DUE Friday, May 8, 1998 - 1:00 p.m.

(hand in to Dr. Duncan's mailbox in OH 104)

Write a 4-6 page paper on one of the following two topics. Your paper should conform to the typographical, style and content formats as spelled out on the syllabus and handouts. Your paper should be typed, double spaced with page numbers and references, where needed. Use the scientific notation for citation references, i.e., put the references with page numbers in the body of the text (Bradie, 1992, 3) and then collect the references at the end of the paper. Use footnotes only for expository material that comments on the text but would interrupt the flow of the argument if it were incorporated into the text.

You should give your paper an appropriate title and indicate, in parentheses, which topic you are writing on. There should, of course, be a separate title page.

Remember: Your paper should aim to be a "thing of beauty and a joy forever." Organization is as crucial as determining what to say and . . . what not to say! Remember that your paper should contain both expository and critical remarks. You should defend your views with reasons.


The concept of time has itself evolved, as this course has illustrated. Given that the Newtonian concept of universal time has been challenged by the special theory of relativity, write a paper which traces this change from the late 19th century up to 1910. Include in your discussion and analysis a coherent treatment of the basic ideas of Newtonian universal time and the proper time of Einstein's special relativity. Be sure to discuss how the elapsed time between events is observer dependent in Einstein's theory of special relativity and how Minkowski took the ideas laid down by the physicist Einstein and crafted a new spatio-temporal structure.


In the context of the special theory and then in the general theory of relativity discuss the possibilities for time travel. Are there spacetimes in Einstein's theory of gravity which allow time travel? If so, give an example and discuss its salient features.


Describe the essential ideas of the famous Twin Paradox of relativity theory. In this paradox there are two twins, one of which leaves the earth and travels on a spaceship at speeds approaching the speed of light, turns around, and returns to the earth. When back together, the twins discover that the one which made the trip is much younger than the stay-at-home twin. You are to give a complete conceptual treatment of this paradox, using the special theory of relativity to determine just how much the two disagree about their respective ages at the end of the trip back on earth. What is the resolution of this paradox? Is the special theory adequate to explain the paradox? Defend your proposed solution with a clear treatment, including spacetime diagrams and the length contraction and time dilation formulae as needed.


Einstein's theory of gravitation predicts that when a sufficiently massive star collapses, it can undergo a catastrophic collapse and form a black hole. What are some current candidates of [binary] star systems which may be black holes. Give a qualitative discussion of the evidence in favor of a black hole in these systems.


If black holes exist, then nature has chosen to provide spacetime some points which have singularities. If the cosmic censorship conjecture is valid, these singularities reside inside event horizons and thus are not directly visible to observers external to the event horizon. If singularities exist, what are the implications for the theories of spacetime structure we have explored in this course? Discuss some implications for nature if the cosmic censorship conjecture is not valid, so that the singularities are visible. What would you expect to find if you drove your spaceship to a point nearby such a 'naked singularity'?