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.
Another issue may also be worth looking into. Neutrinos have a finite magnetic moment (of the order of 10^(-19) times the Bohr maenton according to the Standard Model, but it could be much larger), therefore you would expect superluminal neutrinos to emit Cherenkov radiation.
But unlike Cherenkov radiation emitted by particles in a medium, the radiated power will be infinitely large, because the index of refraction of the vacuum won’t become larger than unity at some high frequency, so there is no high frequency cut-off for the Cherenckov radiation, making the total radiated power divergent.
Of course, if neutrinos really can travel faser than light, then there must be other effects making the Cherenkov radiation finite.So, if there exists a field with some vacuum expectation value that effectively breaks Lorentz invariance for neutrinos, then this must also act as a medium that affects the effective index of refraction of vacuum
Why doesn’t the temperature of the CMB provide an “absolute clock” (at least in principle) such that “relativity of simultaneity” questions can never arise? Yes, I know the temperature varies depending on one’s motion but can’t one correct for that? Surely someone here can explain that in simple words that a non-theorist can understand?
Sean, wouldn’t time travel to the past itself be an example of Lorentz violation? Imagine time travel was possible, and you ended up in the past. By looking around you see you’re in the past (e.g. Elvis on the TV), so wouldn’t this information itself tell you that you are/were travelling faster than light – therefore breaking the idea that an observer should not be able to measure their own velocity?
We already knew that neutrinos move faster than sound through air before this experiment, though.
“We already knew that neutrinos move faster than sound through air before this experiment, though”
Actually, you’re right about that 😉
@relativelydumb:
Why doesn’t the temperature of the CMB provide an “absolute clock” (at least in principle) such that “relativity of simultaneity” questions can never arise?
Because the CMB is just a collection of physical particles, whereas when physicists talk about all reference frames being equal, they mean that the basic equations of physics work the same way in each frame. If you could create a region of space where all the CMB photons were first absorbed and then replaced by a new collection of photons that had the same spectrum but a different average rest frame, an observer in this region at rest relative to this frame wouldn’t see these photons behaving any differently than an observer in a region with CMB photons in the CMB rest frame.
@Alex:
Sean, wouldn’t time travel to the past itself be an example of Lorentz violation? Imagine time travel was possible, and you ended up in the past. By looking around you see you’re in the past (e.g. Elvis on the TV), so wouldn’t this information itself tell you that you are/were travelling faster than light – therefore breaking the idea that an observer should not be able to measure their own velocity?
Relativity just says the laws of physics work the same way in all the sublight inertial frames given by the Lorentz transformation. So, for two objects moving at sublight speeds which are at rest in different frames, there can be no frame-independent sense in which one has a greater speed; but all these inertial frames still all agree about whether something is moving slower than light, at light speed, or faster than light (and the Lorentz transformation would not allow an FTL observer to have his own inertial frame).
I think you’re all missing the larger point of all this: If these results are confirmed, we may soon have a way to reliably predict when CERN is just about to turn on their proton beam.
@Jesse M. Thanks but doesn’t get to the root of what I was trying to ask: why doesn’t the temperture of the CMB provide a clock against which all questions of simultaneity can be resolved? Which is another way (I think) of asking shouldn’t all observers in inertial frames measure the same temp of the CMB and thus be able to know WHEN they are, relative to the time of the universe becoming transparent to the CMB? (note the name I’m using here!).
Thanks but doesn’t get to the root of what I was trying to ask: why doesn’t the temperture of the CMB provide a clock against which all questions of simultaneity can be resolved?
Observers could certainly use this as an agreed-upon universal standard if they chose, but it would be an arbitrary human convention, it would not be a “physically preferred” definition of simultaneity in the sense that physicists are talking about. As I said, a preferred definition of simultaneity would mean that the fundamental laws of physics pick out one frame as “special”, not the particular pattern of matter/energy which is a result of historical contingencies.
Forgive me if this has already been discussed as I am a relative layman in Quantum Mechanics and have not taken the necessary math classes to take the necessary physics classes, but wouldn’t the time necessary for the (relatively) prime causal event to take place, and the time necessary to compose the message to be sent if one is to be sent, mean that by the time the message is sent, any chance of an Antitachyonic Telephone to occur would have passed?
Let’s say that we could send a message at 500c, at what distance and speed of communication after the event, would you have to be to actually create an Antitachyonic Telephone effect? Would you still generate an Antitachyonic Telephone if you achieved FTL Communication/Travel by shortening the distance to be traveled instead of increasing velocity?
I have tried to read up on the nature of FTL causing time travel, but most of the articles I have found were either too technical for my level of knowledge in the subject, or ignored the time necessary for the event to take place and the information to reach Alice so she can tell Bob about it.
From what I have been able to understand about the technology of this, it sounds like you would have to use a Wormhole of some kind to attain causal violations and time travel, but that may be my own lack of understanding of the subject matter.
Any explanations geared towards a Freshman in College would be greatly appreciated, thanks. And again, sorry if the answers should be obvious and I just can’t see them from my vantage point.
Thanks, Jesse, that makes some sense.
Eric,
I am biased anti-SR. After a Ph.D. in physics the only time I had to read, re-read, shake my head in disbelief, read again, give up trying to understand and just apply the math, and 20 years later, go back, re-read, re-disbelief, finally understand what the math is saying (captured in minkowski diagrams) and STILL not believe a word of it (relativity of simultaneity? really?) was with SR. The innocuous statement of “same laws of physics according to every observer” does lead to all the minkowski diagram machinery. I do recommend you read up on that because outside of that mathematical machinery there is NOTHING that will explain to you why you need to give up classical thinking and embrace ‘relativity of simultaneity’, curved mixing time and space (different concepts) and all the mental gymnastic the full SR picture requires. I consider it, to this day, a monster.
When people claim SR ‘has been fully tested’ as Sean in OP. Remember only ONE observer has been fully tested, the one usually at rest in the lab frame or tethered to the earth gravity, there are aether based theories that do not depend on SR. The ‘relativity of observers’ has never been tested, and until we get lab equipment going at the speed of light we will not test it. It does lead to all the philosophical monsters.
Back to your question: the minkowski diagram will show you that if you have FTL, you can easily build time travel see links above in discussion on great ways to see it. OF COURSE THERE ISN”T ANY WAY TO EXPLAIN THIS TO A LAYMAN, BECAUSE IT DOESN”T MEAN ANYTHING (imho) OUTSIDE OF THE LORENTZ MATH. Just read this (http://www.thedelphicfuture.org/2011/09/causality-ftl-opera-and-special.html) which reuses the link above and see that SR with FTL leads to time travel backwards.
I am amused to see people seriously entertaining the idea in this forum, ‘what would it mean?”. It doesn’t mean anything. Time travel backwards is a philosophical monster because it violates causality (receiving a message before it is sent etc) and why this is not dismissed out of hand is bizarre to me. Causality must remain whole. Unfortunately the physics profession, from my standpoint, has tortured itself so much that it is ready to accept just about anything the math models tell it. I vividly remember deciding I would get out of the field of theoretical physics the day I swallowed without questioning that the universe had 23 dimension (string theory class) and the teacher said “that can be problematic for a few folks”. I turned around to my neighbor and asked why, he just rolled his eyes at pointed at the space around us, “what do you see?”. I had been brainwashed. I did finish my PhD without any joy and just got out as fast as I could.
So it is with a certain glee that I hope this result will hold. Until then I will gladly repeat what I consider fundamental philosophical truth, namely that causality is a deeper principle than SR. I don’t care what SR says, there are plenty theories that account for the phenomenology of SR without all the suspension of disbelief. Backward time travel doesn’t mean anything to a human brain and should not be entertained on the basis that ‘the math tells us so’ in violation of causality.
I want to see some sanity restored to the field of physics.
@marc fleury:
When people claim SR ‘has been fully tested’ as Sean in OP. Remember only ONE observer has been fully tested, the one usually at rest in the lab frame or tethered to the earth gravity, there are aether based theories that do not depend on SR.
It’s true that experiments are done on Earth, but it’s simply a matter of doing a mathematical transformation to see how the same events would be described in a coordinate system moving at high speed relative to the Earth; conversely, any theory of physics that violated Lorentz-symmetry should have effects that could be measured (and found to disagree with relativity) in the Earth frame.
Not sure what you mean by “aether based theories that do not depend on SR”. Do you mean theories that actually make different predictions about experimental observations than SR, or do you mean those that make the same predictions but interpret them differently, saying that there is a true aether rest frame but we can’t detect it because rulers moving relative to this frame shrink and clocks moving relative to it slow down, in just the right way so that all ruler/clock systems measure things to be obeying the same laws of physics? If the latter, see the discussion here about why such interpretations are considered highly contrived.
Time travel backwards is a philosophical monster because it violates causality (receiving a message before it is sent etc) and why this is not dismissed out of hand is bizarre to me.
Because the idea of causality violation, while very implausible, need not actually lead to any logical contradictions, one could postulate that the laws of physics only allow self-consistent histories, of which there will always be some possible–see the discussion of the Novikov self-consistency principle along with some of the scientific papers in the notes.
Backward time travel doesn’t mean anything to a human brain and should not be entertained on the basis that ‘the math tells us so’ in violation of causality.
Speak for yourself 😉 I would bet a lot of money that backwards time travel will not end up being possible according to the most fundamental laws of physics, but I don’t find the idea meaningless to my brain (and I would bet nearly as much that this neutrino result doesn’t portend a preferred frame of reference…speaking of which, have you seen this cartoon?)
Whether or not the OPERA results hold, this discussion is a perfect example of how FLT does not necessarily imply backward time travel; only that for particles to travel FTL, they must be non-electromagnetic in nature. In order for backward time travel to be demonstrated (as the knock-knock joke demonstrates) the effect, i.e. the detection of neutrinos in the lab at Gran Sasso would have to be recorded *before* the event at CERN (cause), i.e. the creation of the neutrino beam. This is not what is being measured and therefore cause and effect are not being violated.
As Sean correctly points out, if the OPERA results hold, it only demonstrates that Lorentz invariance is broken for these particular particles (neutrinos are non-EM in nature and not necessarily subject to this invariance). Since Lorentz invariance would be non-applicable to neutrinos, so would the math and logic that leads to the antitachyonic telephone effect.
What is not clear is how these results affect our basic understanding of the fundamental nature of mass-energy and whether there exists a similar Lorentz-type invariance(s) to which all non-EM particles must adhere. For example,
Sean wrote: “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.”
I cannot agree with the “neutrino cone” since they have non-zero mass and therefore their velocity should vary wrt their kinetic energy. This velocity may be truly tachyonic in nature and therefore may vary yet must always be greater than c. However, as illustrated above, this does not necessarily imply any violations of causality.
@Dan T. Benedict:
Whether or not the OPERA results hold, this discussion is a perfect example of how FLT does not necessarily imply backward time travel; only that for particles to travel FTL, they must be non-electromagnetic in nature.
Lorentz-invariance is not supposed to apply only to electromagnetism! Relativity’s prediction is that it applies to all fundamental laws of physics, and it is indeed true that both quantum chromodynamics (which deals with the strong force) and the Standard Model (which unites electromagnetism with the weak force, and also accounts for the strong force although it doesn’t unite it with the other two) are Lorentz-invariant, and of course general relativity (which deals with gravity) is locally Lorentz-invariant. If any of the fundamental laws of physics fail to be locally Lorentz-symmetric, this would be understood as a falsification of relativity.
I cannot agree with the “neutrino cone” since they have non-zero mass and therefore their velocity should vary wrt their kinetic energy.
But unless you assume relativity is correct (in which case FTL neutrinos imply causality violation), you can’t assume anything about how their energy varies with velocity, it’s possible the energy would approach infinity at some finite velocity greater than c (just as an electron’s energy goes to infinity as it approaches c) and give a “neutrino cone”. It’s also possible it wouldn’t, but I think Geroch’s paper was just giving this as a possibility.
Whether an FTL neutrino would have a maximum finite speed or could travel arbitrarily fast but not violate causality, I think this would imply a preferred reference frame. In the case where they could travel arbitrarily fast but not back in time, there would have to be a preferred definition of simultaneity implying a preferred frame. In the case of a finite maximum speed, there would have to be a unique frame where light cones and neutrino cones had their central axes aligned, meaning that in this frame light would travel at the same speed in all directions and so would neutrinos…in other frames of the type assumed in SR, light would still have the same speed in all directions but neutrino speed would have to be direction-dependent).
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Did get there before it set of though? did it? I think not!
It’s not like CERN was built without such things in mind! FLT; CERN are counting on it.
FLT; CERN are counting on it.
Did you mean to write “FTL” (faster than light)? If so I don’t know what you mean when you say they were counting on it, I think nearly all physicists would say the likelihood of FTL particles is extremely low.
Jesse M. #65,
You wrote: “But unless you assume relativity is correct (in which case FTL neutrinos imply causality violation), …”,
and yet the OPERA results shows that the neutrinos were recorded at Gran Sasso *after* the creation of the neutrino beam at CERN, which implies causality has *not* been violated even with a neutrino velocity measured slightly greater than c.
You wrote: “it’s possible the energy would approach infinity at some finite velocity greater than c (just as an electron’s energy goes to infinity as it approaches c) and give a “neutrino cone”.”
and yet a “neutrino cone”, if analogous to a light cone, implies that the neutrinos have a constant velocity (presumably slightly greater than c, if OPERA holds) regardless of the reference frame, otherwise the analogy would not hold (i.e., if neutrino velocity varies, there cannot be a “neutrino cone”).
Finally, you wrote: “Whether an FTL neutrino would have a maximum finite speed or could travel arbitrarily fast but not violate causality, I think this would imply a preferred reference frame.”
and yet a preferred reference frame does exist wrt to *time* (time is not a fundamental law of physics) since all local reference frames are subsets of a cosmological frame that connects all events into a single cosmos that is bounded in time (in the past) by the singularity. This is how we can even designate the universe to be 13.7 billion years old. This preferred frame does not violate relativity, as its laws act as a rule to transform between one frame and another depending on the local conditions that exist in each frame wrt the others.
@Dan T. Benedict:
and yet the OPERA results shows that the neutrinos were recorded at Gran Sasso *after* the creation of the neutrino beam at CERN, which implies causality has *not* been violated even with a neutrino velocity measured slightly greater than c.
I didn’t mean that any FTL signal transmission would involve a causality violation (you could in fact find a different inertial coordinate system where the signal was received earlier than it was sent, but “causality violation” means a cause having an effect in its own past light cone and that wouldn’t be the case for a one-way signal transmission). I just meant that if relativity is correct, then the existence of FTL signals implies it is guaranteed to be physically possible to design an experiment involving these signals where causality is violated, see my comment #33 above for details.
and yet a “neutrino cone”, if analogous to a light cone, implies that the neutrinos have a constant velocity (presumably slightly greater than c, if OPERA holds) regardless of the reference frame, otherwise the analogy would not hold (i.e., if neutrino velocity varies, there cannot be a “neutrino cone”).
No, under the inertial frames given by the Lorentz transformation, it’s easy to show that anything going faster than light must have different speeds in different frames, that’s just a property of the coordinate transformation. The “neutrino cone” idea implies that you could design a different coordinate transformation involving a different set of coordinate systems than those given by the Lorentz transformation, and in these new coordinate systems, neutrinos would have a constant speed while the speed of light rays would vary in different frames. Regardless of which set of coordinate systems you chose, there would be one unique frame where the two sets of cones aligned in the way I described in comment #65.
and yet a preferred reference frame does exist wrt to *time* (time is not a fundamental law of physics) since all local reference frames are subsets of a cosmological frame that connects all events into a single cosmos that is bounded in time (in the past) by the singularity.
There is no unique “cosmological frame”–a “frame” is just a coordinate system, and in the curved spacetime of general relativity you can use absolutely any crazy coordinate system on any given spacetime and the equations of general relativity will still work (see the comments in this article about “diffeomorphism invariance”), so there are an infinite number of different coordinate systems you could use to describe the entire history of the universe. But in any case, as I said earlier physicists would define a “preferred frame” in terms of the fundamental laws of physics working differently in one coordinate system than another, so specific physical events including the Big Bang aren’t really relevant to whether a preferred frame exists or not. Also, a “preferred frame” normally means a preferred inertial frame, and no coordinate system covering a large region of curved spacetime is considered “inertial”. But general relativity is “locally Lorentz-invariant” which basically means if you pick smaller and smaller patches of spacetime to look at, the laws of physics observed by a freefalling observer in that region get arbitrarily close to those seen in an inertial frame in special relativity (see this article on the equivalence principle). So when physicists talk about a preferred frame they really mean a breakdown in this local Lorentz-invariance, so even if you restricted your experiments to a very small region of space and time where the effects of gravity were negligible, you’d be able to pick out one locally inertial frame in which the laws of physics take a “special” form.
Jesse,
thanks for the reply and links.
1/ On Navikov. I was familiar with some of these ideas (the billiard balls I had studied briefly) and they are part of the gobbledigook I refer to. In a way self-consistency is a way of saying time travel without paradoxes by definition of ‘no paradoxes’. Time travel (back) is possible but if you get there you can’t touch”. Of course this makes for great sci-fi, as in the smoke monster in Lost, and back to the future, but I find it silly when it comes to physics. Are we to believe there is a completely separate branch of physics that limits your actions (of which we have no inkling today) just to satisfy the ‘self-consistent’ principle. Which means that yourself in the past are severely constrained (by what?) in what you can do. Again while intellectually amusing it is an example of the suspension of disbelief and complicated complications (which I enjoy) when “no causality violation” takes about 0.30s for my brain to compute as truth at a simple philosophical level. Causality is a deeper principle than SR (or symmetry since you seem to equate the two).
2/ Thanks for the link on SR/Aether BTW it is very informative and i intend to read 1 and 2 later. While I have developed a taste for aether research, I have a training in theoretical physics and renormalization of gauge theories felt normal at some point. I have left the field in disgust after my PhD mostly owning to a distaste for all the math based approaches, which while powerful and I could do them left me profoundly unhappy by being devoid of ‘common sense’ interpretation. I couldn’t connect the whole symmetry thing with ‘reality”. Of late, I have grown to appreciate that these symmetries, limit the possible oscillation and embrace aether as the medium for that oscillation. I have been looking into NYE crystal tensor formulation as with 23 degrees of liberty in the oscillations you can easily build a ‘particle/wave’ picture that has enough variables to address advanced problems like the standard model and gravity. Smolin’s approach to quantum loop gravity is a similar type of approach.
On predictive power. Here is the thing, since then, i have dabbled in biology, finance, macro economics, computers and have found that most science is profoundly messy. I too find profoundly puzzling that “math has such a predictive power” in physics, the link you give gives a great overview.
That is also to say that I don’t relate to the search for ‘beauty and unification’ in the math that so many people seem to get off on. I find the search for beauty in the models as distracting from the search for truth. There is no reason why truth should be beautiful, it is in fact quite ugly in biology and the math only gets you so far, I think it is an affliction of physics as exemplified in the smolin book for example.
But enough meta bla bla. Back to FTL neutrinos, from your comments I gather that you agree that FTL neutrino would imply a violation of lorentz invariance and thus SR locally, almost by definition. I think the question of time travel is void since it is an artefact of the lorentz transform and minkowski diagrams. It would be a great example of “truth doesn’t need to be pretty”, FTL violating neutrinos do not care what Einstein thinks.
I am with you on the cartoon, I will bet you 20 🙂
Going faster then light c, means that the object that is speeding faster as c, is going to catch up with signals that were emitted at c, so it can “see” the past, it is not going into the past !!!
keep on thinking free
Wilhelmus
I agree with you and that is my first ‘interpretation’ of FTL from a classic standpoint. However once you throw in lorentz transformation FTL DOES lead to time travel, hence proof by the absurd as far as I am concerned.
Most laymen don’t realize that the crux of the issue is not simply the speed-of-light (they think this news is great, faster spaceships! Star Trek here we come!) Not so fast! The issue at stake here is the very geometry of space (as we understand it).
I think sean is taking a very reasonable approach.
I would add that it is very likely that there is some systemic issue in how the neutrino speed was measured. It is very unlikely that we would not have noticed this already if it were true, or that we wouldn’t be able to find data that confirmed the observation independently.
The discover would mean that we would be able to determine if a supernova would occur before seeing it and other things. It would also mean that our cosmic horizon may have two frontiers that are of different distances but the exact same age.