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of a kind similar to the ones Einstein performed. Do you know that he

reasoned out his theory, that he did not work in a laboratory?

Yma:

I have heard that; in fact, he worked in a patent office, didn't he?

Mom:

Yes, you are right again.

Let's see if for today we can behave as Einstein did and conduct a thought experiment of our

own to derive the result that moving clocks run slow.

Two Thought Experiments

Suppose that a train is moving to the left past a stationary observer on a platform.

1.

Suppose that on the train, someone turns on a flashlight and directs the beam
horizonatlly at the front wall of the coach.

a.

On the platform, the observer measures as tthe time it takes the light to travel to
the wall. Then explain why the distance the light travels to the wall relative to the
platform is ct.

b.

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

c.

Note that relative to the platform, the distance the train travels during time tis vt
where vis the velocity of the train. Right?

(i)

Explain why the following equation seems reasonable:

ct=ct ′ +vt

(ii)

Next, describe what happens when vis close to c(say, v=9

10

c). Is

the equation still reasonable? Do we have any reason to trust the
original equation in (i)? Do we have reason to distrust it?

2.

Here is another experiment. Now, the person on the train directs the flashlight
vertically at the ceiling. So, the light beam is not shining in the direction of
movement of the train.

a.

Similar to before, on the platform the observer measures as tthe time it takes
the light to travel to the ceiling. The path of the light is shown below. When you
have read (below) part b and the beginning of part c, you should be able to
explain why the drawing makes sense. So, read on.