a moving train, how should the results compare?

Of course, few experimentalists work on moving trains, but they all work on a moving
Earth.
For many purposes, though, the Earth can be considered to be at rest, because the experimental apparatus moves along with it, so the motion makes no real difference. Newton's laws of motion, for example, remain exactly the same in any “inertial” frame of reference, one that is moving with constant speed in a straight line. The Earth's speed is fairly constant, but it spins on its axis and revolves around the Sun, so the motion relative to the Sun is not straight. Still, the path the apparatus follows is almost straight; whether the curvature matters depends on the experiment, and often it does not matter at all.

No one would have been worried if Maxwell's equations had to take a different form in a rotating frame. What they discovered was more disturbing: Maxwell's equations took a different form in an inertial frame. Electromagnetism on a moving train is different from electromagnetism
in a fixed laboratory, even when the train is traveling in a straight line at constant speed.

There was a further complication: it is all very well to say that a train, or the Earth, is moving, but the concept of motion is relative. Mostly we don't notice the movement of the Earth, for example. The Sun's rising in the morning and setting in the evening is
explained
by the Earth's rotation. But we don't
feel
the rotation, we deduce it.

If you sit in a train and look out of the window, you may get the impression that you are fixed and the countryside is rushing past you. Someone standing in a field watching you go past observes the opposite: she is stationary and the train is moving. When we say that the Earth goes around the Sun rather than the Sun going around the Earth, we are making a subtle distinction, because either description is valid, depending on which frame of reference you choose. If the frame is carried along with the Sun, then the Earth moves relative to that frame and the Sun does not. But if the frame is carried along with the Earth, as the planet's inhabitants are, then the Sun is the object that moves.

So what was all the fuss about the heliocentric theory, which holds that the Earth orbits the Sun, not the other way around? Poor Giordano Bruno was burnt to death because he said that one description was correct while the Church preferred the other one. Did he die because of a misunderstanding?

Not exactly. Bruno made a number of claims that the Church viewed as heresies—small matters like the nonexistence of God. His fate would have been much the same if he had never mentioned the heliocentric theory. But there is an important sense in which “the Earth goes around the Sun” is superior to “the Sun goes around the Earth.” The important difference is that the mathematical description of the planets' movements relative to the Sun is much simpler than that of their movements relative to the Earth. An Earth-centered theory is possible but very complicated. Beauty is more significant than mere truth. Many points of view yield true descriptions of nature, but some provide more insight than others.

Now, if all motion is relative, then nothing can be absolutely “at rest.” Newtonian mechanics is consistent with the next-simplest proposal: that all inertial frames are on the same footing. But that is not true of Maxwell's equations.

As the nineteenth century drew to a close, one further intriguing possibility also had to be considered. Since light was believed to be a wave traveling through the aether, then perhaps the aether was at rest. Instead of all motions being relative, some motions—those relative to the aether—might be
absolute.
But that still did not explain why Maxwell's equations are not the same in all inertial frames.

The common theme here is symmetry. Changing from one frame of reference to another is a symmetry operation on space-time. Inertial frames are about translational symmetries; rotating frames are about rotational symmetries. Saying that Newton's laws are the same in any inertial frame is to say that those laws are symmetric under translations at uniform speed. For some reason, Maxwell's equations do not have this property. That seems to suggest that some inertial frames are more inertial than others. And if any inertial frames are special, surely it should be those that are stationary relative to the aether.

The upshot of these problems, then, was two questions, one physical, one mathematical. The physical one was, can motion relative to the aether be detected in experiments? The mathematical one was, what are the symmetries of Maxwell's equations?

The answer to the first was found by Albert Michelson, a US Navy officer who was taking leave to study physics under Helmholtz, and the chemist Edward Morley. They built a sensitive device to measure tiny discrepancies in the speed of light moving in different directions, and concluded that there were no discrepancies. Either the Earth was at rest relative to the aether—which made little sense given that it was circling the Sun—or there was no aether, and light did not obey the usual rules for relative motion.

Einstein attacked the problem from the mathematical direction. He didn't mention the Michelson–Morley experiment in his papers, though he later said he was aware of it and that it had influenced his thinking. Instead of appealing to experiments, he worked out some of the symmetries of Maxwell's equations, which have a novel feature: they mix up space and time. (Einstein did not make the role of symmetry explicit, but it is not far below the surface.) One implication of these weird symmetries is that uniform motion relative to the aether—assuming that such a medium exists—cannot be observed.

Einstein's theory acquired the name “relativity,” because it made unexpected predictions about relative motion and electromagnetism.