HPS 0410 Einstein for Everyone Spring 2007

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Assignment 1. Principle of Relativity

For submission Tuesday, January 9/ Wednesday January 10.

According to the principle of relativity, no experiment conducted within a laboratory can reveal its uniform (=inertial) motion; all that can be revealed is the uniform motion of the laboratory with respect to other bodies.

1. Special relativity tells us that moving rods shrink and moving clocks slow down. The page shows you how to calculate how big these effects are. Two rows for 10,000 mi/sec and 93,000 mi/sec have been left blank. Fill in the blanks.

2. Imagine you are in a moving laboratory. Consider the following experiment : you check to see if your rods have shrunk and clocks slowed. Will this experiment reveal your motion and violate the principle of relativity? Explain.

3. You are in a uniformly moving spaceship that enters an asteroid field. You observe the asteroids of the field rushing past your window (and fear a collision with one). Does this observation constitute an experiment that violates the principle of relativity? Explain.

4. You are inside an airplane drinking coffee. The airplane strikes turbulent air. Your stomach falls and the coffee flies out of the cup. You have no doubt now that you are moving. Does this observation constitute an experiment that violates the principle of relativity? Explain.

For discussion in the recitation.

A. We saw in the lecture, Special relativity: the basics, that a light clock moving at 99.5%c slows by a factor of 10. We also know from computing "beta" factors that a clock moving at 86.6%c slows by a factor of 2. Convince yourself of this second result by considering a light clock which moves transverse to its length at 86.6%c.

B. Use the principle of relativity and the result of A to show that any clock moving at 86.6%c slows by a factor of 2.