Fear of Physics (12 page)

Observations that the clustered mass in the universe appears to be dominated by what we call
dark matter
are at the heart of one of the most exciting and actively pursued mysteries in modern physics. It would require an entire book to describe adequately the efforts to determine what this stuff might be (and, coincidentally, I have already written one). Here, however, I just want to make you aware of it and to demonstrate that this very modern research problem stems from exploiting exactly the same analysis as Cavendish used over two centuries ago to weigh the Earth for the first time.

At this point, you might be tempted to ask why we believe we can push Newton’s Law this far. After all, requiring a whole new source of nonluminous matter to fill the universe seems like a lot to ask for. Why not assume instead that Newton’s Law of Gravity
doesn’t apply on galactic scales and larger? While in fact some physicists have proposed precisely that possibility, I hope my arguments to this point will help make it more understandable why physicists might believe that postulating a universe filled with dark matter is more conservative than throwing out Newton’s Law. Newtonian gravity has worked perfectly thus far to explain the motion of literally everything under the sun. We have no reason to believe it might not apply to larger scales. Moreover, there is a distinguished tradition of overcoming other possible challenges to Newton’s Law. For example, after the planet Uranus was discovered, it was recognized that the motion of this object, the farthest object from the sun in our solar system known at the time, could not be accounted for by Newtonian gravity based on the attraction of the sun and the other planets. Could this be the first hint of breakdown in the Universal Law? Yes, but it was simpler to suppose that its observed motion might be affected by some as yet unseen “dark” object. Careful calculations using Newton’s Law performed in the eighteenth century pinpointed where such an object might be. When telescopes were pointed at this region, the planet Neptune was soon discovered. Similar later observations of Neptune’s motion led to the accidental discovery of Pluto in 1930.

An even earlier example points out the utility of sticking with a law that works. Often confronting the apparent challenges to such a law can lead to exciting new physical discoveries that are not directly related to the law itself. For example, in the seventeenth century the Danish astronomer Ole Roemer observed the motion of the moons of Jupiter and discovered a curious fact. At a certain time of year, the moons reappear from behind Jupiter about four minutes earlier than one would expect from applying Newton’s Law directly. Six months later, the moons are four minutes late.
Roemer deduced that this was not a failure of Newton’s Law, but rather an indication of the fact that light travels at a finite speed. You may remember that light traverses the distance between the Earth and the sun in about eight minutes. Thus, at one time of year, the Earth is eight “light-minutes” closer to Jupiter than it is when it is on the other side of its orbit around the sun. This accounts for the eight-minute difference in timing the orbits of Jupiter’s moons. In this way, Roemer was actually able to estimate the speed of light accurately, over 200 years before it was measured directly.

Thus, while we didn’t know that we could go on weighing larger and larger regions of the universe as we had already weighed the Earth and the sun, doing so was the best bet. It also offers the greatest hope for progress. A single definitive observation may be enough to disprove a theory in physics. But the observed motion of objects in our galaxy and other galaxies is not such a definitive test. It can be explained by the existence of dark matter, for which there is now concurrent support coming from a host of independent arguments about the formation of large-scale structures in the universe. Further observations will tell us whether our stubborn persistence has been well founded, and in so doing we may discover what most of the universe is made from.

I received numerous letters after writing the book about dark matter from individuals who were convinced that the observations I described provided definitive support for their bold new theories, which they claimed “professionals” have been too narrow-minded to consider. I wish I could convince them that open-mindedness in physics involves a stubborn allegiance to well-proven ideas until there is definitive evidence that they must be transcended. Most of the vital revolutions in this century were not based on discarding old ideas as much as on attempting to accommodate
them and using the resultant wisdom to confront existing experimental or theoretical puzzles. In the words of Feynman again, himself one of the most original physicists of our time: “Scientific creativity is imagination in a straitjacket.”
⁹

Consider perhaps the most famous revolution in physics in this century: Einstein’s development of the special theory of relativity. While there is no denying that the result of special relativity was to force a total revision in our notions of space and time, the origin of this idea was a less ambitious attempt to make consistent two well-established physical laws. In fact, the entire thrust of Einstein’s analysis was an effort to rework modern physics into a mold in which it would accomodate Galileo’s relativity principle, developed some three hundred years earlier. Seen in this way, the logic behind Einstein’s theory can be framed quite simply. Galileo argued that the existence of uniform motion required that the laws of physics, as measured by any uniformly moving observer—including one standing still—should be identical. This implies a surprising result: It is impossible to perform any experiment that proves definitively that you are at rest. Any observer moving at a constant velocity with respect to any other observer can claim that he or she is at rest and the other is moving. No experiment that either can perform will distinguish which is moving. We have all had this experience. As you watch the train on the next track from the one you are on depart, it is sometimes hard to tell at first which train is moving. (Of course, if you are traveling on a train in the United States, it quickly becomes easy. Just wait to feel the bumps.)

In perhaps the major development of nineteenth-century physics, James Clerk Maxwell, the preeminent theoretical physicist of his time, put the final touches on a complete theory of electromagnetism, one that explained consistently all of the physical phenomena that now govern our lives—from the origin of
electric currents to the laws behind generators and motors. The crowning glory of this theory was that it “predicted” that light must exist, as I shall describe.

The work of other physicists in the early part of the nineteenth century, in particular, the British scientist Michael Faraday—a former bookbinder’s apprentice who rose to become director of that centerpiece of British science, the Royal Institution—had established a remarkable connection between electric and magnetic forces. At the beginning of the century, it appeared that these two forces, which were well known to natural philosophers, were distinct. Indeed, on first glimpse, they are. Magnets, for example, always have two “poles,” a north and a south. North poles attract south poles and vice versa. If you cut a magnet in half, however, you do not produce an isolated north or south pole. You produce two new smaller magnets, each of which has two poles. Electric charge, on the other hand, comes in two types, named positive and negative by Ben Franklin. Negative charges attract positive ones and vice versa. However, unlike magnets, positive and negative charges can be easily isolated.

Over the course of the first half of the century, new connections between electricity and magnetism began to emerge. First it was established that magnetic fields, that is, magnets, could be created by moving electric charges, that is, currents. Next it was shown that a magnet would deflect the motion of a moving electric charge. In a much bigger surprise, it was shown (by Faraday and, independently, by the American physicist Joseph Henry) that a moving magnet can actually create an electric field and cause a current to flow.

There is an interesting story associated with the latter, which I can’t resist relating (especially in these times of political debate
over funding such projects as the Superconducting Supercollider, of which I shall speak later). Faraday, as director of the Royal Institution, was performing “pure” research—that is, he was attempting to discover the fundamental nature of electric and magnetic forces, not necessarily in the search for possible technological applications. (This was probably before the era in which such a distinction was significant, in any case.) In fact, however, essentially all of modern technology was made possible because of this research: the principle behind which all electric power is generated today, the principles behind the concept of the electric motor, and so on. During Faraday’s tenure as director of the Royal Institution, his laboratory was visited by the Prime Minister of England, who bemoaned this abstract research and wondered aloud whether there was any use at all in these gimmicks being built in the lab. Faraday replied promptly that these results were very important, so important that one day Her Majesty’s government would tax them! He was right.

Returning to the point of this history, by the middle of the nineteenth century it was clear that there was some fundamental relationship between electricity and magnetism, but no unified picture of these phenomena was yet available. It was Maxwell’s great contribution to unify the electric and magnetic forces into a single theory—to show that these two distinct forces were really just different sides of the same coin. In particular, Maxwell extended the previous results to argue very generally that any changing electric field would create a magnetic field, and, in turn, any changing magnetic field would create an electric field. Thus, for example, if you measure an electric charge at rest, you will measure an electric field. If you run past the same charge, you will also measure a magnetic field. Which you see depends upon
your state of motion. One person’s electric field is another person’s magnetic field. They are really just different aspects of the same thing!

As interesting as this result was for natural philosophy, there was another consequence that was perhaps more significant. If I jiggle an electric charge up and down, I will produce a magnetic field due to the changing motion of the charge. If the motion of the charge is itself continually changing, I will in fact produce a
changing
magnetic field. This changing magnetic field will in turn produce a changing electric field, which will in turn produce a changing magnetic field, and so on. An “electromagnetic” disturbance, or wave, will move outward. This is a remarkable result. More remarkable perhaps was the fact that Maxwell could calculate, based purely on the measured strengths of the electric and magnetic forces between static and moving charges, how fast this disturbance should move. The result? The wave of moving electric and magnetic fields should propagate at a speed identical to that at which light is measured to travel. Not surprisingly, in fact, it turns out that light is nothing other than an electromagnetic wave, whose speed is fixed in terms of two fundamental constants in nature: the strength of the electric force between charged particles and the strength of the magnetic force between magnets.

I cannot overstress how significant a development this was for physics. The nature of light has played a role in all the major developments of physics in this century. For the moment I want to focus on just one. Einstein was, of course, familiar with Maxwell’s results on electromagnetism. To his great credit, he also recognized clearly that they implied a fundamental paradox that threatened to overthrow the notion of Galilean relativity.

Galileo told us that the laws of physics should be independent of where one measures them, as long as you are in a state of uniform
motion. Thus, for example, two different observers, one in a laboratory on a boat floating at a constant velocity downstream and one in a laboratory fixed on shore, should measure the strength of the electric force between fixed electric charges located 1 meter apart in their respective laboratories to be exactly the same. Similarly, the force between two magnets 1 meter apart should be measured to be the same independent of which lab one performs the measurement in.

On the other hand, Maxwell tells us that if we jiggle a charge up and down, we will always produce an electromagnetic wave that moves away from us at a speed fixed by the laws of electromagnetism. Thus, an observer on the boat who jiggles a charge will see an electromagnetic wave travel away at this speed. Similarly, an observer on the ground who jiggles a charge will produce an electromagnetic wave that moves away from him or her at this speed. The only way these two statements can apparently be consistent is if the observer on the ground measures the electromagnetic wave produced by the observer on the boat to have a different velocity than the wave he or she produces on the ground.

But, as Einstein realized, there was a problem with this. Say I am “riding” next to a light wave, he proposed, at almost the speed of this wave. I imagine myself at rest, and as I look at a spot fixed to be next to me, which has an electromagnetic wave traveling slowly across it, I see a changing electric and magnetic field at that spot. Maxwell tells me that these changing fields should generate an electromagnetic wave traveling outward at the speed fixed by the laws of physics, but instead all I see is a wave moving slowly past me.

Einstein was thus faced with the following apparent problem. Either give up the principle of relativity, which appears to make
physics possible by saying that the laws of physics are independent of where you measure them, as long as you are in a state of uniform motion; or give up Maxwell’s beautiful theory of electromagnetism and electromagnetic waves. In a truly
revolutionary
move, he chose to give up neither. Instead, knowing that these fundamental ideas were too sensible to be incorrect, he made the bold decision that, instead, one should consider changing the notions of space and time themselves to see whether these two apparently contradictory requirements could be satisfied at the same time.