I believe there needs to be an intelligent discussion somewhere about the possibility that theories with time loops can be rendered consistent by nondeterministic (probabilistic) physics, and specifically about the possibility that genuinely spacelike neutrino effects - which, let us recall, were earlier claimed by MINOS, as well as more recently by OPERA - can find a place in such a framework. By "genuinely spacelike effects", I mean that I am not talking about theories of superluminal neutrinos in which light travels slower than the neutrino because (e.g.) it's stuck on a braneworld, whereas neutrinos travel in the off-brane hyperspace and saturate the true relativistic speed limit. Also, I'm not talking about theories in which there is an absolute time and Lorentz symmetry is emergent. I wanted to have this discussion in the relativity forum last week, but ran up against the policy in that forum that all discussion of the OPERA experiment shall be confined to a https://www.physicsforums.com/showthread.php?t=532620". So I'll try here. I want to start by pointing out that there is a huge existing physics literature on tachyons and closed timelike curves. It's not as if these are ideas without a history. There has even been at least one paper, years ago, on the interaction of neutrinos with closed timelike curves in the extra dimensions. There is also a long history of attempts to derive quantum mechanics itself from the existence of closed timelike curves or from future-to-past causation, that should also be taken into account in such a discussion. It may be that the nondeterminism of quantum mechanics allows time loop paradoxes to be avoided, but it may also be that the peculiar nature of quantum probability somehow arises from the existence of closed timelike curves. This isn't just a whimsical notion of mine; there's a lot of prior thinking on that subject. Last week, I guessed that people would start seriously thinking about time loops, in the context of OPERA, when models began to be made in which neutrinos are genuine tachyons - again, by genuine, I mean that they move in a genuinely spacelike way. However, as it turns out, the first paper (that I saw) in which OPERA's observations are explained by a genuinely spacelike effect, doesn't employ tachyons at all. The paper is http://arxiv.org/abs/1110.1162" [Broken], and the concept is that there is an interaction with spontaneous neutrino-antineutrino pair creation. That is, the neutrino leaves Switzerland; a pair creation has occurred somewhere in between Switzerland and Italy; the antineutrino annihilates with the Swiss neutrino; and it's the spontaneously created neutrino which arrives in Italy. It's an extremely interesting idea, a very obvious one once you hear it, and I think the quantum gravity fans of this forum should especially ponder the resemblance of this account to Hawking radiation, another effect in which half of a virtual pair manages to escape and be seen. But if this is what OPERA is detecting, and if relativity still holds, then can't we create paradoxes, by having machines in relative motion beaming neutrinos at each other, machines that are programmed to respond to each other in a paradoxical way? Machine 1 sends its beam only if it received a beam from machine 2, and machine 2 doesn't send its beam only if it received a beam from machine 1, that sort of thing. However, this is where nondeterminism can save the day. If this is not a rigidly deterministic effect, then we can create such a setup and what we observe will simply be one of the internally consistent space-time histories. For example, machine 1 detects neutrinos coming, not from machine 2, but from the vacuum, and it sends its message, but its own beam is too weak to trigger machine 2. It seems that an improbable-sounding outcome like this is the most likely consistent resolution to the paradoxical setup I described, and I have to hope that in the near future someone will start to develop theoretical frameworks in which one can actually calculate probabilities for different globally consistent resolutions. CERN is having a special seminar this Friday to discuss the theoretical options if OPERA's results are for real. It will be interesting to see if they consider this option.