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This test consists of 5 short answer questions, 10 short essay questions, and 1 (of 3) essay topics.

Short Answer Questions

1. Greene suggests that black holes may be elementary particles that have undergone _____.

2. Kaluza's theory suggested that electromagnetism was carried by ripples in _____.

3. About how long after the big bang were stars formed?

4. Which of the following is true regarding the tearing of space-time according to string theory?

5. There are many possible Calabi-Yau spaces, but only shapes with which of the following characteristics are considered real possibilities?

Short Essay Questions

1. Why are superparticles important to string theory, and how has research into these particles affected the field of string theory?

2. In the context of the big bang, what is symmetry breaking?

3. Describe the phenomenon of winding in string theory.

4. What is the origin of M-theory, and what are its basic characteristics?

5. Greene suggests that black holes are very similar to, and might in fact be, elementary particles. What evidence supports this suggestion?

6. Describe the history of space-time tears in physics.

7. What did Morrison and Greene discover together, and why is it important?

8. What is a wormhole, and how is it formed?

9. Describe the difficulties in studying the entropy of a black hole.

10. Are the extra-dimensions demanded by string theory, space or time dimensions? How are those dimensions experienced in everyday life?

Essay Topics

Write an essay for ONE of the following topics:

Essay Topic 1

Black Holes

Black holes are the most massive objects in our universe. They contain deep mysteries and relatively little is known about them. They are incredibly powerful, able to out-muscle light itself, piece the fabric of space-time, and perhaps even create new universes.

Part 1) Describe the history of our knowledge of black holes: How and why they were first theorized about, and how they were first discovered by observation.

Part 2) How is a black hole formed? Explain the dominant theories about the formation of black holes, being sure to address features such as the event horizon. Explain some of the more esoteric possibilities as well.

Part 3) Black holes have driven forward theory and discovery for a long time. Explain some of the ways that black holes have inspired scientists to push forward our knowledge of the universe.

Essay Topic 2

The Big Crunch

Due to the far-reaching space-warping effects of gravity, it turns out that there is a specific critical density to our universe that determines in what way the universe will end. This density is still largely unknown, although it appears that we are close to the critical density. Disturbingly, observations of the known universe have shown that visible matter makes up only about 23% of the necessary mass. The difference is made up by dark matter and dark energy.

Part 1) Describe how gravity shapes our universe at very large scales. How does the density of the universe determine its ultimate fate?

Part 2) One possible ending of the universe is that the density is too great, and the universe will collapse. Describe how this collapse could occur, paying particular attention to the conclusions of string theory.

Part 3) Another possibility is the endless expansion of the universe due to low density. Describe the way that this could occur, thinking critically about what it means for space to expand at an increasing rate.

Essay Topic 3

Accelerated Evidence

In this book, the author presents many thought problems to help the reader work through difficult concepts. The unintuitive concepts of special and general relativity receive particular attention. These theories fly in the face of observations made in everyday life, but at the speeds and scales that they deal with, they have been confirmed to be exactly correct. Furthermore, they form one of the cornerstones of modern physics. This essay deals with thought problems that illustrate the underlying principles of special and general relativity. The essay should include ample explanations and transitions so that it is cohesive and makes sense.

Part 1) Describe a number of novel thought problems that would demonstrate the principles of special relativity, that motion is relative, and that time and space warp for an object moving near the speed of light. Each thought problem should be robust enough that it requires multiple sentences to explain. Each problem should clearly demonstrate the principle in question, and explained fully, with a succinct conclusion.

Part 2) Imagine that a space traveler is locked inside a ship, and cannot use any senses or tools to observe anything outside of the room he is occupying. Propose a number of experiments that the traveler could perform to determine what the motion of the spacecraft is. Be sure to include a discussion of constant-velocity motion, accelerated motion, gravitational acceleration, and orbital (circular) motion.

Part 3) Repeat the analysis performed in part 1 for the case of general relativity. Demonstrate the equivalence between acceleration and gravity, the warping of space-time caused by massive objects, and the straight-line motion of objects through curved space.

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