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Relativity 3

problems that involve inertial frames of reference. General relativity,published by

Einstein a decade later, describes the relationship between gravity and the geometrical

structure of space and time. The special theory has had an enormous impact on much

of physics, and we shall concentrate on it here.

Postulates of Special Relativity

Two postulates underlie special relativity. The first, the principle of relativity,states:

The laws of physics are the same in all inertial frames of reference.

This postulate follows from the absence of a universal frame of reference. If the laws

of physics were different for different observers in relative motion, the observers could

find from these differences which of them were “stationary” in space and which were

“moving.” But such a distinction does not exist, and the principle of relativity expresses

this fact.

The second postulate is based on the results of many experiments:

The speed of light in free space has the same value in all inertial frames of

reference.

This speed is 2.998  108 m/s to four significant figures.

To appreciate how remarkable these postulates are, let us look at a hypothetical

experiment basically no different from actual ones that have been carried out in a

number of ways. Suppose I turn on a searchlight just as you fly past in a spacecraft

at a speed of 2  108 m /s (Fig. 1.1). We both measure the speed of the light waves

from the searchlight using identical instruments. From the ground I find their speed

to be 3  108 m /s as usual. “Common sense” tells me that you ought to find a speed

of (3 2)  108 m/s, or only 1  108 m /s, for the same light waves. But you also

find their speed to be 3  108 m/s, even though to me you seem to be moving parallel

to the waves at 2  108 m/s.

Figure 1.1The speed of light is the same to all observers.

(a) b) c)

c = 3 ✕ 108 m/s

c = 3 ✕ 108 m/s

v = 2 ✕ 108 m/s

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