AST 309 (46575) Fall 2003
Quiz 3: Study List

Review Sessions

Review sessions have been scheduled for the following times and places: Tuesday, December 2nd and Wednesday, December 3rd from 5pm-6:30pm in ECJ 1.202.

Be sure to bring your calculator on the day of the quiz, as well as to the review session! You will not need your astrolabe.

Reminder

You are reminded to make handwritten notes to yourself on one side of an 8.5x11-inch piece of paper, which you may consult during the quiz. These notes will count 10% of your grade. The quiz questions will emphasize your ability to reason and think, not memorize isolated facts, and the notes are intended to reduce your reliance on rote memorization. Your notes must be signed and attached to your quiz when you hand it in.

Study Questions

• What are the basic assumptions of the theory of relativity? Explain how these basic assumptions result in the following phenomena for an observer A and an observer B who moves at a constant speed on a straight line relative to observer A: (1) Clocks that A carries with him and which A says are synchronized, are found by B to be desynchronized. (2) A and B have identical clocks, but A says that B's clock runs more slowly than A's, whereas B says that A's clock runs more slowly than B's. (3) A and B have identical meter sticks, but A says that B's meter stick is shorter than A's, whereas B says that A's meter stick is shorter than B's. How are the apparent paradoxes between A's and B's measurements resolved?
• Draw a diagram of a light-beam clock. Show that if the clock moves, it "ticks" slowly. If the clock moves at half the speed of light, how slowly does it tick? Demonstrate this in terms of the path of the light in the clock. Why can't the clock move faster than the speed of light?
• Explain the phenomenon of the aberration of starlight, in terms of relativity. Hint: Think of wavecrests falling flat on a runway, and consider how it appears from the point of view of the pilot of a spacecraft which is whizzing past in level flight.
• Draw a diagram of Epstein's Cosmic Speedometer (space-time diagram). Draw arrows on it representing an object at rest, an object moving at 1/2 the speed of light, and an object moving at the speed of light. Label the axes on the diagram, and show how the diagram can be used to measure (1) proper time, (2) coordinate time, (3) space. Define both coordinate time and proper time.
• Show how Epstein's space-time diagram illustrates the shrinking of moving objects and the fact that we will measure clocks on a moving object to be unsynchronized, even though to observers travelling with the object they are synchronized. Use the space-time diagram to solve problems in relativity such as the Barn-Door paradox.
• What is the Twin Paradox? Explain the Twin Paradox, using Epstein's space-time diagram. How is the paradox resolved? Use Epstein's space-time diagram to estimate the difference in ages between the two twins, given the velocity of the travelling twin and the distance of his trip.
• Show how the Epstein space-time diagram can be used to explain the Big Bang, and the fact that we see galaxies at great distances from us even though the matter that makes up the visible universe once was packed into a volume no bigger than a baseball.
• Show that the dynamical mass of a moving object must increase over its proper (rest) mass. If clocks on the moving object are running at half their normal speed, how much greater is the mass of the object than when it was at rest? Show that light has momentum (Hint: Think of comets and light sails). Show therefore that energy has mass.
• Light will fall in a gravitational field. Show how this fact implies that clocks in a gravitational field must run slowly. Show how this in turn leads to the conclusion that spacetime is curved in a gravitational field. Show how the motion of objects in a gravitational field can be explained in terms of the object "falling" along a geodesic in curved spacetime. Be sure to be able to explain what a geodesic is!
• Show that a gravitational field must distort both spacetime and spacespace, and how this leads to the conclusion that a light beam will be deflected twice as much if relativity is true than if only Newtonian gravity is taken into account. Explain how the distortion of spacespace affects the orbits of planets and the motion of a gyroscope in orbit around the Earth.
• If the Earth had a hole drilled straight through its center, would a bullet travel faster or slower through the hole than it would if the Earth were not there? What would happen if we substituted a light beam for the bullet? Explain both phenomena in terms of the curvature of spacetime (use a diagram).
• Sketch a space-time diagram of a black hole, and show that although it takes a finite amount of proper time for an object falling into the black hole to get to the event horizon, from the point of view of an external observer the same process takes an infinite amount of coordinate time.
• Explain how antimatter can be interpreted as ordinary matter travelling backwards in time.
• Explain how, in principle, a time machine might be built to enable something to travel (a) forwards in time and (b) backwards in time. What limitations and constraints might apply in each case?