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Fall 2009 ASTR 2030 Review for Th Sep 17 Midterm

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This midterm will test special relativity. This means Thorne Ch 1, and everything we went through on special relativity in class. Useful resources:

The midterm will be a 45 minute, closed-book test. There will be 20 multiple choice questions, each worth 1 point, plus two short answer questions, each worth 5 points, for a maximum possible 30 points.

Review Questions

  1. Electromagnetism. What role did electromagnetism play in leading up to the theory of special relativity? What are electromagnetic waves? Why did 19th century physicists believe that an aether must exist?

  2. History. What fundamental idea did Einstein have that led to the theory of special relativity? 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? What is an inertial frame?

  4. Speed. What does speed mean in special relativity? How does an observer measure speed?

  5. Velocities. What postulate of special relativity implies that velocities do not add? What aspect of space and time must be changed to allow velocities not to add?

  6. Paradoxes. What is the solution to most paradoxes in special relativity? Give some examples of apparent paradoxes in special relativity.

  7. Spacetime Diagram. What is a spacetime diagram? On a spacetime diagram, draw possible worldlines of an object. What angle relative to vertical must a worldline of an object follow on a spacetime diagram? Draw possible worldlines of light. What angle relative to vertical must a worldline of light follow on a spacetime diagram? 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?

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

  9. 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 (“now lines”) on a spacetime diagram. How do these lines change for observers with different velocities relative to each other?

  10. 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. Explain in words.

  11. 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. Explain in words.

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

  13. Relativistic travel. You go on a trip from Earth to a distant place (like the center of the Galaxy) at near the speed of light. Give an account of your experience. Describe the rates at which you see your own clock to tick, a clock on Earth behind you, and a clock on your destination ahead of you. Compare your perception to that of folk watching you back on Earth.

  14. 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.

  15. Redshift, blueshift. Explain what redshift and blueshift mean.

  16. 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 2009 Sep 10