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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. What is one possible way that the three dimensions we observe could have been "stretched out"?

2. According to the standard model of the big bang, which of the following is true of the four fundamental forces during the first moments of the universe?

3. When the universe is at its smallest possible size, which other property is also at its maximum?

4. The discovery of the tearing of space-time came from cooperation between experts in physics and _____.

5. How many total dimensions are required by string theory?

Short Essay Questions

1. What is the string-coupling constant, and why is it important?

2. What is a virtual string pair, and how is it formed?

3. How is the shape of the Calabi-Yau space is determined?

4. How are strings affected by extra dimensions?

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

6. What is the major difference between the big bang with and without string theory?

7. What is the strong-weak duality?

8. Describe the state of the universe's expansion, including what its ultimate fate might be.

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

10. Describe the big bang according to string theory.

Essay Topics

Write an essay for ONE of the following topics:

Essay Topic 1

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 2

The Two-Slit Enigma

The two-slit experiment is so famous as to be ubiquitous in modern physics. It succinctly illustrates the wave-nature of particles and the very mysterious interference that these particles experience even when there are no other waves to interact with. Perform a short research project on the two-slit experiment, using the book as a starting point, and citing at least two other sources.

Part 1) Describe the history of the experiment, including the original motivation for performing it, and variations that have been performed since.

Part 2) Describe in detail the results of the experiment in its major variations. What are the implications of the experiment and some typical explanations for the results? Explain why these results are so important and unusual.

Part 3) Devise a version of the two-slit experiment that you would perform, given sufficient resources and time, either for scientific purposes, aesthetic interests, or simple curiosity. Be sure to describe the set-up and state what you expect the results to be.

Essay Topic 3

The Extra Dimensions

It turns out that string theory depends upon the existence of six extra dimensions. This is a seemingly impossible proposition, but it is in fact entirely reasonable for our universe to have extra dimensions of which we are not aware. This is a feature almost unique to string theory, and it has important implications.

Part 1) Describe the history of theories of extra dimensions, particularly the Kaluza-Klein theory. What important things did these theories achieve, and why were these theories abandoned? Why does string theory require these dimensions?

Part 2) Explain what is meant by extra dimensions. How does our world interface with these dimensions, and why can we not observe them in everyday life? Provide examples that illustrate how small dimensions work, and why they can go unnoticed.

Part 3) Why are extra dimensions important in the field of string theory? Do their number, size, and shape have any importance or are they arbitrary? How many dimensions does string theory predict, and is it possible for one or more dimensions to be an extra dimension of time?

(see the answer keys)

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