Science Matters (24 page)

The principle of relativity can be stated simply as “Every observer sees the same laws of nature,” but in practice, it is easier to break this principle into two parts, based on how the observers and their frames of reference are moving. The easier part we call special relativity, and it deals with the special case of reference frames that do not accelerate. In the Newtonian sense, special relativity is concerned only with observers in uniform motion, with no forces to alter their motion.

On the other hand, general relativity applies to all frames of reference, whether they accelerate or not. General relativity contains special relativity as a special case, but is itself a lot harder to deal with mathematically. We’ll treat special and general relativity separately, tackling the simpler theory first.

One more point should be made about the place of relativity in modern scientific research. Although the theory of relativity has the aura of being in the forefront of modern science, in fact it has been around since 1905 and is regarded by physicists as a familiar and well-verified part of their world.

If the laws of nature must be the same for all observers moving at constant speed, then all such observers must agree with Maxwell’s
description of the laws of electricity and magnetism. Since the speed of light is a constant built into Maxwell’s equations, it follows that all observers must measure the same value for the speed of light. If they didn’t, different observers would find different sets of Maxwell equations.

This conclusion, in and of itself, already violates our intuition. Think about a simple example: You stand on a railroad car moving 50 miles per hour and throw a baseball forward at 50 miles per hour. Naturally someone on the ground will see the baseball moving at 100 miles per hour—the speed of the train plus the speed of the baseball. But if instead of throwing a baseball you shine a flashlight, the principle of relativity says that someone on the ground must see the light moving at a speed of 186,000 miles per second, not 186,000 miles per second plus 50 miles per hour.

This sort of basic contradiction between the way we think the universe ought to behave and the idea that the laws of nature have universal validity first led Albert Einstein to think about the theory of relativity. In the late nineteenth century, there were three ways in which the problem could have been resolved:

1. Maxwell’s equations could have been wrong; or,
   
2. the principle of relativity could have been wrong; or,
   
3. our intuitive ideas about space and time could have been wrong.
   

The last possibility arises because to calculate speed, we have to divide the distance traveled by the time it takes for the travel to occur. In our intuitive thinking about the problem of the flashlight, for example, we assumed that a clock on the ground and a clock on the railroad car would both run at the same speed. In reality, this might or might not be true—you never know until you actually make measurements.

During the 1920s, serious theories proposed modifications to Maxwell’s equations to make the speed of light depend on the motion of the source. When these modifications were tested (for example, by measuring light emitted by a double-star system both when the star is coming toward us and going away), they failed. In fact, we can say that both Maxwell and Einstein have been abundantly supported by the data. That leaves only the third possibility, that there is something wrong about our intuitive notions about the way different observers see things like clocks and yardsticks.

According to Einstein, he came to the realization that moving clocks might not run at the same rate as stationary ones while riding in a streetcar in Bern. Looking at a clock on a tower, he realized that if the streetcar moved away from the clock at the speed of light, it would look to him as if the clock had stopped. Einstein would, in effect, be riding outward from the clock perched on a single crest of a light wave. His pocket watch, on the other hand, would be moving with him and hence would continue to tick along in its usual manner. Thus, he reasoned, it is at least worth considering the possibility that our usual assumption that time is the same for all observers is simply wrong when things move at speeds near the speed of light.

We instinctively think something is wrong with the idea that light travels at exactly the same speed whether from a moving or stationary flashlight. We base our prejudice on a lifetime’s experience with moving objects. But how much of this experience was garnered while moving at speeds close to the speed of light? None of us has ever moved even close to 186,000 miles per second, so, strictly speaking, we have no experience whatsoever about how light or baseballs should behave at such speeds. The only thing actually violated by the example of the relativistic flashlight is our untutored expectation that nature should be the
same at high velocities as it is at low ones. But this is only an assumption and, like other assumptions, it must be tested against experiment before we can accept it.

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.

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.

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.