The Solar System

CHAPTER 5 | GRAVITY 91

Th e word accelerated is important. If either

spaceship were to fi re its rockets, then its veloc-

ity would change. Th e crew of that ship would

know it because they would feel the accelera-

tion pressing them into their couches.

Accelerated motion, therefore, is diff erent—the

pilots of the spaceships can always tell which

ship is accelerating and which is not. Th e pos-

tulates of relativity discussed here apply only to

the special case of observers in uniform motion,

which means unaccelerated motion. Th at is why

the theory is called the special theory of

relativity.

Th e fi rst postulate led Einstein to the con-

clusion that the speed of light must be constant

for all observers. No matter how you are mov-

ing, your measurement of the speed of light has

to give the same result (Figure 5-11b). Th is

became the second postulate of special

relativity:

Second postulate: Th e speed of light is

constant and will be the same for all observ-

ers independent of their motion relative to

the light source.

Remember, this is required by the fi rst postu-

late; if the speed of light were not constant,

then the pilots of the spaceships could measure

the speed of light inside their spaceships and

decide who was moving.

Once Einstein had accepted the basic pos-

tulates of relativity, he was led to some startling

discoveries. Newton’s laws of motion and grav-

ity worked well as long as distances were small

and velocities were low. But when Einstein

began to think about very large distances or

very high velocities, he realized that Newton’s

laws were no longer adequate to describe what

happens. Instead, the postulates led Einstein to

derive a more accurate description of nature

now known as the special theory of relativity. It

predicts some peculiar eff ects. For example,

special relativity shows that the observed mass

of a moving particle depends on its velocity.

Th e higher the velocity, the greater the mass of

the particle. Th is is not signifi cant at low veloci-

ties, but it becomes very important as the velocity approaches the

speed of light. Such increases in mass are actually observed when-

ever physicists accelerate atomic particles to high velocities

(■ Figure 5-12).

Th is discovery led to yet another insight. Th e relativistic

equations that describe the energy of a moving particle predict

It is obvious!

You are moving,

and I’m not.

I get

299,792.459 km/s.

How about you?

No, I’m

not moving.

You are!

Same here.

a

b

■ Figure 5-11

(a) The principle of relativity says that observers can never detect their
uniform motion, except relative to other objects. Thus, neither of these trav-
elers can decide who is moving and who is not. (b) If the velocity of light
depended on the motion of the observer through space, then these travelers
could perform measurements inside their spaceships to discover who was
moving. If the principle of relativity is correct, then the velocity of light
must be a constant when measured by any observer.