|HPS 0410||Einstein for Everyone||Spring 2008|
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For submission Monday January 14/ Tuesday January 15.
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. You have equipped your spaceship laboratory with the finest of instruments. You have a pure platinum yardstick, machined to be exactly one yard in length, and an atomic clock that ticks off the seconds with unimaginable accuracy. Your spaceship laboratory is set in motion at 99.5% of the speed of light with you inside, carefully observing what your rod and clock do. Special relativity tells us that your rod shrinks to 10% of its length and your clock runs ten times slower. You check to see if this is so. You know that the distance from your nose to the tip of your outstretched arm is about one yard; your yardstick still tells you it is a yard. You know your resting pulse rate is roughly one beat per second; your atomic clock agrees. Your pulse still beats at roughly one beat per second.
Why do these attempts to detect rod shrinking and clock slowing fail?
If they did not fail, why would your success at measuing rods shrinking and clocks slowing amount to a violation of the principle of relativity.
For discussion in the recitation.
A. 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.
B. 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.
C. We saw in the chapter 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.
D. 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.
E. Imagine you have a gun that can fire a particle at 100,000 miles per second. You are in a spaceship moving at 100,000 miles per second with respect to the earth. You point the gun in the direction of your motion and fire. Would the earthbound observer see the particle travel at 200,000=100,000+100,000 miles per second? Show that he could not since that would violate the principle of relativity, when that principle is combined with the light postulate.* How rapidly would you (the spaceship observer) judge the particle moving?
Recall: The light postulate states that all uniformly moving observers measure the same speed for light whatever may be the velocity of the body that emits the light.