Science Matters (25 page)

Because the speed of light,
c
, is such a large number, the conversion of a little bit of mass can produce a lot of energy. By the same token, it requires a great deal of energy to produce even a small particle. A block of cement small enough to fit under your kitchen table could run the entire United States for over a year if it were converted completely to energy.

Scientists have been able to verify all of these predictions of special relativity. For example, physicists routinely use particle accelerators to take bunches of protons and electrons up to speeds near that of light. The speeding particles are kept in a designated track by large magnets, and the force exerted by the magnets has to be adjusted to take account of the fact that the particles’ masses increase. Every time one of these machines operates it confirms predictions of the theory of relativity.

By the same token, accelerators work by manipulating long, strung-out bunches of particles. As the particles accelerate, these bunches shorten, and the machine is adjusted to take this effect into account. Thus, the fact that accelerators work is also evidence for the prediction of length contraction.

Finally, about 20 percent of all electrical power in the United
States is produced by nuclear reactors. Reactors work because nuclear reactions convert small amounts of mass into large amounts of energy, in keeping with Einstein’s famous formula. Thus, the equivalence of matter and energy is confirmed every day by commercial power companies.

In many ways, the philosophical consequences of the theory of relativity are as important as the practical results that flow from it. It was the first of the modern theories that revolutionized the old, mechanical, Newtonian view of the world. Relativity substituted equal observers for the classic approach by which all laws were referred to a single, correct “God’s-eye” frame of reference. But relativity did not consign Newton to the garbage dump of history. It simply extended our knowledge into ultrafast domains that Newton never investigated. When we apply the equations of relativity to the modest speeds where Newtonian mechanics has worked in the past, relativistic equations reduce to the same ones that Newton first wrote down three centuries ago. So Einstein didn’t really replace Newton; he encompassed and expanded Newton’s work.

Finally, and perhaps most important, the theory of relativity is not simply a statement that “everything is relative,” even though it is usually expressed that way in casual party chitchat. What is “relative” in relativity are descriptions of specific events. But the crucial aspects of knowledge, the laws of nature, are most emphatically not relative. Every observer in the universe, regardless of his or her state of motion, must obey the same physical laws. Thermodynamics, Maxwell’s equations, and quantum mechanics apply to every observer, and do not vary from one to another.

Imagine yourself in a windowless spaceship accelerating at exactly one g, the equivalent of Earth’s gravity. Could you tell if you were in space or on Earth? The answer is no. If you drop a ball in the spaceship, as far as you are concerned the ball falls to the floor. Looking at this event from a stationary frame outside the spaceship, we would say that the floor had accelerated upward and hit the stationary ball. But inside the sealed-off ship the ball appears to fall, just as it would on Earth. No experiment you could do would tell you whether you were in an accelerating spaceship or stationary on Earth. Thus, acceleration and gravity must be equivalent at some deep level, and what we call gravity must be an effect of our frame of reference. This equivalence is the central thesis of Einstein’s theory.

The central idea of general relativity is that someone in an accelerating frame of reference (such as a rocket ship) experiences exactly the same effects as those normally associated with the force of gravity. Einstein saw a connection between changes in motion (what Newton would have called the action of a force) and the geometry of reference frames. The result of his thinking, published in 1916, was the general theory of relativity—the theory that still stands as our most complete theory of gravitation.

The long wait between the special and general theories was due primarily to the complexity of the mathematics Einstein had to develop to express his ideas. The fact that theoretical physicists are now trying to replace the theory with one more attuned to the notions of quantum mechanics in no way diminishes relativity’s impact on science. We will first present a simple way of visualizing general relativity (minus the complex mathematics), then discuss some tests that support it.

Imagine taking a sheet of tough plastic and stretching it tightly over a large, rigid frame. Imagine further that you had painted a rectangular grid on the flat surface. If you carefully rolled a lightweight ball bearing along one of the grid lines, it would continue to roll along the straight line. The only way you could get it to deviate from the grid line would be to exert a force on it (e.g., by blowing on the ball bearing or by bringing up a magnet). This picture represents the classical Newtonian way of looking at all forces, including gravity. Objects move in a straight line unless a force causes them to do otherwise.

General relativity approaches the problem of motion in a completely different way. Imagine placing a heavy lead ball on the sheet of stretched plastic we’ve just discussed. The lead sphere will weigh the plastic down, distorting and warping it. If you now rolled the ball bearing across the plastic, it would follow a path that carried it nearer the lead sphere than it would otherwise have gone. Newton would say that an attractive force (such as gravity) existed between the two, but Einstein would interpret the same phenomenon differently. He would say that the presence of the lead weight warped the space in its vicinity, and that this warping caused a change in the ball bearing’s motion. For Einstein, there were no forces in the Newtonian sense, only changes in the geometry of space.

The relativistic interpretation of the solar system, then, is that the sun warps the space around it and the planets move around in this space like marbles rolling around the inside of a bowl. In fact, if you use relativity to calculate what happens to the original grid of straight lines when you drop a mass onto it, you find that the original lines are deformed into closed elliptical curves—precisely the paths followed by planets. A good way to keep things straight is to remember that:

but

Einstein believed that not just gravity, but all forces would ultimately be explained in this geometrical way. In fact, he spent the last half of his life in a futile search for a unified theory of forces. Progress toward this goal came about only after yet another way of describing forces—through the exchange of elementary particles—had been developed. Thus, general relativity remains a magnificent but isolated chapter in the sciences; Einstein’s theory encompassed and superseded Newtonian gravity, and will itself soon be encompassed and superseded by a theory of quantum gravity.

Unlike special relativity, general relativity is not buttressed by lots of experimental evidence. The reasons for this lack of evidence are partly theoretical and partly technical. Like special relativity, general relativity encompasses Newton’s physics. For normal, everyday phenomena, general relativity gives predictions that are virtually the same as those of Newtonian gravity. Thus, unless we are able to make extremely precise measurements, the two cannot be distinguished in a laboratory setting. It is only in the region of very large masses or very short distances
that the warping of space becomes so pronounced that the two theories differ significantly, and such conditions are not available to experimenters.

There are only three classic tests of general relativity. These are (1) the precise shape of planetary orbits, (2) the bending of light near the sun’s rim, and (3) the gravitational redshift.

Because planetary orbits are elliptical there is a point where the planet comes closest to the sun. We call this point the perihelion (from the Greek for “near the sun”). In a simple Newtonian situation, the perihelion would be at the same point in space through all time—the orbit would not shift. In fact, many forces act to push the perihelion of a planet a little farther along each time it goes around. The gravitational effects of the other planets, particularly Jupiter, are the most important. But before Einstein published his theory, the measured perihelion advance of the planet Mercury exceeded the predicted value by about 43 seconds of arc per century. General relativity predicted that the (very small) warping of space by the mass of the sun would produce exactly this much advance in the perihelion. This retrodiction was rightly taken to be a great triumph for the theory.

Today scientists use radar ranging to make extremely accurate determinations of the orbital positions of the planets, and the perihelion shifts for Venus, Earth, and Mars have been measured and found, like that of Mercury, to be precisely as predicted by general relativity. This is probably the most stringent test of the theory available at this time.

The best-known test of general relativity involves the bending of light rays that pass close to the rim of the sun. The measurement of this predicted effect in a 1919 eclipse catapulted Einstein to a position of international prominence. Today, we perform this test with radio waves instead of light, and the sources of the
radiation are quasars, not stars. Radio waves can be detected anytime (they are not blotted out by the sun), so scientists can conduct this test under normal conditions, rather than having to wait for an eclipse. The measurements agree with the predictions of relativity to better than 1 percent, another remarkable verification of the theory.

Finally, relativity predicts that as a photon climbs upward in a gravitational field (as it would in leaving Earth’s surface), some energy is drained from it by the uphill motion. In this the photon is no different from a baseball, which slows down as it gains height. Since the photon must continue to move at the speed of light, however, we see its loss of energy as a lengthening of the wavelength of the light—a shift toward the red. Thus, a flashlight beam seen from an airplane will be slightly redder than that same beam seen from the ground. Like the above two predictions, this too has been borne out by experiment.

For over half a century, there were only three tests of general relativity, but each has seemed to supply supporting evidence. Today, however, with advanced electronic systems capable of making very precise measurements, there are many tests of the theory. In fact, you test the theory every time you use the Global Positioning System. This system requires that we know the position of satellites in orbit to a high degree of accuracy, which requires in turn that we have very precise clocks on those satellites. In fact, the satellites of the GPS have onboard atomic clocks accurate to thirteen decimal places. When the system calculates a position using data from those clocks, it has to take into account relativistic effects like time dilation because those satellite clocks are moving. In a sense, then, relativity (both special and general) has moved from forefront science to applied engineering during the last few decades.

The most spectacular prediction of general relativity is the existence of black holes. To understand the odd behavior of a black hole, go back to the analogy of the stretched plastic sheet and the lead weight. Imagine that we had a way of adding more and more mass to the lead sphere without increasing its size. As the ball got heavier and heavier, the distortion of the plastic would get bigger and bigger. Eventually the plastic might deform to the extent that the weight would neck off and separate itself from the rest of the surface. The distorting plastic sheet might even close up completely, wrapping the lead ball out of sight for good and leaving a reformed plastic sheet in its wake.

In just the same way, relativity predicts that when a large enough mass is concentrated in a small enough volume, it distorts the space around it so severely that a part of space wraps itself up and leaves the rest of normal space behind. A mass that has done this is said to have formed a black hole. You can think of the black hole as an object so massive and so dense that nothing, not even light, can muster enough energy to escape from its surface. Once something falls in, it can never get out. A material that absorbs all light that falls on it is black, which is how this particular beast received its ominous name.

Theorists talk about three different kinds of black holes. Galactic black holes are huge things located at the center of galaxies such as the Milky Way They typically have masses a million times that of a star like the sun, and can be detected by measuring the radiation from material falling into them. And although a mass of a million suns may seem large, remember that galaxies typically have tens of billions of stars in them, so the central black hole is really a small part of the entire structure. It appears that most galaxies have a massive black hole at their center.

Stellar black holes result from the death throes of very massive stars, as discussed in Chapter 10. If a single star goes through this process, it would be very difficult to detect the black hole, since it neither absorbs nor emits radiation. Instead, astronomers look for double star systems in which an ordinary star and an unseen companion are in orbit. By observing the motion of the visible star, they can discover the properties of the unseen companion. Using this technique, astronomers have identified a few dozen candidates for stellar black holes in our galaxy.

Finally, some theories predict the existence of objects called quantum black holes, much smaller than a single proton. These sorts of black holes remain a theoretical possibility, but as yet there is no evidence that they exist.