Let’s see how much you’ve picked up with these experiments and the reading – answer as best as you can. (No peeking at the answers until you’re done!) Just relax and see what jumps to mind when you read the question. You can also print these out and jot down your answers in your science notebook.
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1. What’s wrong with the statement “moving clocks run slow”? Can you find this or a similar “relativistically incorrect” statement in a book on relativity?
2. Suppose two triplets leave Earth at the same time and undertake roundtrip space journeys of identical length and at the same speed but in opposite directions. When they return, will they be the same age or will one be older? How will their ages compare with their third sibling, who stayed at home on Earth?
3. In 1999, scientists discovered a planetary system orbiting a star 44 light-years from Earth. How far into the future could you travel by taking a high-speed trip to this star and returning immediately back to Earth? Under what conditions would you achieve this maximum future travel? How long would you judge the trip to take?
4. Suppose the twin in the spaceship traveled at 0.6c instead of 0.8c. By how much would the twins’ ages differ when the traveling twin returns to Earth?
5. A famous “paradox” of relativity is the following: A high-speed runner carries a 10-foot-long pole toward a barn that is 10 feet long and has doors open at both ends. The runner is going so fast that, from the point of view of the farmer who owns the barn, the pole is only 5 feet long. Clearly, the farmer can close both barn doors and trap the runner in the barn. But to the runner, the pole is 10 feet long and the barn, rushing toward the runner, is only 5 feet long. So clearly the runner can’t be in the barn with both doors closed. Can you resolve the paradox, using the fact that events simultaneous in one reference frame aren’t simultaneous in another? (By the way, the speed required here is 0.866c.)
6. Right now it’s “the present,” but is it “the present” everywhere? Explain your answer.
7. What’s wrong with the definition “the past consists of those events that have already happened”?
8. You throw a bunch of subatomic particles into a closed box, the walls of which block the passage of matter but not energy. Must the number of particles in the box remain the same? Explain.
9. You drop a large rock and a small rock. Because of its larger mass, the gravitational force on the larger rock is greater. Why doesn’t the larger rock fall with greater acceleration?
10. An airplane flying from San Francisco to Tokyo first heads north toward the coast of Alaska. Why? How is this analogous to what happens in general relativity’s description of gravity?
11. In special relativity, we stressed that time dilation is reciprocal: When we’re moving relative to each other, I see your clock running slow, and you see mine running slow. Now we have gravitational time dilation in general relativity: If you’re closer to Earth or another gravitating body than I am, I see your clock running slow. Do you expect this effect to be reciprocal too, or will you see my clock running fast?
12. Gravity seems a pretty formidable force if you’re trying to lift a heavy object or scale a cliff. In what sense, though, is gravity on Earth (and indeed throughout our solar system) weak?
13. If the Earth suddenly shrank to become a black hole, with no change in mass, what would happen to the moon in its circular orbit?
14. If you were falling into a black hole and looked at your watch, would you notice time “slowing down”? Justify your answer using basic principles of relativity.
15. You are on a jet flying 600 mph through calm air. You open a bag of peanuts while the slight attendant pours your tea into a cup on your tray. Why do you suppose that you don’t have to take into account the jet’s motion when the tea and peanuts travel at 600 mph?
16. Many people think astronauts in space are weightless because there’s no gravity in space. How would Newton argue against this?
17. Maxwell’s equations predict the existence of EM waves (light) going at speed c… but with respect to what? Relative to what?
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