The Astronomy Book

150

of distance per units of time.
Therefore, the constancy of the
speed of light must be due to an
inconstancy in the flow of time.
Objects observed to be traveling
faster through space are moving
more slowly through time. Clocks
on the station and on the train are
ticking at different rates, depending
on the frame of reference from
which they are observed. On the
moving train, Bob sees his clock
ticking away as normal, but to the
observer Pat on the platform, the
train’s clock is moving very slowly.
The passenger on the speeding
train will not notice any slowing
of time. The mechanisms by

which time is measured—such

as the swing of a pendulum, the

vibration of a quartz crystal, or the

behavior of an atom—are physical

phenomena obeying universal laws.

According to special relativity,

laws remain unchanged within

the reference frame—the moving

train, or any other set of objects

moving together.

Energy is mass

The impact of this dilation of time

has far-reaching effects, which

Einstein gradually pieced together

into a single general theory

of relativity in 1915. One early

breakthrough was the discovery

THE THEORY OF RELATIVITY

of E=mc^2 , which states that

E (energy) is equal to mass (m)

multiplied by the square of the

speed of light (c). c^2 is a very

large number—about 90 million

billion—and so a small amount

of mass contains a huge quantity

of energy. This is evident in a

nuclear explosion when mass

is converted to free energy.

Returning to the train thought

experiment, the two observers

now throw tennis balls at each

other. The balls collide and bounce

back to each person (both Pat

and Bob have very good aim).

If both observers were in the same

reference frame, the described

motion of the balls would occur

because the balls had the same

mass and were thrown with the

same force. But in this experiment

the balls are in different reference

frames—one stationary, the other

moving at close to the speed of light.

Pat would see Bob’s ball moving

much more slowly than his own due

to the time dilation, yet when they

collide, both balls are knocked back

to their owners. The only way this

could work is if Bob’s slow tennis

ball is heavier, or contains more

mass, than Pat’s tennis ball.

As an object’s velocity (v) approaches light speed (c), the object
becomes increasingly squashed in the direction of travel when viewed
by a stationary observer. This is not merely an illusion. In the observer’s
frame of reference, the object’s shape really does change.

v =0 v =0.3c v =0.6c v =0.9c

Albert Einstein Einstein was born in Germany^

but spent his formative years in

Switzerland. He was an average

student, and then struggled to

find teaching work, ending up

at the patent office in Bern. After

the success of his 1905 papers,

Einstein took university posts in

Bern, Zurich, and then in Berlin,

where he presented his general

theory in 1915. With the rise of

Nazism in 1933, Einstein moved

to the United States, where he

settled at Princeton University.

There he spent the rest of his

days trying to link relativity

with quantum mechanics.

He failed to do so, and no one

else has succeeded yet either.

A leading pacifist voice for many

years, in 1939 Einstein was

instrumental in alerting Allies

to the dangers that Germany

might build a nuclear weapon.

He declined to be involved in

the Manhattan Project that built

the first atomic bombs. An avid

violinist, Einstein stated that

he often thought in music.

Key work

1915 Relativity: the Special and

the General Theory