Can Neutrinos Kill Their Own Grandfathers?

Building in part on my talk at the time conference, Scott Aaronson has a blog post about entropy and complexity that you should go read right now. It’s similar to one I’ve been contemplating myself, but more clever and original.

Back yet? Scott did foolishly at the end of the post mention the faster-than-light neutrino business. Which of course led to questions, in response to one of which he commented thusly:

Closed timelike curves seem to me to be a different order of strangeness from anything thus far discovered in physics—like maybe 1000 times stranger than relativity, QM, virtual particles, and black holes put together. And I don’t understand how one could have tachyonic neutrinos without getting CTCs as well—would anyone who accepts that possibility be kind enough to explain it to me?

The problem Scott is alluding to is that, in relativity, it’s the speed-of-light barrier that prevents particles (or anything) from zipping around and meeting themselves in the past — a closed loop in spacetime. On a diagram in which time stretches vertically and space horizontally, the possible paths of light from any event define light cones, and physical particles have to stay inside these light cones. “Spacelike” trajectories that leave the light cones simply aren’t allowed in the conventional way of doing things.

What you don’t see in this spacetime diagram is a slice representing “the universe at one fixed time,” because that kind of thing is completely observer-dependent in relativity. In particular, if you could move on a spacelike trajectory, there would be observers who would insist that you are traveling backwards in time. Once you can go faster than light, in other words, you can go back in time and meet yourself in the past. This is Scott’s reason for skepticism about the faster-than-light neutrinos: if you open that door even just a crack, all hell breaks loose.

But rest easy! It doesn’t necessarily follow. Theorists are more than ingenious enough to come up with ways to allow particles to move faster than light without letting them travel along closed curves through spacetime. One minor technical note: if some particle moves faster than light, it’s not “closed timelike curves” that we should be worried about, it’s “closed spacelike curves on which physical particles move.”

But we shouldn’t necessarily even worry about that. The usual argument that faster than light implies the ability to travel on a closed loop assumes Lorentz invariance; but if we discover a true FTL particle, your first guess should be that Lorentz invariance is broken. (Not your only possible guess, but a reasonable one.) Consider, for example, the existence of a heretofore unobserved fluid pervading the universe with a well-defined rest frame, that neutrinos interact with but photons do not. Or a vector field with similar properties. There are various ways we could imagine some background that actually picks out a preferred frame of reference, violating Lorentz invariance spontaneously.

If that’s true, the argument that FTL implies closed loops through spacetime no longer works. Even if neutrinos are able to sneak outside light cones, there may nevertheless be “neutrino cones” to which they are still confined. These neutrino cones could be a little bit broader than ordinary light cones, but they could still define a fixed notion of “going forward in time” that even neutrinos couldn’t violate.

There’s a nice (although technical) discussion of this in a short paper by Robert Geroch. Read Section 2 for the math, Section 3 for the words. From the discussion:

In short, the causal cones of special relativity, from this perspective, have no special place over and above the cones of any other system. This is democracy of causal cones with a vengeance. This, of course, is not the traditional view. That view — that the special relativity causal cones have a preferred role in physics — arises, I suspect, from the fact that a number of other systems — electromagnetism, the spin-s fields, etc — employ precisely those same cones as their own. And, indeed, it may be the case that the physical world is organized around such a commonality of cones. On the other hand, it is entirely possible that there exist any number of other systems — not yet observed (or maybe they have been!) — that employ quite different sets of causal cones. And the cones of these “other systems” could very well lie outside the null cones of special relativity, i.e., these systems could very well manifest superluminal signals. None of this would contradict our fundamental ideas about how physics is structured: An initial-value formulation, causal cones governing signals, etc.

The odds are still long against the OPERA result being right at face value. But even if it’s right, it doesn’t immediately imply that neutrinos are time-travelers.

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106 Responses to Can Neutrinos Kill Their Own Grandfathers?

  1. Bee says:

    The problem is that the ‘other cones’ are not invariant under Lorentz-transformations. You’d need a different transformation for each, which wrecks your notion of how a point transforms. (Been there, done that.) That’s the same problem you have in DSR.

    In any case, to maybe address Scott’s problem, note the following: The worldline of a tachyon (draw it) has no direction. If you boost it and it drops in the lower half of the Minkowski plane, there’s no sense in saying it goes backwards in time. You could equally well say it goes forwards in time, just into the other direction. There is no problem with that kind of propagation as long as you have a consistent time evolution. The problem with the grandfather comes along only if you add an arrow of time. It’s the arrow of time that necessarily has to single out a forward direction. That then however will also tell you which way the tachyon moves ‘forward.’

  2. Neal J. King says:

    Viewpoint from a related angle:

  3. Ellipsis says:

    however, as Bee says, we know that neutrinos can interact (weakly) with other particles confined to normal light cones. So you still end up with problems that are essentially analogous to Einstein’s thought experiment showing that energetic photons must be affected by gravity: i.e. you send a neutrino off from Earth at its faster than light speed, then somewhere around alpha centauri or wherever it interacts weakly and a photon is generated, and that photon flies back to Earth, interacts electromagnetically, and your poor grandfather pays the price. so it takes more than just separating the fields to preserve causality — one would need to introduce time delays in interactions, and all sorts of other ad hoc things. not worth it for an undoubtedly erroneous experimental result!

  4. Jim Harrison says:

    As I understand it, the theory that the universe will end in a big snap predicts that c will come to differ between photons of more or less energy in the run up to the conclusion. Does the possibility that certain neutrinos travel faster than light have any conceivable connection with this idea?

  5. Fair enough that a neutrino is not a large mass object, let alone a person, but I would be careful. When a paradigm shift in physics occurs it often extends beyond current expectations. As a material scientist we saw this with the application of Quantum tunneling, first for semiconductors and then for polymers. What was small and experimentally proven , had large scale implications. We even see it for entanglement. It was first just electrons and photons et al. that could be entangled, which was big enough news in itself. Everyone assumed that it was a fundamental effect of the tiny however, which turned out not to be the case. We now entangle things as large as fullerenes. If the speed of light is not the limitation constant for anything, it is very possible it is not neutrino specific. In addition to that, while a person may not be able to travel to the past via this potential discovery, it is not unreasonable to think that we can carry information at this rate through an almost binary process. Thousands of neutrinos with one spin or another. Information to the past is still pretty important, and could result in the grandpa killing paradox being a real one.

  6. Ellipsis says:

    on second thought, I’m not sure if my above comment is so simple. I should learn my lesson — an experimentalist should think twice before challenging a theorist on theory. anyway, my comment above can be ignored.

  7. Jay Fox says:

    I’m having a hard time understanding why this is such a controversy. We are talking about a tiny amount of speed over the speed of light, which itself has been shown to vary under certain conditions.

    Einstein posited that as speed increases, so does mass (or energy). So how much does a photon weigh? Could it be that “light speed” is the fastest that something with the mass of a photon can travel, but something weighing less than that might go a bit faster?

    It would seem to me that gravitational lensing of light from distant galaxies implies some mass to those photons. Otherwise, what would the gravity be acting on?

    Do we have the ability to see if neutrinos are similarly steered by gravity? Is the effect the same, or is it slightly different?

    We know that photons carry some miniscule kind of weight, or a solar sail (shouldn’t that be a photon sail?) wouldn’t work. Still, a sail must be massive since each photon carries so little (weight/mass/energy). Neutrinos, being smaller, lighter, less massive, go right through the sail without even slowing down, presumably.

    We are not talking about speeds significantly greater than light speed, just something barely measurable. If you take mass into account, it seems to me that one should EXPECT higher speeds of matter that is lighter than a photon. Not huge increases, but something. None of this should prompt ideas of grandfather paradoxes, as getting to the speeds necessary would require shedding most of the mass.

    It is interesting to note that they had to do tests over a pretty big distance to find this anomaly. Even then, the time difference is miniscule. Certainly not enough to advantage traders, even if we could somehow devise communication methods using these particles. We’d first have to find a way to interact with them. Just detecting them seems to be hard enough.

  8. Jesse M. says:

    @Jay Fox:
    I’m having a hard time understanding why this is such a controversy. We are talking about a tiny amount of speed over the speed of light, which itself has been shown to vary under certain conditions.

    If all laws of physics work the same in the different inertial reference frames given by the Lorentz transformation, then any faster-than-light signalling, no matter how small, can be used to send signals backwards in time. If A is the event of the signal being sent and B is the event of the signal being received, such that the signal would need to travel just a fraction faster than light to get from A to B, then it is always possible to find a different frame where A and B are simultaneous (the signal is sent at exactly the same time it’s received, even if the two locations are light-years apart) and also frames where B occurred before A. This is a technical consequence of something called the relativity of simultaneity in SR. And if the laws of physics work the same way in every frame, then if it’s possible in one frame to have a signal that received at the exact moment it’s sent, then this must be possible in every frame; this leads to the possibility that if two slower-than-light observers (call them Alice and Bob) are moving apart at slower-than-light speeds, then Alice can send a signal to Bob which is instantaneous in her frame but backwards in time in his, and Bob can send a reply to Alice which is instantaneous in his frame but backwards in time in hers, with the net result that she receives the reply before she sent the original signal! This is the “tachyonic antitelephone” Count Iblis mentioned in comment #12, and there are some spacetime diagrams showing how it would work on this page:

  9. Jesse M. says:

    Oh, and I should add that while you’re correct that the speed of light “has been shown to vary” when light is traveling through a medium like air or water (due to the photons being continually absorbed and re-emitted by the medium), the constant c that appears in the equations of relativity refers solely to the speed of light in a vacuum, and there is no convincing evidence that this constant can vary.

  10. Marc Fleury says:


    thanks for the discussion. It was a relief to find your blog. I read with great interest your ‘lorentz violation paper” and what you call the modern aether. I have been looking into this (purely by intellectual curiousity) and mostly because the lorentz invariance and all the ‘observer neutrality’ was just too repulsive to my brain.

    In any case. I do not understand why this would imply time travel. Again if lorentz falls then maybe we should stop hurting our brains with this space-time thing, in other words who cares what space-time diagrams say, they are irrelevant.

    I would like to hear comments on the fact that the main difference from 1987a and Opera is that in opera the neutrinos go through EARTH CRUST. A compressed ether. A compressed media has a higher velocity of waves. Aether would provide a simple approach to this problem.

    Why don’t you use the blog to pursue more sci-fi scenarios. The caution around the results is right and welcome but the speculation should be going wild. Bring the aether back. (Are you at all familiar with Beckmann’s work? do you give it any value?).

    As a side note, I enjoy the comments almost as much as the OP.

  11. Marc Fleury says:

    Jesse M,

    thanks for the clear expose and the link to the minkowski diagram explaining the paradox. I think we can take this further.

    a/ Opera is wrong. Then move on it all holds there is no time travel.
    b/ Opera is right. According to minkowski diagrams then we can receive a message before sending it, which is of course a contradiction. We have proven by the absurd that SR is false.

    Or as is said very well in your original link
    “faster than light travel or communication, special relativity and causality cannot coexist.”

    I think the possibility that Special relativity is wrong should be seriously considered. Personally I can’t wait, I have a long standing beef with SR (which I never had with GR) that i could never swallow “relativity of simultaneity”.

    If FTL is true, SR has got to go. Causality is a much deeper philosophical hole. I know which one I sacrifice in a heartbeat. I can’t wait to see how this unfolds.

  12. drm says:

    Maybe speed of light violations only count if you get caught. Neutrinos interact so weakly as to be barely detectable in the first place. Hence, they are a very weak channel for carrying information faster than light. In that case, the observational (and casuality) consequences are all practical purposes almost nil.

  13. So half spin nuetrino, nuetral one, jitter bugs boson while older photon, spin one slow dances taking longer till done?

  14. Baby Bones says:

    Let’s say that the experiment is right; then, we should look closely at what the tiny number in excess of c is suggesting. I think it possibly suggests that c is minutely higher than we expected and that the speed of light that has been measured in experiments is a local speed wherein light is effectively slowed down by the medium it travels through (even if that medium is the “vacuum” on or nearby Earth). After all, the neutrino is hardly affected by any medium, even solid rock, but light is affected by almost every medium it travels through.

    Another idea is that light gets an effective mass through some sort of interaction with the vacuum.

    If the neutrino is really faster than light, and is a time traveller, we would have to combine that fact with the many world’s hypothesis about all possible futures within the tiny time difference and every one of those futures would have copies of neutrinos that would move through our present and exert a ghostly gravitational pull. That could add up to a lot of mass-energy coming from the future, and maybe that is dark energy or dark matter.

  15. TimG says:

    Jorge (#21): On the contrary, they’ve learned that truly shocking, not-yet-confirmed results almost always end up being wrong, and only occasionally end up being right.

  16. Elmer Fudd says:

    If neutrinos travel backwards in time, does that mean they will be created at some future point in time rather than during the big bang?

  17. Needs more illustrations and pictures, for people who are not good at music, but interested in science and physics.

  18. marc fleury says:

    Repeat after me, time travel TO THE PAST is impossible. Time travel to THE FUTURE, a trivial result of time dilation. There are ways to get at time dilation without all the machinery of minkowsky space. Causality is a deeper principle than special relativity. In short, do not talk ‘lightly’ about backwards time travel as it invalidates causality and I will always rule it as absurd. Opera, if true, is a proof by the absurd that special relativity is wrong.

    Also I yearn for a simplification of physics on the basis of aether approaches. It is no mean feat given the Michelson-Morley type of experiments, which have “exquisite precision” according to Sean. I always like to remind people that while we observe time dilation for the muons coming down to earth, the reciprocity, that muons observe muons on earth dilating slowly has never been observed. The “equisite precision” has not been for ‘every observer’. It makes me sad to already read about short cuts in higher dimensions and what not, I want aether, a 19th century understanding of “mechanics” with all the modern math flavor a la Sean, to be taken seriously.

    I think in 20 years we will ask each other, where were you when they announced Opera?

  19. Neutrinos are governed by weak interactions and gravitation. I do not think it unreasonable that the mediators of all forces travel at light speed. Do not know if that might affect neutrino speed.

  20. Paul Stankus says:

    I like to start lectures on relativity by putting the idea of “proper time” or subjective time in a central role. A simple statement of SR, which bridges over to GR, is that proper time experienced by any object traveling along a path is purely a function of the path itself; ie all objects (particles, physicists) following the same path experience the same increment of subjective time passing.

    With the “everyone gets their own cone” conception, this appealing picture of proper time as a function of path is one of the things that has to be surrendered. For a path which is outside the photon cone but inside the neutrino cone, those two types of particles obviously experience different amounts of proper time (technically, the photon would have negative proper time squared, while the neutrino would have positive proper time squared).

    So, don’t be too sanguine thinking that the “each their own cone” is some kind of simple fix. Accommodating superluminal neutrinos will require erasing a lot of stuff, waaaaay up the page, and starting over to re-define even such basic concepts as proper time or rest frames.

    (I think this is similar to Bee’s remark above; BTW, note to Bee: regarding “(Been there, done that.),” what work does this refer to? Links, references?)

  21. Pingback: ماذا لو كانت النيوترينات أسرع من سرعة الضوء؟ | فوضى! – مدونة مَعين بن جنيد

  22. Mike says:

    Just heard a great joke:

    Neutrino. Who’s there? Knock knock.


  23. Jesse M. says:

    Mike, I heard a different version:

    The bartender says, “we don’t serve neutrinos in here.” A neutrino walks into a bar.

    Of course even before the FTL study, there were other such neutrino jokes:

    A neutrino passes through a bar.

  24. Justin Loe says:

    The following is worth noting: “Luca Stanco, a senior member of the Opera collaboration (who also worked on the ZEUS experiment with me several years ago). He points out that although he is a member of Opera, he did not sign the arXiv preprint because while he supported the seminar and release of results, he considers the analysis “preliminary” due at least in part to worries like those I describe… Four other senior members of Opera also removed their names from the author list for this result.” source: