Einstein is most famous for his two theories of relativity. It is sometimes said that special relativity would have been discovered in a few years without Einstein, but if it were not for him, the world would still be waiting for general relativity. These two theories are critical to modern physics and are used in important applications every day.

Part 1) Describe the discovery of the theory of special relativity. What thoughts caused Einstein to first contemplate this theory, and how did it develop. Explain the underlying principles of special relativity.

Part 2) Repeat the above analysis for the theory of general relativity.

Part 3) Compare and contrast the discoveries of these two theories. Make an assessment of which has been more important historically. Describe succinctly the difference between these theories.

Part 4) Research and describe some of the ways that each of these theories affect technology and ongoing physics research.

Essay Topic 2

Black Holes Redux

String theory provides some tantalizing possibilities for explaining the nature of black holes. These incredibly powerful cosmic objects were part of the reason that string theory was created in the first place. Their incredible extremes have been the point that most other theories get off the train, but string theory is able to handle these problems deftly. Part 1) Why can string theory analyze black holes where other theories fail? Include a discussion of quantum mechanics, general relativity, and entropy as they relate to this subject.

Part 2) String theory predicts the possibility of dramatic tears in space-time called conifold transitions. Explain what these events are and how they relate to the formation and structure of black holes.

Part 3) Explain the theory that black holes and elementary particles are different phases of the same material. Explain what phase-transition is and how this concept relates to black holes. If true, what are the implications of this concept?

Essay Topic 3

The Calabi-Yau Space

The shape of the extra dimensions in our world turns out to be critical to the properties and physical laws that we observe every day. The particular shape of these spaces has been determined to be a Calabi-Yau shape, a class of exotic multi-dimensional shapes.

Part 1) Describe the importance of the shape of the extra dimensions. Why is this importance only relevant to string theory? What would the effects be if these shapes were different?

Part 2) Use descriptions from the book to explain the nature of Calabi-Yau spaces. What unusual characteristics do they have? What would it be like to move through such a space?

Part 3) Explain some of the work that has been done to relate the shape of the Calabi-Yau space to properties of particles in our universe. How is the shape of the Calabi-Yau space studied and improved? What are some shortcomings of this method?

(see the answer keys)

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