The Elegant Universe: Superstrings, Hidden Dimensions, and the Quest For… Test | Mid-Book Test - Hard

Brian Greene
This set of Lesson Plans consists of approximately 185 pages of tests, essay questions, lessons, and other teaching materials.
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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. Black holes are dense and massive cosmological bodies. What unique distinction do they have?

2. Which of the following is not one of the four fundamental forces of the universe?

3. Which of the following is a correct statement, based on the theory of special relativity?

4. According to general relativity, all objects that have mass have what effect on space-time?

5. Which of the following was the first string theory?

Short Essay Questions

1. Referring to the experiment described in question Short Essay #6, what would the three observers see according to the theory of special relativity?

2. How many string theories are there and how did there come to be multiple theories?

3. List the four fundamental forces of the universe, their functions, and describe where and at what scales they are most commonly observed.

4. What is the relationship between light, electricity, and magnetism?

5. Describe the structure of an atom.

6. Describe a black hole, including some of its physical properties and methods by which it can be detected.

7. Describe the symmetry between the electromagnetism and the weak force that is predicted by quantum electroweak theory.

8. Describe some of the problems with uniting quantum mechanics and general relativity.

9. Three observers carry out an experiment. From the same starting point, they observe a beam of light move directly away from them. One observer stays at rest at the starting point. One observer "chases" the beam at half the speed of light. The last observer chases the beam at exactly the speed of light. Describe what these observers would note about the beam of light according to Newtonian (pre-relativity) physics and thinking.

10. What are super-partners?

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 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?

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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