Hi Ken,
"I found the Feynman reference -- it was a very similar example addressed in Wheeler/Feynman's 1949 paper (not the 1945 one). Check it out -- they conclude that all these paradoxes rely on an "all-or-nothing" sort of interaction, but once you allow continuous interactions (say, a glancing blow due to a slightly-misaligned trajectory through a CTC) there's always a resolution."
The Novikov Conjecture would not be necessary if Polchinski's paradox was not a reality, i.e., if there were no self-inconsistent CTCs in GR solns. But, there are such CTCs in GR and the only resolution of cases like Polchinski's paradox, besides pointing to their highly improbable nature, is that *something* will happen to prevent violations of the principle of non-contradiction. The Novikov Conjecture is an addendum to GR. Essentially, I'm trying to find out if your approach suggests an underlying physical mechanism that would prove Novikov's conjecture.
"Now this question I'm surprised to hear coming from a "Block World Kindred Spirit"... To me, one of the biggest advantages of the block universe framework is that it *is* a consistency principle, in and of itself! Paradoxes can't happen in a block universe, by definition."
That reality is a BW doesn't rule out the existence of self inconsistencies, it would just be a BW with self inconsistencies. How would we describe such a reality? We don't know because our brains are wired in accord with the principle of non-contradiction. As physicists we tacitly assume that reality doesn't contain such violations, otherwise physics fails. So, I'm with you in that belief and I'm trying to find out how GR needs to be modified.
"So GR doesn't need any new consistency principle as long as you don't impose so many boundary conditions that there's no solution, and QM wouldn't need one either if we re-build it along the lines I suggest in my essay. I would hope that adding a generic constraint on the allowed boundary conditions would naturally prevent overconstrained problems in classical GR (such as this one)."
I don't understand how self-inconsistent CTCs result from "overconstrained problems." A CTC is simply a curve on the spacetime manifold whose metric is given by some soln to Einstein's equations. If there were a problem with EEs being overly constrained in these cases, why is only one curve on the spacetime manifold affected?
"Well, everything's mysterious until you understand it... :-) They've done interference experiments with buckyballs, which are pretty darn big. Is the "force" that keeps those C60 molecules from hitting the dark fringes "mysterious" or not?"
Are you claiming that the "Bohm force," responsible for interference in the twin-slit experiment, provides the physical mechanism underwriting Novikov's Conjecture? In that case you've blurred an important distinction between screened-off particles and non-screened-off particles, e.g., macroscopic objects.
"Regardless, you wouldn't ever *feel* such a quantum effect; you would just see the end result. That's because if you are measuring one set of parameters (like a force), then Heisenberg says you're losing information about some other parameters, and in my approach it's always in the unknown parameters where the "mysterious" quantum effects would come into play. (After all, the parameters that you measure are imposed as a boundary condition on the system.)"
I still don't see how the uncertainty associated with boundary conditions for any particular trajectory would serve to *absolutely prevent* the instantiation of that trajectory. Again, that argument could be applied to ANY trajectory, so why does ANYTHING have a trajectory?
According to statistical mechanics, there is an exceedingly small probability that all the air molecules in my office might suddenly move to the other side of the room. I'm not worried about this occurrence because the probability is low, but that's not why there is no "problem." There is no "problem" because I can compute the consequences to me, the room and its other contents should that happen. The problem with self-inconsistent CTCs is that we can't compute their consequences. So, either the universe contains phenomena we can't analyze or it doesn't, in which case GR is to be corrected/amended. I'm just trying to figure out how you, via your approach, propose to amend it.
"For that last part of your question, it sounds like you're trying to back me into a corner where I have to choose between free will and the block universe. I doubt that such a corner exists, but if it did, I'd come down on the side of the block universe every time."
No, I'm not addressing the issue of free will. Again, I'm trying to find out if your approach suggests an underlying physical mechanism that would ultimately prove Novikov's conjecture.
Thanks very much for your response, Ken. I think we're almost done!
Mark
