28.2

The Postulates of Special Relativity

Einstein built his theory of special relativity on two fundamental assumptions or postulates about the way nature behaves.

| The Postulates of Special Relativity

1. | The Relativity Postulate. The laws of physics are the same in every inertial reference frame.
2. | The Speed of Light Postulate. The speed of light in a vacuum, measured in any inertial reference frame, always has the same value of c, no matter how fast the source of light and the observer are moving relative to each other.

It is not too difficult to accept the relativity postulate. For instance, in Figure 28-1 each observer, using his own inertial reference frame, can make measurements on the motion of the space shuttle. The relativity postulate asserts that both observers find their data to be consistent with Newton’s laws of motion. Similarly, both observers find that the behavior of the electronics on the space shuttle is described by the laws of electro-magnetism. According to the relativity postulate, any inertial reference frame is as good as any other for expressing the laws of physics. As far as inertial reference frames are concerned, nature does not play favorites.
Since the laws of physics are the same in all inertial reference frames, there is no experiment that can distinguish between an inertial frame that is at rest and one that is moving at a constant velocity. When you are seated on the aircraft in Figure 28-1, for instance, it is just as valid to say that you are at rest and the earth is moving as it is to say the converse. It is not possible to single out one particular inertial reference frame as being at “absolute rest.” Consequently, it is meaningless to talk about the “absolute velocity” of an object—that is, its velocity measured relative to a reference frame at “absolute rest.” Thus, the earth moves relative to the sun, which itself moves relative to the center of our galaxy. And the galaxy moves relative to other galaxies, and so on. According to Einstein, only the relative velocity between objects, not their absolute velocities, can be measured and is physically meaningful.
Whereas the relativity postulate seems plausible, the speed of light postulate defies common sense. For instance, Figure 28-2 illustrates a person standing on the bed of a truck that is moving at a constant speed of 15 m/s relative to the ground. Now, suppose you are standing on the ground and the person on the truck shines a flashlight at you. The person on the truck observes the speed of light to be c. What do you measure for the speed of light? You might guess that the speed of light would be c + 15 m/s. However, this guess is inconsistent with the speed of light postulate, which states that all observers in inertial reference frames measure the speed of light to be c—nothing more, nothing less. Therefore, you must also measure the speed of light to be c, the same as that measured by the person on the truck. According to the speed of light postulate, the fact that the flashlight is moving has no influence whatsoever on the speed of the light approaching you. This property of light, although surprising, has been verified many times by experiment.

Figure 28-2 Both the person on the truck and the observer on the earth measure the speed of the light to be c, regardless of the speed of the truck.

Since waves, such as water waves and sound waves, require a medium through which to propagate, it was natural for scientists before Einstein to assume that light did too. This hypothetical medium was called the luminiferous ether and was assumed to fill all of space. Furthermore, it was believed that light traveled at the speed c only when measured with respect to the ether. According to this view, an observer moving relative to the ether would measure a speed for light that was slower or faster than c, depending on whether the observer moved with or against the light, respectively. During the years 1883–1887, however, the American scientists A. A. Michelson and E. W. Morley carried out a series of famous experiments whose results were not consistent with the ether theory. Their results indicated that the speed of light is indeed the same in all inertial reference frames and does not depend on the motion of the observer. These experiments, and others, led eventually to the demise of the ether theory and the acceptance of the theory of special relativity.
CONCEPTS AT A GLANCE The remainder of this chapter reexamines, from the viewpoint of special relativity, a number of fundamental concepts that have been discussed in earlier chapters from the viewpoint of classical physics. These concepts are time, length, momentum, kinetic energy, and the addition of velocities. We will see that each is modified by special relativity in a way that depends on the speed v of a moving object relative to the speed c of light in a vacuum. Figure 28-3 illustrates that when the object moves slowly (v is much smaller than ), the modification is negligibly small, and the classical version of each concept provides an accurate description of reality. However, when the object moves so rapidly that v is an appreciable fraction of the speed of light, the effects of special relativity must be considered. The gold panel in Figure 28-3 lists the various equations that convey the modifications imposed by special relativity. Each of these equations will be discussed in later sections of this chapter.

Figure 28-3 CONCEPTS AT A GLANCE This chart emphasizes that it is the speed v of a moving object, as compared to the speed c of light in a vacuum, that determines whether the effects of special relativity are measurably important. Albert Einstein (1879–1955), the author of the theory of special relativity, is one of the most famous scientists of the twentieth century. (Hulton Archive/Getty Images)

It is important to realize that the modifications imposed by special relativity do not imply that the classical concepts of time, length, momentum, kinetic energy, and the addition of velocities, as developed by Newton and others, are wrong. They are just limited to speeds that are very small compared to the speed of light. In contrast, the relativistic view of the concepts applies to all speeds between zero and the speed of light.

Copyright © 2007 John Wiley & Sons, Inc. All rights reserved.