This is the third of four articles on teaching special relativity in the first week of an introductory physics course.1,2 With Einstein's second postulate that the speed of light is the same to all observers, we could use the light pulse clock to introduce time dilation. But we had difficulty introducing the Lorentz contraction until we saw the movie “Time Dilation, an Experiment with Mu-Mesons” by David Frisch and James Smith.3,4 The movie demonstrates that time dilation and the Lorentz contraction are essentially two sides of the same coin. Here we take the muon's point of view for a more intuitive understanding of the Lorentz contraction, and use the results of the movie to provide an insight into the way we interpret experimental results involving special relativity.

Topics
Fundamental constants, Special relativity, Leptons, Mesons, Educational aids, Teaching
1.
E.
Huggins
, “
Special relativity in week one: 1) The principle of relativity
,”
Phys. Teach.
49
,
148
–
151
(March
2011
).
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2.
E.
Huggins
, “
Special relativity in week one: 2) All clocks run slow
,”
Phys. Teach.
49
,
220
–
221
(April
2011
).
Google Scholar
Crossref
Search ADS
 
3.
The movie “Time Dilation, an Experiment with Mu-Mesons” was produced by Educational Services Inc., 47 Galen St., Watertown, MA. Because of the importance of this movie in our introduction to the Lorentz contraction, we negotiated for two years to get permission to include the movie in our $10 CD available at www.Physics2000.com. (The movie was previously available only on a $300 16-mm film.)
4.
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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Crossref
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5.
A negative muon decays into a negative electron and two neutrinos.
6.
On page 346 of Ref. 4 is a full-page graph of the muon lifetime data. From this data, we can check that the muon half-life is 1.5 μs. Starting with 568 muons, and dividing successively by 2, we expect that there should be 284, 142, 71, 35, and 17 muons remaining at the end of 1, 2, 3, 4, and 5 half-lives, respectively. These half-lives should occur at times of 1, 1.5, 3, 4.5, 6, and 7.5 μs. From the graph of Mt. Washington data, we find that there are 293, 143, 77, 35, and 11 muons remaining at these times, in rather good agreement with the prediction. A direct comparison for a 1.5 μs. half-life is 568, 284, 142, 71, 35, and 17 predicted. 568, 293, 143, 77, 35, and 11 observed. This count should make a good student assignment.
7.
Some texts and articles confuse the muon half-life with the muon mean life, which is 2.2 μs. A mean lifetime is when 1/e = 1/2.7, rather 1/2, of the particles remain. (e is Euler's number.)
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© 2011 American Association of Physics Teachers.
2011
American Association of Physics Teachers
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