Experiment 7 Tests of Special Relativity - Three Movies

Discussion:

We have seen in experiments 4 and 6 a test of one of the predictions of special relativity: the relativistic expression for energy used for the electron energy in the derivation of the shift in energy of Compton scattered photons. Other tests of special relativity usually require extensive apparatus and considerable time. The work today should be considered as three demonstration experiments, each taking about a half hour. Two of these are outside the practicality of an undergraduate lab. The third is relatively trivial and could easily be performed in our laboratory, but probably not in a half hour.

The first film is a direct demonstration of time dilation and illustrates beautifully that time intervals are measured dif- ferently in systems that are in relative motion. The second film is a direct demonstration of the failure of the classical expression for kinetic energy at high velocities. These exper- iments are described in handouts you will be given and should be read carefully so you are prepared to observe the techniques and results asked for below. The third film concerns the conversion of mass to energy in positron annihilation. Several properties of this reaction are illustrated.

Procedure:

Observe each film and take notes of the various techniques used and all data that is presented. Record the various pieces of equipment used. Actually, the opportunity to observe other laboratory settings and other equipment (most of which predates the equipment you have used and will use in our laboratory) is one of several benefits to be derived from these films. Take advantage of it. In addition, take enough notes that a descrip- tive narrative of some 200 words can be written on each film.

Report:

As a minimum your report should contain the following:
  1. An abstract of about 100 words putting forth the main points of the experiments. Abstracts are self contained accounts of experiments. They tell what was done and what was found. For examples of the style to be used, refer to any physics journal. In particular, see copies of The American Journal of Physics.
  2. Follow the abstract with the descriptive narratives mentioned above.
  3. For each of the films, write a critique in which you answer questions such as the following: To what extent is the result proved? How could the point be made more strongly? What could be done to improve the precision of the result? What points could be more clearly made?
  4. Do the following calculations in relation to the individual experiments.

  1. Time dilation:

    Using the given

    = 0.9952 (average),

    find the expected time dilation. Give a clear statement of exactly what times are involved and to which frames they apply.

  2. Ultimate speed:

    Perform the calculations and reproduce the graphs of v² versus E shown in the film for both the Newtonian and relativistic cases.

  3. Positron annihilation:

    The statement is made in the film that a single photon cannot be produced. Prove this statement.

If you choose, these points and calculations can be made integral parts of your narrative.

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