# SECOND PAPER ASSIGNMENT

## 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.

### TOPIC #1

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.
### TOPIC #2

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.
### TOPIC #3

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.
### TOPIC #4

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.
### TOPIC #5

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'?