Time loops and those superluminal neutrinos

[mitchell porter]

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" , 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.

 

[Demystifier]

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.

No, superluminal velocities cannot be used to create paradoxes in that way. See
http://xxx.lanl.gov/abs/gr-qc/0403121

 

[mitchell porter]

The paper that I linked (arxiv:1110.1162) does not involve a closed timelike curve, it involves a Feynman zigzag "sideways in time". The worldline of the neutrino emitted in Switzerland turns into an antineutrino and then into a neutrino again, with the inflection points corresponding to pair creation or pair annihilation. These pair events might be understood as arising from a scalar condensate with a nonzero VEV, but the paper doesn't address that detail.

Isn't your paper just assuming the existence of a vector field on the space-time manifold which is everywhere nonzero and nonsingular (the gradient of the entropy scalar), and then defining time in terms of this vector field? In effect, you just assume that space-time is globally time-orientable. Also, I don't see any argument against paradoxes being created by effects that are superluminal with respect to your "thermodynamic arrow of time". If physics is Lorentz invariant with respect to your "physical time" (distinct from the coordinate time with which you started), then "physical superluminality" should still lead to paradox, unless you have some extra factor, like nondeterminism.

edit: Assuming the existence of superluminal velocities, how does your approach avoid the sort of paradox illustrated in figure 5 http://www.theculture.org/rich/sharpblue/archives/000089.html"?

 

[qsa]

Mitchell,
do any of these so called superluminal theories predict a speed of JUST 1.000003 c or anywhere close. If not then be very carefull, anyway, the number itself sounds dodgy.

 

[mitchell porter]

qsa, I think no one on Earth predicted that neutrinos with an energy of between 15 and 45 GeV travel at just slightly over the speed of light, nor does that even resemble any pre-OPERA superluminal theory. But after the fact, people are trying to contrive models which explain these results, earlier superluminal neutrino observations from MINOS, and the "non-superluminal" neutrinos from Supernova SN1987A, and a few are claiming limited success in matching all that data. However, until arxiv:1110.1162 (Ahluwalia et al), none of these were models in which causal loops can be created. I had a prior interest in time-loop theories, as one possible explanation of quantum mechanics, so I'm seizing the moment to achieve conceptual progress on several fronts.

I agree that the results from OPERA do look exactly like a systematic error, but for now they are simply unexplained, and it should be very instructive to see how far one can get in a model that does not have Lorentz violation, but does have time loops.

 

[Demystifier]

Isn't your paper just assuming the existence of a vector field on the space-time manifold which is everywhere nonzero and nonsingular (the gradient of the entropy scalar), and then defining time in terms of this vector field?

No, time exists even without that vector field. But without that vector field, the time ARROW does not exist.

In effect, you just assume that space-time is globally time-orientable.

No, I don't. I only assume that entropy density is defined everywhere.

Also, I don't see any argument against paradoxes being created by effects that are superluminal with respect to your "thermodynamic arrow of time".

I don't even understand what does it mean to be "superluminal with respect to the thermodynamic arrow of time".

edit: Assuming the existence of superluminal velocities, how does your approach avoid the sort of paradox illustrated in figure 5 http://www.theculture.org/rich/sharpblue/archives/000089.html"?

That's the crucial question. And my answer is: At least one of the arrows points in the wrong direction, in the sense that the direction of the thermodynamic time arrow is actually the opposite one.

 

[mitchell porter]

I just want to say I haven't forgotten this discussion! But there's rather a lot to think about. :-)

 

[mitchell porter]

I should try to state plainly what the implications are if OPERA's effect is real and if four-dimensional physics is Lorentz invariant.

In the rest frame of the Earth, OPERA's results say that if you create a beam of mu-neutrinos at one location (Switzerland), you will detect a handful of tau-neutrinos further along the beam path (in Italy), with a timing that indicates they traveled there at about 1.00003 times the speed of light.

But in the rest frame of an observer moving extremely fast in the direction of the beam, OPERA's results say that the rate of spontaneous emission of tau-antineutrinos in Italy, now, is sensitive to whether there will be an apparatus capable of absorbing ultrarelativistic mu-antineutrinos in Switzerland, a very short time into the future.

edit: This might be modeled as a form of http://physics.stackexchange.com/questions/3357/what-is-time-teleportation/3463#3463".