6. A Riddle Solved

I really should have read Deutsch's work on Closed Time-like Curves in more detail. The solution to the problem of the billiard ball interfering with itself relies, like a photon interfering with itself, on a branching universe. There is a possible universe in which the introduction of the ball to the CTC is frustrated. The actual universe is a superposition of this state and the state where it is not. Strangely, as soon as I worked this out I found it easy to carry out the experiment without being myself frustrated by a sudden lack of volition. Once again our old friend 'maximum entropy' is at work. \[Tr_{CTC}[U(\rho _{}A\otimes \rho _{CTC})U]\]