In our initial article on teaching special relativity in the first week of an introductory physics course, we used the principle of relativity and Maxwell's theory of light to derive Einstein's second postulate (that the speed of light is the same to all observers).1 In this paper we study thought experiments involving a light pulse clock moving past us with uniform motion at a speed v. Using Einstein's second postulate and the Pythagorean theorem, we see that the light pulse clock runs slow by a factor √1 − v2/c2. We then show that it is a direct consequence of the principle of relativity that all clocks moving by us the same way run slow by precisely the same factor.
REFERENCES
1.
Elisha
Huggins
, “Special relativity in week one: 1) The principle of relativity
,” Phys. Teach.
49
, 148
–150
(Feb. 2011
).2.
To get the formula for the rate of the astronaut's clock, consider the right triangle of Fig. 3. The vertical leg, the distance we see that our light pulse travels in one bounce, is the speed of light c times the length of our nanosecond tus. Calling t astronaut the longer length of time we see that the astronaut's light pulse takes to travel between mirrors, the hypotenuse is c times t astronaut. The horizontal leg is the distance the astronaut's clock travels at a speed v during this time, namely vt astronaut. From the Pythagorean theorem we get (ct astronaut)2 = (ctus)2 + (vt astronaut)2, which we can solve to get as the length of the astronaut's longer nanosecond.
3.
That real clocks run slow is beautifully illustrated in the movie by Frisch and Smith, “Time Dilation, an Experiment with Mu‐Mesons,” that is the focus of our next article. A detailed discussion of the movie appears in
David H.
Frisch
and James H.
Smith
, “Measurement of the relativistic time dilation using μ mesons
,” Am. J. Phys.
31
, 342
–355
(May 1963
).
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© 2011 American Association of Physics Teachers.
2011
American Association of Physics Teachers
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