Let’s explore some of the remarkable consequences of the principle of relativity with an open mind and see how the predictions of the theory stack up against experiment.
Time Dilation
A clock ticks off equal bits of time. Anything that “ticks” can be used to measure time’s passage. Think about a clock made from a flashing strobe light, a mirror, and an instrument that records the arrival of a light beam. Each “tick” of the clock consists of a light flash, the transit of light to the mirror and back, and the click (or whatever) of the instrument when the light returns. If the arrival of the light in the instrument triggers the next flash of the bulb, the clock will “tick” regularly. You could imagine adjusting the distance to the mirror so that the “ticks” of the light clock were synchronized with the ticks of any other kind of clock—the pendulum of a grandfather’s clock, the vibrations in your quartz wristwatch, and so on. Despite its strange appearance, the “light clock” is a perfectly ordinary clock.
Imagine two light clocks, each held perpendicular to the ground, one next to you and the other going by in a car moving at a constant velocity. We arrange things so that both bulbs flash as they pass each other. The light in the stationary clock travels up to its mirror and back. Meanwhile, the light in the moving clock moves upward as the entire clock travels along to the right. As a result, the light in the moving clock as seen by an observer on the ground must travel in a sawtooth pattern as shown.
The principle of relativity says the speed of light must be the same in all frames of reference. Light in the moving clock has to travel a longer distance so it must take longer to reach its destination than light in the stationary clock, which only has to travel up and down. The ground-based observer will see both lights flash, then he will hear his own clock tick, and only later will he hear the moving clock tick. This pattern will be repeated with each click, and the moving clock will fall farther and farther behind its stationary counterpart. If the speed of light is the same for all observers, it follows that moving clocks run slower. This effect is known as time dilation.
The “light clock” is constructed from a flashing light, a mirror, and a receiver. Each “tick” of the clock is the time it takes for light to make the round trip.
Many people’s first response to this argument is that it is built on an illusion—that the moving clock isn’t “really” running slower. As teachers, we have learned to recognize the use of “really” as a tip-off to a Newtonian frame of mind, and to use this objection to bring our students face-to-face with the real core of the theory of relativity. For the fact of the matter is that when someone says that the moving clock doesn’t “really” slow down, what he or she means is that the clock appears normal to an observer moving with it. In the jargon of the physicist, the clock appears normal in its “proper” frame of reference.
Albert Einstein realized that a moving light clock appears to be running at different speeds for different observers. The faster a clock moves relative to the observer, the farther its light must travel, but the speed of light is constant. (The mirror moves along with the truck.) Einstein concluded that as a clock approaches the speed of light, time appears to move more slowly.
The assumption hidden in the objection is that somehow the proper frame is “right” and other frames are “wrong,” and that only the proper frame should be consulted if you want to know what the clock “really” is doing. But the central thesis of relativity is that there are no “right” frames of reference—no privileged positions from which events ought to be viewed. Every observer—every frame of reference—has an equal right to be heard when descriptions of physical events are given.
What is even more disturbing than the counterintuitive notion of time dilation is that the effect actually exists in nature. There are many proofs of this statement, but the most dramatic experiment was performed by scientists at the University of Michigan. They strapped extremely accurate atomic clocks into first-class seats on aircraft making round-the-world flights and, after the journey was completed, compared the readings on those clocks to readings on clocks that had been left on the ground. As expected, the moving clocks had slowed down slightly.
So time dilation, as well as being easy to derive from the principle of relativity, is also supported by experiment. As difficult as it may seem to square with our intuition, clocks in moving frames of reference run more slowly than stationary ones. In our normal experience this slowdown is much too small to measure except with the most precise instruments: a clock that had been moving at 60 miles per hour since the beginning of the universe would have lost less than one second by now.
If the velocity of the moving clock is small compared to the speed of light, the width of the sawtooth will be small and the distance traveled by the two light beams will be almost the same. It is only when the sawtooth spreads out (i.e., when the velocity of the clock approaches that of light) that appreciable differences appear. You don’t have to give up your intuition about clocks for everyday experience quite yet, but if humans ever develop spaceships that travel near light speed, time dilation may wreak havoc with future genealogists. Slowly aging space travelers could return from a voyage younger than their earthbound children!
You can test your understanding of time dilation by convincing yourself that an observer traveling next to the moving clock will think that the clock on the ground has slowed down.
Other Predictions of Special Relativity
Einstein called the kind of exercise we just went through for the moving clock a “gedanken experiment” (from the German denken—to think). It’s a technique that allows you to grasp the essential behavior of things like clocks, even though performing that particular experiment might be technically difficult. Other “gedanken experiments” allowed Einstein to draw startling conclusions from his special theory of relativity:
1. Moving yardsticks are shorter than stationary ones.
When an object moves, it contracts—physically shrinks—along the direction of motion. Thus, a baseball moving at or near the speed of light will look flattened, like a cookie viewed edge-on.
2. Moving objects are more massive.
The faster an object moves, the greater its mass becomes and the harder it is to deflect it from its course. As its velocity approaches the speed of light, the mass of any object approaches infinity. This result leads to the common misconception that nothing can move faster than the speed of light. Relativity doesn’t say that at all—it just says that nothing now moving at less than the speed of light can be accelerated to and past that speed. There’s still room for Warp Drive!
3. E = mc.2
The most famous outcome of the theory of relativity is the equivalence of mass and energy. This simple equation has been elevated to the level of folklore, perhaps the only equation of physics to enjoy that status. It says, in effect, that mass is just one more form of energy. Mass can disappear provided an equivalent amount of energy in another form takes its place. More strikingly, if there is a lot of energy available (for example, in the collision between two particles), some of that energy can be converted into mass, and a new particle can be created where none existed before. The new particle isn’t created “out of nothing,” but from energy taken from another source.
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.
Experimental Confirmation
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 t
hat 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.
Some Philosophical Remarks About Relativity
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.
GENERAL RELATIVITY
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:
For Newton, motion is along curved
lines in a flat space.
but
For Einstein, motion is along straight lines
in a curved space.
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.
Tests of General Relativity
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 triu
mph 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.
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