Mark,
Let me first construct the background for the argument in my paper.
Over time there were a bit of back and forth arguments between the supporters and the opponents of time travel:
1. Friedman, Novikov, Thorn, and others considered the idea.
2. Polchinski countered with an inconsistent self-collision of a billiard ball for traversable wormholes.
3. Friedman et al. considered glancing collisions to overcome this objection.
4. Rama and Sen discussed collisions of 2 objects of different mass which rendered the glancing collision idea useless because the smaller mass can bounce off the larger one.
5. Krasnikov countered Rama and Sen by eliminating the initial conditions leading to the inconsistent interaction and considering self-consistent CTC "ghost" objects.
6. My paper where the billiard ball breaks in a consistent self-interaction. (who said we should use billiard balls and not eggs for example?)
Now your argument corresponds to item 2, the Polchinski paradox. You say: "Now it may well be the case that this ball is too small to affect the geometry of the CTC, but nonetheless, it must be represented in the SET." This is OK, but the typical counter-argument is that the self-collision can occur far away from the mouths of the traversable wormhole where general relativity effects can be negligible.
Then you state: "However, in this case, we see that no SET can be constructed for the ball moving along the CTC, thus we do not have a solution of Einstein's equations. So the "paradoxical question" is, what WILL happen when I roll the ball along this trajectory? And the answer is, we don't know because GR is the only theory we have that tells us about the curvature of spacetime and it doesn't provide a solution for that situation."
I am not sure this is true. I recall seeing some time ago a Phys Rev Lett paper by Matt Visser showing that you only need arbitrary small amounts of negative energy to create a traversable wormhole with the emphasis on traversable. Now while the wormhole solution is an exact solution, the GR equations are local and one can do for example a computer simulation of what would happen if a billiard ball would enter a wormhole and therefore I do not see any conceptual objection about a solution which is not in a closed mathematical form.
I am not sure from your posting if you are for or against time travel. The need for infinite forces in my argument against time travel arise only in the chain of the arguments 1 to 6 above and the whole sequence is a silly tit for tat series of gedanken experiments. From a more realistic perspective, simply the energy conditions are enough to kill any time travel scenario. From a mathematical physics perspective, the Kay-Radzikowski-Wald result does the trick. In general any argument involving QM ends in the need for a complete quantum gravity theory which proponents of time travel celebrate as the lack of a definite disproof of a CTC space. On the classical side under mild approximations far away from the mouths of the wormhole, I think that the argument is settled unless someone will find a clever counter argument to my paper.
About the first principle in the essay, please ask your questions, I will gladly discuss it.
Thanks,
Florin
