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.
If they did travel faster than light, would we need to add more dimensions to our picture of the universe? Everybody seems to say that we have to “rewrite” Einstein, but why would you rewrite something that already works? Wouldn’t you just build on it, and add another term or two?
One good thing that may come of this result is more awareness that “ultimate speed in nature” (which is the foundation of special relativity”) is a logically distinct concept from the speed of light (or any other physical particle). If the ultimate speed of nature is saturated by neutrinos instead of light, I don’t see why this should necessarily change much the structure of special relativity. Of course, matching all we know about light is a different story.
As for the idea that you can have two independent Lorentz symmetries, one for neutrinos and one for all the rest, this is great at the level of free particles. Going from free particles to interacting fields, it seems to be hard to reconcile this idea with constraints from effective field theory, which tell you there is a large number of relevant and marginal operators in any Lorentz violating version of the standard model. It seems a priori hard to imagine one can break LI in one sector while this breaking not leaking and contaminating all the rest of physics with large observable consequences.
Be honest, are you writing this from the future to throw us off the scent? =P
Thanks for the food for the thought, Sean.
Paul Krugman has a post on solving the financial crisis by going back in time 😉
http://krugman.blogs.nytimes.com/2011/09/24/solving-the-financial-crisis/
I was thinking about this yesterday. If the neutrinos are really traveling faster than light wouldn’t they have been detected before they were emitted?
Whats the big deal about CTC’s – GR already has many solution with CTC’s
Moshe, it is hard to imagine, but we’re already imagining a hypothetical world in which we really did detect muon neutrinos moving faster than light, so the standards are a bit different.
Mark, just because there are solutions doesn’t mean they describe reality. There are proofs that CTC’s can’t arise in nonsingular evolution from well-behaved initial data obeying the null energy condition.
Thanks, Sean — that helps!
To clarify, I’m perfectly comfortable with the idea that, even if there’s a speed limit that plays the role of “c” in special relativity (i.e., the role of defining the causal structure), there’s no a priori reason for that limit to be identical with the speed of photons through the vacuum (it could be slightly greater, for example).
But to whatever extent I was thinking this through at all, I thought that Einstein derived SR in the first place through careful consideration of Maxwell’s equations, and it was Maxwell’s equations that picked out the speed of photons as being special. So, if the true speed limit turned out to be the speed of certain high-energy neutrinos rather than photons, I suppose we’d say that something like SR might still be true, but Einstein’s original derivation of it from Maxwell’s equations only worked by a “happy accident”?
The c in special relativity is *the* reference-frame-independent speed of the universe.
To define a causal cone different from that of special relativity,
one needs to sacrifice reference-frame-independence.
Note that actual light travels rather close to c:
The upper limit on the rest energy of a photon is rather low.
IIRC it allows photon frequencies as least as low as 60 Hz.
Visible light frequencies are considerably higher.
A visible light photon has an energy at least a million million times its rest energy
Slow light was not the problem.
Scott, I think this idea would amount to abandoning the idea of one true speed limit for absolutely everything. Yes, Maxwell’s equations pick out c as special, although that speed could be special even if nothing moved at it (e.g. in a world where all particles were massive). This idea would be that there are different special speeds for different kinds of particles, abandoning the universality of Lorentz invariance (which came from Maxwell’s equations).
It case it’s not clear, all this is incredibly unlikely, but should be kept in mind as a logical possibility.
Mark Weitzman #6: Just to elaborate on Sean’s answer, probably the biggest deal about CTCs is that, if they exist, then you need some way to deal with causal consistency problems (i.e., grandfather paradoxes)! Now, there are ways to deal with grandfather paradoxes—one elegant resolution, due to David Deutsch, uses quantum mechanics—but if you want those solutions, then not surprisingly you generally “pay a price elsewhere”! So for example, finding a consistent solution around the CTC could be an incredibly-hard computational problem—so you then need to accept either that CTCs would give us computational superpowers, or that there’s some mysterious meta-principle that prevents us from using CTCs for that purpose. (For more about this, see this paper by myself and John Watrous, or section 10 of my survey article “Why Philosophers Should Care About Computational Complexity.”)
See also here:
http://en.wikipedia.org/wiki/Tachyonic_antitelephone
for a simple demonstration
I KNEW the theorists wouldn’t let us down! (well done to Scott and Sean). On a slightly more serious note: is there any constraint (other than it hasn’t been observed before) on the speed of these neutrinos relative to c? Could the result be 1.5c say and still be plausible given the reasoning laid out above? With a special definition of “plausible” I suppose…..
I thought Lorentz/CPT violations were pretty much ruled out with observations like the MINOS Far Detector.
On the other hand, Goldman Sachs should be interested in this, since they make a lot of money by running a “wire” con on other traders. They already pay extra to get their trading machines closer to the trading floor than anyone else so they can see and react to others’ bids before those others can react to theirs. (See The Sting or Queen of Hearts to see how this works.) If G&S could use a high speed neutrino link, they could beat anyone else relying solely on electronic data flow. Imagine the efficiencies and stability that this could introduce into the market. The mind boggles.
If they discover that his lets them kill their own grandparents, that might be a good idea.
Thiotimoline!
Kaleberg, your inflammatory remarks are not appreciated.
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@ Sean Carroll said:
“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… There are various ways we could imagine some background that actually picks out a preferred frame of reference, violating Lorentz invariance spontaneously.”
This is analyzable.
The only obvious candidate for your fluid would be the CMB frame, which is accessible by moving at ~369 km/s towards the red shift pole (α, δ) = (23h 11m 57s, +7.22) [1][2]. In other words, you can access this frame by moving with a velocity of a bit over 0.1% of c towards a spot between Pisces and Pegasus. This is true even if the motion is contained (briefly) within a system residing on earth.
First observation: If neutrinos are shifted based on some special relationship to the CMB frame, a reasonable inference (not strictly proven) is that Lorentz violation should maximize at the poles of the CMB dipole. Another reasonable inference is that neutrinos would appear slightly slower than c if directed towards one pole, and slightly faster than c only if directed towards the other pole. Finally, by symmetry the neutrino paths should have neutral behavior — a velocity of c — only for radial paths in the equatorial plane between the two poles, that is, at 90 degrees from each pole.
Second observation: SN1987A seemed to limit neutrino velocities down to a range quite close to c. The implication for the Lorentz violation hypothesis is that SN1987A should reside close to the equatorial plane of the CMB dipole, else it could not have produced this seemingly ordinary result.
I took the trouble to calculate that. To my surprise, the angle between SN1987A and the red shift pole (α, δ) = (23h 11m 57s, +7.22) is 98.861 degrees, or only about 9 degrees away from the optimum orientation. Thus the celestial location of SN1987A is at least approximately compatible with your Lorentz violation idea. Again, interesting, and statistically a bit unexpected.
The inability to disprove your hypothesis via the singular but strong SN1987A data point means that it’s worth asking the next question: What are the exact timestamps for all of the detected neutrinos, and has anyone analyzed the OPERA data by indexing individual neutrino detections to their path orientations and directions relative to the CMB dipole? The conversion from time stamps to celestial vectors would require only standard astronomical tables and simple geometry.
Hypothesis: If your idea of Lorentz violations is related to real superluminal neutrino results, then the celestial neutrino path vectors aligned most closely with the CMB poles should show the strongest deviations from c. One pole group should show consistent high-sigma sub-c velocities, and the other should show similarly high-sigma velocities that are slightly in excess of c.
———-
[1] Lineweaver, C.H. et al: The Dipole Observed in the COBE DMR 4 Year Data. The Astrophysical Journal, 470, 38-42 (1996). Online: http://adsabs.harvard.edu/full/1996ApJ…470…38L
[2] The blue shift pole of the CMB dipole is located at (α, δ) = (11h 11m 57s, -7.22)
Looks like we need to discover a new line of physics.
It’s really funny to see how theorists as you try everything to save physical theories on which you “trust”. You always blame systematic errors, uncertainties on experiments, etc. And try to confort yourselfves by thinking “even if the experiment is right, it doesn’t change a thing” and then try to give some complicated explanations that not even you really believe.
It is the same attitude physics took when some experiments were revealed such as those of Michelson and Morley and not to say about those leading to appearence of quantum mechanics.
I’m not assuring that the conclusion that neutrions travel faster than light is truth. Indeed it may be wrong. I’m only saying that you haven’t learned a thing from past experience.
Wow – up to this point, I was able to follow, not just the post and the linked post and all the related wikis, but almost every one of the reader replies here. But, now I read about “neutrions”, and that entire conceit just evaporates. Why aren’t we reading more about neutrions? Has the finding of faster-than-light-speed neutrions been confirmed to the same six-sigma level, or is there some shakiness in that? I can’t get this image out of my head of 65 billion neutrions per second transversing my left nostril, some of which are bubbling around at the edge of the detectable universe, none of which have enough mass to actually interact in any way beyond detection; I keep feeling something just has to blow.
Well the only thing that blows is that you prefer to do nonsense jokes about a grammar mistake instead of getting the point of a comment. NEUTRINOS. Are you happy now?
I’m trying to understand the basic concept of Geroch’s paper–when he talks about other physical systems having different causal cones, does he mean that these systems would no longer obey Lorentz-symmetric laws, but rather would have some different symmetry involving a different speed constant? It seems to that if you have the conditions 1) All physical systems obey Lorentz-symmetric equations, and 2) there are some physical systems that can be used to transmit FTL messages, then together these should automatically imply 3) it is possible to bounce FTL signals back and forth between two observers in such a way that the first observer receives the “answer” signal before he sent the original message (the “tachyonic antitelephone” mentioned by Count Iblis above).
Well Jorge, your point was pretty silly to begin with. No where in Sean’s post was there any mention of systematic errors. This post was, in effect, saying: “Suppose it is true, what would happen? Does it necessarily imply time travel?” That is, your point claiming that Physicists are not trying to figure out the consequences of what FTL neutrinos are, was made about an article where a Physicist was trying to figure out the potential consequences of FTL neutrinos.
So nonsense jokes are perfect reasonable way to respond to a completely nonsense comment.