An Illustrated Guide Relativity by Unknown

Author:Unknown
Language: eng
Format: epub
Published: 2011-01-07T03:00:05.762000+00:00

6.2 Time dilation

135

You’re comparing the reading of your clock now ct

ct

with the reading of my clock in the past! It’s your Ј

clock that’s running slow.

No! you’re the one who’s comparing

the reading of your clock now with the reading of my clock in the past!

E

C

xЈ

B

D

Your clock is running

slow compared to mine.

Our clocks have been

synchronized!

x

A

136

Consequences

The little characters in the figure on the previous page are both claiming that the other clock is running slow. The easiest way to see this is to Lorentz transform to a frame in which the ground- and car-frames are moving in opposite directions at the same speed. This lets you see the two frames in a completely symmetric fashion. The result of such a transformation is shown here.

Now, the ground-frame observer compares the reading of the ground-frame clock at B with the reading of the car-frame clock at D. Since the two clocks were synchronized at A, this is the same thing as comparing the lengths of AB and AD, and clearly AD is shorter than AB. So the reading of the car-clock at D will be earlier than the reading of the ground-clock at B, and the ground-frame observer at B will conclude that the car-frame clock is running slow compared to the ground-frame clock.

The car-frame observer compares the reading of the car-frame clock at E with the reading of the ground-frame clock at B. AB is shorter than AE. So the reading of the ground-clock at B will be earlier than the reading of the car-clock at E, and the car-frame observer at E will conclude that the ground-frame clock is running slow compared to the car-frame clock.

So what we have discovered is that moving clocks are always observed to be running slower. This effect is known as time dilation.

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