Fall 2003 ASTR 2030 Homepage

Fall 2003 ASTR 2030 Midterm Review

The midterm will test everything covered during the semester so far. This means the Prologue and Chapters 1 to 3 of Thorne, plus the parts of the Special Relativity and Black Hole websites that we went through in class.

The midterm a 75 minute test. Do 8 of questions 1 to 10 (2 points each) and 4 of questions 11 to 15 (6 points each). The maximum score is 40 points.

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 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? Which postulate or postulates distinguish special relativity from its predecessor, classical Galilean space and time?

4. Spacetime Diagram. What is a spacetime diagram? On a spacetime diagram, draw possible worldlines of an object. Draw possible worldlines of light. What is the lightcone, and why is it so-called? Draw a line which is neither a worldline of an object nor a wordline of light; what do such lines represent?

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. 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.

8. 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.

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

10. 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?

11. 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.

12. 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?

13. No hair theorem. What does the "no-hair" theorem of black holes state?

14. River model of black holes. Explain to a friend the river model of black holes. At what speed does the river fall? What happens when the river exceeds the speed of light? If nothing can move faster than light, how can the river move faster than light?

15. You approach a Black Hole. Explain how you can see multiple images of the same object when you approach a black hole. What is the difference between a stable and an unstable orbit? What is the photon sphere? See Approaching the Black Hole.

16. You fall into a Black Hole. Give an account of what you experience if you fall into a black hole. Do tides rip you apart before or after you pass the event horizon? Do you see the entire past or future of the Universe pass by? See Falling to the Singularity of the Black Hole. Explain what you experience using the river model of black holes.

17. You watch a friend fall into a Black Hole. Describe what you see. See Orbiting the Black Hole. Explain what you see using the river model of black holes. In particular, explain the redshifting and freezing at the horizon. If nothing can escape from a black hole, how can its gravity escape?

18. Principle of Equivalence. What is the Principle of Equivalence? From the Principle of Equivalence deduce: (a) the existence of gravitational redshift; (b) that gravity must bend the path of light; (c) that spacetime is curved.

19. Schwarzschild geometry. How do you spell Schwarzschild? What does the Schwarzschild geometry represent? What is the Schwarzschild radius? What is an embedding diagram? Give an account of the Schwarzschild geometry.

Updated 2003 Sep 29