4

b.

On the train, the length of time it takes the light to reach the ceiling is measured
as t ′ . Then relative to the train, the light travels a distance ct ′ . Right?

c.

As before, relative to the platform, the distance the train travels during time tis
vtwhere vis the velocity of the train. Right?

(i)

Explain why the distances are related in the following way:

(ct)2

=(ct ′ )2

+(vt)2

(ii)

Show that tand t are related through the equation:

′

′ =t1

t

-v2
c2

(iii)

Explain what happens as v→c.

(iv)

Compare this relationship betweentand t with the relationship you

considered in part 1.c. (take v=9

10

′

cfor example). Which equation do

you trust more and why? Which do you think Einstein proposed?

(iv)

Explain why one conclusion of Einstein's theory of relativity is that
moving clocks run slow relative to a stationary observer.

Exercise: Suppose identical twins part at age 20. One of them remains on earth while the

other spends 10 earth-years traveling in space in a space ship whose speed is 1
2

c. What are

the ages of the twins when the ship returns to earth? Answer the same question if the space
ship travels at 9

10

c.