Spring 2007 ASTR 3740 Homepage

Spring 2007 ASTR 3740 Midterm Review

The midterm will test everything covered during the semester so far.

The midterm will be a 50 minute test.

For 2 point questions, your answer should consist of one or two clear, grammatically correct sentences. Answers to questions with more points should be proportionately longer.

You get -1 point for each time you misspell Schwarzschild.

Review Questions

1. Electromagnetism. What role did electromagnetism play in leading up to the Theory of Special Relativity? What are electromagnetic waves?

2. History. Contrast the contributions of Young, Maxwell, Michelson & Morley, Fitzgerald, Lorentz, Poincaré, and Einstein to the historical development of the Theory of Special Relativity.

3. Postulates of Special Relativity. What are the postulates of special relativity? What is an inertial frame? Which postulate or postulates distinguish special relativity from its predecessor, classical Galilean space and time?

4. Spacetime Diagram. Make sure you thoroughly understand spacetime diagrams. Simultaneity, lightcone. Review time dilation, Lorentz contraction, the twin paradox.

5. Simultaneity. What does it mean in special relativity for two events to be simultaneous? Describe a practical method by which simultaneity can be defined in special relativity. Draw lines of simultaneity on a spacetime diagram. How do these lines change for observers with different velocities relative to each other?

6. Lorentz Transformation. What is a Lorentz transformation? What happens to a spacetime diagram when it is subjected to a Lorentz transformation?

7. Four Vectors. Make sure you thoroughly understand four vectors. What is a four vector? How does it transform under Lorentz transformations? Give some examples of four vectors.

8. Time Dilation. On a spacetime diagram, show how two people moving relative to each other can both consider each other's clock to run slow.

9. Lorentz Contraction. On a spacetime diagram, show how two people moving relative to each other can both consider each other's ruler to be contracted.

10. Energy Momentum. Why are energy and momentum described by a 4-vector in special relativity? How does E = m c2 emerge from the special relativistic description of energy? How is the invariant spacetime length of the energy-momentum 4-vector related to rest mass?

11. Twin paradox. What is the twin paradox? Explain the twin paradox with the help of a spacetime diagram.

12. The Spacetime Wheel. What is the invariant spacetime distance between two events on a spacetime diagram? How does the invariant spacetime distance change under a Lorentz transformation? How does the spacetime distance differ from the ordinary distance between two points in 3-dimensional space? What is proper time? What is proper distance? How are proper time and proper distance related to the invariant spacetime distance? When an ordinary wheel rotates, the angle of the wheel about its axis changes. When the spacetime wheel rotates, what is happening?

13. What things actually look like at relativistic speeds. Why are you not normally aware of relativistic effects? If you move through a scene at relativistic speeds, do you see objects whizzing by simply Lorentz-contracted and time-dilated? Answer: No, the because of the light travel time. Explain how light travel time affects appearances. Give an account of the rules of relativistic perspective: draw the scene on a celestial sphere, stretch the celestial sphere into a celestial ellipsoid, and place the observer at a focus of the celestial ellipsoid. Give an account of the 4 relativistic effects: (a) aberration; (b) redshifting and blueshifting; (c) dimming and brightening; (d) the apparent rate at which clocks tick.

14. Superluminal motion. Blobs are seen to emerge from the nucleus of the quasar 3C273 at about 8 times the speed of light. Does this contradict special relativity? Explain. The blobs are thought to be part of a jet powered by a black hole at the center of the galaxy housing the quasars, and that there is a second jet emerging in the exact opposite direction from the jet that we see. Why do we not see the second jet?

Updated 2007 Feb 14