A. Questions for Submission

7.1 Conventionality of Geometry

1. What does Reichenbach mean when he refers to a 'universal force'?
2. Why would the existence of such a force confound our attempts to measure the geometry of space?
3. General relativity says that spacetime is curved. Does the possibility of universal forces challenge this claim?

7.2 Time travel

1. What is a closed timelike curve? Give an example of a spacetime containing a closed timelike curve, and discuss the sense in which this describes a kind of time travel.
2. What is the grandfather paradox? Is it a problem for spacetimes with closed timelike curves?
3. Explain the notion of a 'global constraint' and how this might be used to avoid the Grandfather Paradox. Do you think it succeeds?

Optional Further Discussion

• In a universe with closed timelike curves, it is possible for a particle to (consistently) collide with its past self. Use the diagram below to illustrate how this is possible. Be sure to label the time and space axes.

(Hint: An ordinary collision between a moving particle (A) and a particle at rest (B) is drawn below.)