1. Principle of Relativity

For submission in Canvas
Canvas question may have different formats.

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. This 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 measuring rods shrinking and clocks slowing amount to a violation of the principle of relativity.

3. Two spaceships pass a planet, moving in opposite directions. A planet observer judges each to be moving at 100,000 miles per second. An observer on one of the spaceships measures the speed of the other spaceship.

spaceships

(a) According to classical physics, what speed will that spaceship observer measure for the other spaceship? Is this speed faster than light?

(b) According to relativity theory, what speed will that spaceship observer measure for the other spaceship? Is this speed faster than light?

A. What is inertial motion? An inertial observer? Accelerated motion? Absolute motion? Relative motion? A light clock?

B. 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.

C. 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.

D. It follows from the principle of relativity and the light postulate that a light clock slows when set in motion. If the light clock uses rods aligned with the direction of motion, it also follows that they shrink in length. But isn't a light clock an odd sort of clock that no one really uses? Why should conclusions about fanciful light clocks also hold for ordinary, real clocks? (Hint: What might be possible if those same conclusions did not hold for ordinary, real clocks?)

E. The relativistic slowing of clocks and shrinking of rods is invisible to observers moving with the clocks and the rods. How can we observe these effects?

F. Imagine that 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 an earthbound observer judge the particle to travel at 200,000=100,000+100,000 miles per second? Show that the earthbound observer 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 to be moving?

G. The arguments we have investigated show that relativity theory prohibits us accelerating an object past the speed of light. Do any of them rule out objects that have always been traveling faster than light (or, possibly, were created initially already moving faster than light)?

Assignment 1. Principle of Relativity