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.
Hi Jesse m,
Of course I meant faster than light, the detectors on the LHC look to me like they have been designed in order to have a dual purpose; one one them is manipulate FLT plasma (QGP) in order to create a type of time travel. Its amazing what you can do when you use all of the detectors in entangled unison; in order to create complex manifolds.
Sorry, but that just how it looks to me.
For light time stopped, for the neutrino; it had its first tick! It covered the whole of the first second and it never travelled back in time.
I have the same question as Ellipsis (#28).
For neutrinos to be confined to their own cones, in a way that we can’t use them to mess with our timeline, shouldn’t we not be able to even detect them?
(better read #28, he asked it better than I)
Traveling faster than light could be traveling without light and it could be extra dark.
I have thought about time travel and have considered many different theories. I came to my ultimate theory and conclusion that time is neither linier nor conical in space or time. Time is helical; therefore there is no speed at which time will encounter itself in the past because there is no past relevant to the position of time on the helix.
http://arxiv.org/abs/1109.6562 — anybody want to comment on this?
The relativistic mass equation implies mass must be an imaginary number for FTL. It is also known that neutrinos oscillate to different varieties as they move and they have a tiny mass.
Since the experiment measured the speed of Tau neutrinos only, I think it is possible that oscillation to Tau neutrino phase switches mass to an imaginary number and only the neutrinos born in that phase has FTL property. (And also the ones born in other phases never reach FTL even when they switch to Tau phase because they still would need to gain energy to speed up also. That still maybe possible if they pass through high energy cosmic ray etc. zone in space while in that phase. So maybe the 1987a supernova neutrinos never passed such a zone so they never had a chance to speed up.)
I also have a simple explanation why FTL does not mean going back in time for neutrinos.
Imagine an an FTL spaceship going from Earth to Mars and the astronaut watching a movie broadcast from Earth. The movie would really run in backwards because the ship is moving faster than the radio waves. This implies time is also running backwards for the astronaut.
But this analogy does not apply to an FTL neutrino because neutrinos does not interact w/ EM fields. So the neutrino can never watch the broadcast.
Actually the big problem with FTL particles (and other Lorentz violating theories) is that it violates local stress-energy conservation. To an observer that crosses path with an FTL particle, they would see a pair of identical particles spontaneously created, and then traveling in opposite directions from the point in space-time where the FTL particle crossed the observers path.
Simple put there is no way you can “see” a FTL particle coming at you, because it always out races its own signal, leaving the observer “surprised” by its sudden appearance out of thin air. So if you subscribe to the information theoretic interpretation of entropy, even one FTL particle would contribute an infinite amount of entropy to any local neighborhood through which it travels.
Unfortunately even if you violate local conservation of stress-energy just a tiny smidge, it would add up to huge consequences in things like solar and galactic evolution. Now don’t quote me on this because this is not even a back of the envelop calculation, but if FTL neutrinos where produced with the density to be observed at the rate they were claimed to have been observed, then the sun should have collapsed into a black hole within the first couple hundred million years of its formation, due to the observed spontaneous creation of extra mass. And a careful reading of their paper will reveal that the MLE used assumed no dispersal in the neutrino speeds, so the conclusion from the estimator is that every neutrino produced is an FTL neutrino.
In some sense particles travel backwards in time everywhere in space-time (just always slower than the speed of ligth): they are called their anti-particle partner. Its at least a mathematical nicety.
In the end the analysis needs to be rerun to include MLEs for both the speed of the neutrinos, and the dispersal of velocities
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@FB36–you’re misunderstanding the reason people say FTL leads to time travel in relativity, it has nothing whatsoever to do with visual appearances, you really need to understand the concept of the relativity of simultaneity in different inertial frames given by the Lorentz transformation, and the idea of relativity that the laws of physics should work the same way in all these different inertial frames. See my comment #33 above for some more info.
Please help. I am having a difficult time figuring something out. When we speak of a “spacelike” trajectory I take that to mean a trajectory through the fabric of space/time. The shortest distance between A and B through the fabric of space time is a straight line, but said straight line can be curved since the fabric of space time is warped. Any signal faster than c would violate causality, unless we have a different causality cones for different particles. But why is this necessary? If space/time is curved then we could have short cuts (wormholes) or particles could use extra dimensions traversing a “straighter” line between A and B than the one permitted by the space/time fabric. So, a signal could travel faster than c without actually moving faster than c. My question is; would this violate causality or the Lorentz covariance? Could particles be temporarily trapped in this “subspace” arriving at their destination before c would permit it? Would this be a violation of causality, and if so why? I have not been able to find an answer to the question, please help.
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@walter: When we speak of a “spacelike” trajectory I take that to mean a trajectory through the fabric of space/time.
All trajectories are understood to be trajectories though spacetime, but they are divided into three categories: “timelike”, “lightlike” and “spacelike”. All you really need to know for this discussion is that a “timelike” trajectory is a path that could be taken by a particle moving slower than light, a “lightlike” trajectory is one that could be taken by a particle moving at the speed of light, and a “spacelike” trajectory is one that could only be taken by a particle moving faster than light (of course even if no such particles exist, we can still define such trajectories in terms of whatever coordinate system we use). There’s a little more on the distinction between these three types in the wiki article on spacetime (see in particular the section “spacetime intervals” for how timelike, lightlike and spacelike intervals are defined in special relativity, and also the section “spacetime in general relativity”).
If space/time is curved then we could have short cuts (wormholes) or particles could use extra dimensions traversing a “straighter” line between A and B than the one permitted by the space/time fabric.
A particle traveling through a wormhole or any other such “short cut” allowed by general relativity is still traveling through the same spacetime, just a strangely curved region of it (see the diagram of a 2D space with a wormhole in it on this page), so it’s still “locally” moving slower than light which travels through the same region even if it gets somewhere faster than a light beam which took the “long way”. Things might get more complicated if we were talking about “short cuts” allowed by string theory, like the idea that 3D space might be a kind of membrane in a higher-dimensional space, so if it wasn’t perfectly “flat” in this higher dimensional space a particle might take a shortcut by leaving the brane, traveling through the extra dimension and then returning to the brane. I think this probably would avoid the possibility of time travel though I’m not perfectly sure.
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You do realize that this leaves a possibility that photonic mass has a greater impact on the overall mas of the universe? I think dark matter could be in hot water….
All these discussions of trim-travel – in the sense of “killing you grandfather” and reverse causality since the whole concepts violates everythingwe know about space-time. A particle cannot mee themselves in the past because a particle can occupy more than one position in space-time.Thie simple, elegant fact has been around for a long time yet most physicists who dream about time travel seem to willfully ignore it.
“Consider, for example, the existence of a heretofore unobserved fluid pervading the universe with a well-defined rest frame…” Aether theory makes a comeback!
Suppose a neutrino can indeed travel faster than light. It does not mean that it travels backwards in time. If a photon takes 4 years to travel from the sun to Alpha Centauri, and a neutrino travels at an amazingly fast speed of 110% of C, then it takes slightly less than 4 years to reach Alpha Centauri. It does not arrive before it left (which is what would happen if it could travel backwards in time.
What happens is that the neutrino conveys information from the sun to alpha centauri faster than a photon can.
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actually, if these results are verified it would mean that there must be more than one particle that can travel faster than light, and the cosmic speed barrier is broken.
introduce particle “polly”. polly is similar to a photon or neutrino in that it is very very small and is emmited by star “a”. it reaches relativistic speeds instantaneously and begins its journey through space to our receiver “b”.
traditionally we would say that this particle moves from point a to point b. it takes a measurable time depending on the distance. this time can be measured and thus we derive the speed.
in our 4th deminsional world, this makes sense as this is how we percieve things. we watch them move from a to b. the event of emmision happens at a defineable point sometime prior to the event of receiving and there is some measurable time between the two, and these events will be in that order, no matter what because we cannot go back in time right? event a precedes event b because event a is a cause of event b and so on.
But if you think about it, the particle really exists at all points between point a to point b.
follow with me. if you were to percieve the world with a 5th deminsional attitude, we would see a bunch of elongated snakes of humans. well really, we would see the universe is stuffed full of stuff, stretched from its birth or origin to the end or death. the universe would be observed to be infinitely dense and infinitely full.
of course this doesnt make sense to us, because just as 2 dimensional creatures cannot make sense of a 3rd dimensional depth, and a 3rd dimensional creature cannot understand the fluidity of time, we do not readily grasp the concept of seeing all time at once.
What happens to photons when we slow them down? they decay, very rapidly. but if we leave a photon at c, it will go on for billions of years. that is how we see such far distances in space. or so we understand. but if we think about it in a 5th dimensional way, we are just moving down a road along our 5th dimensional path. and if we go further, to encompass all possible paths at once, then we are thinking even higher, sixth dimensional. (i know i am rambling, i dont want to post a novel and i am sure lots of you are breaking out your crack pot stamps, sorry but this does make sense.)
this 6th dimensional idea means that not only does polly our particle exist at all points from a to b at once, but also all possibilities of pollys fate do as well. polly does not choose (for kicks, polly is sentient…) her path, but rather navigates her way through a maze of possible paths by making decisions. (this gets back to neutrinos being ftl… i swear!)
now reckon this to a jet fighter traveling at mach 2 in a world of beings that can only sense thier surroundings using their ears. if you were to ask them what the ultimate speed is… they would tell you mach 1. even though the jet is travelling faster, our blind friends cannot measure it because the only means of observation are thier ears and thus they would only observe the jet to move at mach 1.
so back to polly and us…
we only had our eyes to observe the particles of our universe until recently. hence it would only make sense that we would assume that the fastest visible thing that we can see is actually where our speed barrier lay.
string theory tells us through math that our imagined 5th and 6th and beyond deminsions are there, so this shouldnt be science fiction to anyone. but if we had whatever 5th deminsional entities may use to observe thier surroundings, i think that the speed of light would seem rediculously slow, seeing as how everything happens all at once, and as close as infinately fast as could be reasoned. so who cares if the neutrinos move faster than photons. if you stop thinking about c as being some barrier that we cannot cross and start thinking of it as simply the fastest that something can go that we can watch from beginning to end, then it really should be no big deal.
so back to polly and her journey. can we not model her as existing at all points a to b with us only being able to observe certain features of her existance, and those features only being able to be seen as moving speed “x”?
this way, when we encounter FTL particles, they are just more excited. we cant track a neutrino and its path from a to b. so it would stand to reason that the bits we can observe just happen faster, slightly above our observable parameters?
everything happening all at once when we put ourselves in its shoes, a much different world indeed.
i dunno, you all prolly think i am a nutcase, but it makes sense to me. i sincerely hope someone would be willing to address this idea with me or at least shoot it down somehow.
-Aaron
I have a possible cause for the extra speed of the neutrino. The Scarnhorst effect, which noted as early as 1994, that QED and other quantum field theories, modified the speed of the force carrier accorded to amount of energy in near by fields, the effect is rather small for light, but it scales as the inverse four power of the mass of the fermion in the theory, so for it neutrinos its some billions of billions times bigger. To generate the effect we require that neutrino feel some fifth force, and that there is a binding background field (that doesn’t scatter) in ordinary matter. I’ve been investigating the existance of such a field for the last five or so years, and it seems, not only perfectly allowable, but it could also solve dark energy. Given an additional U(1) force for neutrino (an axial force, left hand-right hand), a background sea to cancel the additional charges on nucleons, and the Scarnhorst effect, we can generate an faster than light speed for neutrinos.
Each field has its only speed of propagator (light etc), which must be the same in the vacuum, however depending on the energy in any background field (of the same type), the speed of propagator can vary. Neutrinos would still travel at the speed of light in the vacuum, but would closely approach the increased speed of the new forces propagator in a background field with negative (i.e. binding) energy. Since the neutrino is still technically slower than the relavistic speed no breaking radiation would be emitted.
See my blog Axitronics for more details.
I’m no physicist, but I don’t buy the idea of time-related problems with neutrinos – it just lends credence to some whackier ideas that have little empirical evidence at present to comfort their theorizers.
It is wholly an assumption that nothing moves faster than light.
Einsteins’ thought experiment merely suggested the appearance of time travel by viewing light from an earlier period – not actual time travel! The fact that you can view something ‘out of time’ does not mean time travel has taken place – only the illusion of it. In actuality you would be in the same time viewing a past event and unable to interract with it.
Now, this assumption that nothing moves faster than light is upended with the neutrino speed measurements. I prefer to assume a different view on the matter. That is, I see that the speed of light is the maximum speed of a photon *given its particular mass*. Another particle’s limit may be something different. I think this in no small part because a particle’s velocity is related both to its mass and the energy it has been given. Light may not be able to go beyond a certain speed, but, in my hypothesis, a smaller particle would be able to. The corollary of this is that the smaller the particle, the faster it can move and at zero mass we have infinite energy – which is exactly what we have *before* the formation of subatomic particles in the ‘big bang’: infinite energy at zero volume. Einstein proposed that E=mc^2 may not be quite right. Probably, for us, we should find the speed limit of the smallest particle and rework the equation by replacing ‘c’ with a variable for whatever that something is, be it a neutrino or something else. In summary, I postulate that a neutrino has a slightly lower mass than a photon and that this accounts for the recent measurements.
I am not alone in this view: http://usersguidetotheuniverse.com/?p=2181
Sean, I posted on your other entry regarding faster than light neutrinos that in certain frameworks, namely those of 6 dimensions, neutrinos and gravity might be able to travel backwards in time:
http://arxiv.org/abs/gr-qc/0603045
However, this is only likely if the dimensional shortcut comprises of a 6 dimensional framework instead of 5 dimensions, and according to this paper, gravity and neutrinos would take the path of least resistance to avoid forming a closed timelike curve.
I agree with Conrad F.! and this article’s primary point in general is exactly what I have been thinking whenever I saw a report on this experiment.
Getting from an event to a receiver faster than light does not mean that the object is going back in time. The object will be a significant distance away from its Grandfather (the source). When it arrives it could look back and witness a time prior to when the source occurred due to the light having been overtaken by the object as it traveled but if it were to return to the same space it came from, it would have to travel in the opposite direction, reversing this effect so that once it arrived, time would have passed at the source. So no killing the grandfather.
To suggest that it would be possible would be like claiming that because light reaches us from an explosion before the sound does, we would be somehow capable of preventing that sound from being created.
Perhaps realtivity considers time as being stuck too closely to light’s speed for how it really is. Perhaps certain objects can squeeze into a gap between light speed and infinite time.