Friday, May 22, 2020

Is faster-than-light travel possible?

Einstein said that nothing can travel faster than the speed of light. You have probably heard something like that. But is this really correct? This is what we will talk about today.


But first, a quick YouTube announcement. My channel has seen a lot of new subscribers in the past year. And I have noticed that the newcomers are really confused each time I upload a music video. They’re like oh my god she sings, what’s that? So, to make it easier for you, I will no longer post my music videos here, but I have set up a separate channel for those. This means if you want to continue seeing my music videos, please go and subscribe to my other channel.

Now about faster than light travel. To get the obvious out of the way, no one currently knows how to travel faster than light, so in this sense it’s not possible. But you already knew that and it’s not what I want to talk about. Instead, I want to talk about whether it is possible in principle. Like, is there anything actually preventing us from ever developing a technology for faster than light travel?

To find out let us first have a look at what Einstein really said. Einstein’s theory of Special Relativity contains a speed that all observers will measure to be the same. One can show that this is the speed of massless particles. And since the particles of light are, for all we currently know, massless, we usually identify this invariant speed with the speed of light. But if it turned out one day that the particles of light have a small, nonzero mass, then we would still have this invariant speed in Einstein’s theory, it just would not be the speed of light any more.

Next, Einstein also showed that if you have any particle which moves slower than the speed of light, then you cannot accelerate it to faster than the speed of light. You cannot do that because it would take an infinite amount of energy. And this is why you often hear that the speed of light is an upper limit.

However, there is nothing in Einstein’s theory that forbids a particle to move faster than light. You just don’t know how to accelerate anything to such a speed. So really Einstein did not rule out faster than light motion, he just said, no idea how to get there. However, there is a problem with particles that go faster than light, which is that for some observers they look like they go backwards in time. Really, that’s what the mathematics says.

And that, so the argument goes, is a big problem because once you can travel back in time, you can create causal paradoxes, the so-called “grandfather paradoxes”. The idea is, that you could go back in time, kill your own grandfather – accidentally, we hope – so that you would never be born and could not have travelled back in time to kill him, which does not make any sense whatsoever.

So, faster than light travel is a problem because it can lead to causal inconsistencies. At least that’s what most physicists will tell you or maybe have already told you. I will now explain why this is complete nonsense.

It’s not even hard to see what’s wrong with this argument. Imagine you have a particle that goes right to left backwards in time, what would it look like? It would look like a particle going left to right forward in time. These two descriptions are mathematically just entirely identical. A particle does not know which direction of time is forward.

*Our observation that forward in time is different than backward in time comes from entropy increase. It arises from the behavior of large numbers of particles together. If you have many particles together, you can still in principle reverse any particular process in time, but the reversed process will usually be extremely unlikely. Take the example of mixing dough. It’s very easy to get it mixed up and very difficult to unmix, though that is in principle possible.

In any case, you probably don’t need convincing that we do have an arrow of time and that arrow of time points towards more wrinkles. One direction is forward, the other one is not. That’s pretty obvious. Now the reason for the grandfather paradox is not faster than light travel, but it’s that these stories screw up the direction of the arrow of time. You are going back in time, yet you are getting older. *That is the inconsistency. But as long as you have a consistent arrow of time, there is nothing physically wrong with faster-than-light travel.

So, really, the argument from causal paradoxes is rubbish, they are easy to prevent, you just have to demand a consistent arrow of time. But there is another problem with faster-than-light travel and that comes from quantum mechanics. If you take into account quantum mechanics, then a particle that travels faster than light will destroy the universe, basically, which would be unfortunate. Also, it should already have happened, so the existence of faster-than-light particles seems to not agree with what we observe.

The reason is that particles which move faster than light can have negative energy. And in quantum mechanics you can create pairs of new particles provided you conserve the total energy. Now, if you have particles with negative energy, you can pair them with particles of positive energy, and then you can create arbitrarily many of these pairs from nothing. Physicists then say that the vacuum is unstable. Btw, since it is a common confusion, let me mention that anti-particles do NOT have negative energy. But faster than light particles can have negative energy.

This is clearly something to worry about. However, the conclusion depends on how seriously you take quantum theory. Personally I think quantum theory is not itself fundamental, but it is only an approximation to a better theory that has not yet been developed. The best evidence for this is the measurement problem which I talked about in an earlier video. So I think that this supposed problem with the vacuum instability comes from taking quantum mechanics too seriously.

Also, you can circumvent the problem with the negative energies if you travel faster than light by using wormholes because in this case you can use entirely normal particles. Wormholes are basically shortcuts in space. Instead of taking the long way from here to Andromeda, you could hop into one end of a wormhole and just reappear at the other end. Unfortunately, there are good reasons to think that wormholes don’t exist which I talked about in an earlier video.

In summary, there is no reason in principle why faster than light travel or faster than light communication is impossible. Maybe we just have not figured out how to do it.

317 comments:

  1. This comment has been removed by the author.

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    1. This comment has been removed by the author.

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    2. John, Instead of all this FileDropper nonsense, wouldn't it be easier, both for you and your potential readers, just to post your paper on Vixra ( https://vixra.org/ ) ? That's what it is there for. There would also be a permanent record of your contribution and when it was first made.

      Regards

      John R Ramsden

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    3. John,

      You need to set up your own blog, like Sabine's, with a comment section in which people can comment on your paper. It only takes a few minutes to do this.

      Most physicists will see an error right away, but it really is not relevant to Sabine's blog or her interests.

      Dave

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  2. Your verbal presentations here have been interesting and informative but the substance is the same as the text so to me really unnecessary.
    Following your conclusion that "Maybe we just have not figured out how to do it" must inevitably lead us to speculate on the existence of geometries beyond the space/time four dimensional world of General Relativity.
    Given that this the hobbyhorse of Cranks and Science fiction profiteers it must inevitably cause serious mathematicians and theoreticians to pause out side of string theory.
    Other than string theory is there any evidence of an alternate geometry? Is String Theory more than a convenient mathematical contrivance at the present time?
    The two questions are purely rhetorical.

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    1. Lockley,

      Some people prefer the written word, some prefer the spoken one. I am trying to find a time-efficient way to present content to both audiences, and (after quite some trial and error) this solution kind of works. For some purposes, I quite like having a medium that allows to show simple graphics. It can make things much easier.

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    2. Forgot to say, you don't need to change GR to have faster than light travel. Really as I said, there is nothing in Einstein's theory that forbids it. In fact, this is even easier to see in GR because most space-times (think FRW) have a preferred foliation already (usually induced by matter).

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  3. I'm very glad that you post now about this topic Sabine: following your submission to the APOD hosted Shapley - Curtis great debate anniversary (https://apod.nasa.gov/debate/debate100th.html) I have been recently trying to find out more about your argument.

    The first point, that c could be greater than the speed of light if photons are not massless, I think I understand well. To make sure I read the rest correctly, when subsequently you mention the speed of light, that is to be read as the speed of massless particles, in the case that photons are slower (in particular for the arguments of infinite energy acceleration and negative energy), is that correct?

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  4. Bonob,

    "To make sure I read the rest correctly, when subsequently you mention the speed of light, that is to be read as the speed of massless particles"

    Yes, unfortunately it only occurred to me after recording the video that I should have said that explicitly.

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  5. Dough is not that difficult to un-mix! Feed the farmer and the chickens and you will get back the eggs and the flour!

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    1. In case your response was not just intended to be amusing: that way of ‘unmixing’ does not decrease the total entropy in the universe though, so that’s just redefining ‘mixing’ relative to what the author intended.

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    2. My apt Confusion: Esteemed's intention notwithstanding, Muses indeed demure the matter.

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  6. Sabine,

    You have missed the real reason while traveling back in time is incompatible with General Relativity: It postulates the uniqueness (single-valuedness) of the metric tensor, modulo diffeomorphisms, for each spacetime point. The particular form of the theory does not even matter, as long as there is a surjective mapping from the metric to the stress-energy tensor. Anything like "time travel" would imply two different "objects", i.e. two different stress-energy tensors at the same spacetime point, the "initial" one and the "traveled back in time" one, breaking this surjectivity.

    Note that this is not an issue in Special Relativity, or even in the QFT on a curved spacetime. As long as we treat the spacetime itself as a background, there is no requirement for the uniqueness of the stress energy tensor in the theory.

    For the same reason it is impossible to enter or exit, or, for that matter, to observe, a closed spacetime curve. Best one can do is to run into a Cauchy horizon, I think.

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    1. Sergei,

      "Anything like "time travel" would imply two different "objects", i.e. two different stress-energy tensors at the same spacetime point, the "initial" one and the "traveled back in time" one, breaking this surjectivity."

      No, it would not. You are really confused about what "faster than light" travel means. Just because something can go faster than light does not mean you have causation backwards in time. These are just not the same things, as I explained in my video. You can easily prevent any kinds of paradoxa by noticing the existence of an arrow of time. (I am certainly not claiming this is a new insight. It is however a badly communicated one.)

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    2. > You are really confused about what "faster than light" travel means.

      Uh... I don't think I am. Indeed FTL and time travel are different things. GR does not preclude FTL, only the time travel. We don't disagree at all here. Though FTL would be hard to deal with numerically as an IVP, as I had mentioned in the other comment.

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    3. Good then, it seems we agree. This is what I said in my video.

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    4. Sergei wrote:
      > Indeed FTL and time travel are different things. GR does not preclude FTL, only the time travel.

      Sergei, it is an elementary (and very well known) fact that FTL even in special relativity implies time travel. In one frame, you go faster than light. In another frame you have gone backward in time. Simple.

      It is also straightforward to draw a specetime diagram in which you do this twice and end up in the past light-cone of the point you started at.

      I think you are thinking of just standing still and reversing your direction of time. Yes, then you would collide with yourself a nanosecond (or femtosecond or whatever) earlier.

      Time travel in relativity necessarily also involves spatial displacement.

      Kip Thorne goes into this in some detail in his Black Holes and Time Warps, so if you want to be combative about this, please fight it out with the Nobel laureate Professor Thorne. (I talked with Kip about this when I took GR from him back in 1975-76: this has been well-known for a very long time!)

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  7. The following was triggered by "Our observation that forward in time is different than backward in time comes from entropy increase."

    I just don't get the "entropy determines the Arrow of Time" principle (if it is one). To me, it seems that the arrow of time determines (the growth of) entropy, that is, entropy is statistically likely to increase in the order that events happen. Perhaps that is also consistent with the triggering phrase, but I have gotten the impression that at least some physichists actually do consider entropy growth to be a causal factor rather than just a correlation, which to me is the cart pushing the horse.

    For me, the order of time is determined by the order in which I experience events, which in turn is determined by my memories of those events (both internally and externally--as I type characters here the further back they are on the page, the further back they occurred in time). Digging up fossils would be another instance of external memory.

    At the same time entropy is generally increasing (there is perhaps more nonsense on the page then when I started), but it seems to me that I could observe a (rare) occurrence of entropy decrease without that having any effect on my perceived direction of time. For example, I could start backspacing and reducing the entropy of this page and I would still perceive time going forward as I did so. (In that case I would be relying on internal memory.)

    Of course, other than that slight triggering I enjoyed the post and learned from it.

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    1. JimV,

      Well, you can of course just postulate a fundamental arrow of time, but the point is that it is not necessary, entropy increase give you one and that is all you really need.

      That entropy is statistically likely to increase is a tautology because entropy counts how statistically likely a state is. Really the relevant part of the arrow of time is not that entropy wants to increase per se, but that the universe started from an initial state that was statisically unlikely. We started from low entropy. This is known as the "past hypothesis" and really without it you can't explain anything about the universe. Probably the must under-appreciated hypothesis in science ever.

      And, yes, you can indeed observe a spontaneous decrease of entropy in small systems. In fact, people have done that. It makes headlines of the type that physicists reversed time and similar things. This interpretation however makes no sense because the direction of time is the aggregate effect. So what it really means is that you have fluctuations around the mean. Doesn't make a good headline though. (This is not to belittle the experiments per se, usually on tiny quantum systems, which are in fact quite interesting.)

      Or, to put it differently, if entropy decreases in some small system that you happen to observe, this bears no relevance to the likely evolution of the system that is you.

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    2. Thank you for the reply. I'm sorry I still don't get it (why we should think about time as entropy growth rather than as new (unrecorded) events occurring; granted, entropy growth is important in itself), other than perhaps a vague hint that I should think more about. Meanwhile,

      a) The statistically likely growth of entropy does make a fine tautalogy but that does not diminish its importance (to me). Afterall, creationists dismiss "survival of the fittest" as just a tautalogy but it still provides a mechanism, as does the basis of entropy's statistical likelihood. That is, I think a billiards-table simulation based on high-school physics will demonstrate how entropy grows as more events occur. (Faster balls tend to lose energy to slower balls.)

      b) About the low-entropy starting point, it occurs to me to wonder this: what if another Big Bang event were to occur now somewhere in the observable universe, following by the postulated inflation period (assuming that theory is correct). After that BB2 inflated and produced new stars and galactic structures, what would be the difference between what its inhabitants would see 14 billion years from now and what we see today? (Due to that BB2 starting at our current entropy+BB2_entropy rather than just BB2_entropy.)

      Probably that is an old question with an old answer, but it is new to me. Not that I deserve an answer. My guess is that universe would look much the same, but would again have a much higher entropy than it started with at BB2. However, for me that would relocate the issue from "why did the universe start with such a low entropy" to "how do Big Bangs produce such a reservoir of low entropy", or something like that.

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    3. Hi JimV,

      a) I didn't mean to say it's unimportant. I just meant to say that the statement that the universe is likely to evolve into the most likely state only explains observations together with the assumption that started from an unlikely state. (Otherwise you sit in thermal equilibrium forever, up to small fluctuations.)

      b) Yes, excellent question. In fact, entropy increase/the arrow of time is the biggest problem with the idea that the evolution of the universe is cyclic. This really only works if you find a way to decrease entropy. I don't know what you mean, however, with "another big bang event somewhere in the observable universe". The big bang is an event for the whole universe, it's not a local one.

      (Btw, Sean Carroll's book "From Here to Eternity" is basically about this question.)

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    4. I do not understand how someone can be sure initial state at the big bang had low entropy. How did you calculate it?
      A lot of your blog deals with nonsense about fine tuning, when you say someone to put it true should know in advance probability distribution of phisical theories to calculate parameter as fine tuned.

      But now you are saying that you know probability distribution ( or system phase space) for all possible universes and are able to calculate entropy related to initial big bang state? Could you start with simply description of this state?

      Is it related to the fact it was "concentrated" ( big density, big temperature)? Is black hole state of low entropy or maximum entropy?

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    5. Kakaz,

      "I do not understand how someone can be sure initial state at the big bang had low entropy. How did you calculate it?"

      You are missing the point. If the initial state did not have low entropy you can't explain why our universe evolved in the way that we observe. Please look up "Past hypothesis".

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  8. Another point, regarding faster than light travel.

    There are plenty of spacetimes that contain superluminal matter flows. For example, is easy to create one from a 4+1 Schwarzschild by applying a dimensional reduction with respect to one of the U(1) Killing vectors. You end up with an asymptotically flat spherically symmetric 3+1 spacetime with the stress energy tensor that violates the Dominant energy condition that does not contradict the covariant formulation of General Relativity.

    However, if you were to cast it into a Cauchy problem, you would find that, while you can find a suitable initial hypersurface (unlike, say, in the Godel spacetime), you cannot evolve it, as the evolution equations would not be globally hyperbolic (because of the FTL effects), and so you would run into problems trying to "push" the initial slice even one step along any timelike direction.

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    1. World's fully with people who will tell you that a non-globally hyperbolic space is a good thing, not a bad. In any case, I don't see the relevance. Are there manifolds with weird causal structure? Yes. Does this rule out faster than light travel? No.

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    2. There was a paper submitted a few years ago, one author named Luk as I recall, that demonstrated how the timelike region in a Kerr black hole is similar to that Sergei shows here. There is no spatial surface that is an evolute of another. This is similar to the Donaldson et al theorems on exotic R^4 spaces that are homeomorphic but not diffeomorphic.

      It is not clear that an observer can fall into a Kerr black hole and reach this interior region. The inner horizon is a Cauchy horizon that may act as a mass-inflation singularity that might have nasty and lethal surprises.

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    3. Doesn't rule out, nope. All one needs is enough negative energy to build an Alcubierre drive or a similar setup.


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  9. Thanks for this; very interesting!

    One thought that I have is the kind of conclusion we draw here depends on our attitude to the description of reality in SR and other theories.

    So if travelling faster than the invariant speed in SR in some frame would imply, geometrically, that you would be going backwards in time in whatever frame we're talking about, we can regard this telling us that either:

    1. That, were you able to find a way to accelerate to a speed faster than c you would go backwards in time;
    2. That, as there are a bunch of paradoxes associated with going backwards in time, this must mean that you cannot ever go faster than c (and you point out reasons why this isn't a very good argument);

    Or, and I think that this might be the case, 3. that the weird implication of going backwards in time occurs because the particular geometric description of reality that we are using here, while hugely powerful and incisive, breaks down in certain situations. So similarly to how we think that the prediction of GR that a black hole will form an actual honest-to-goodness singularity is indicative of the theory breaking down in this regime, so going backwards in time is perhaps a sign that we have overextended the applicability of the description we are using.

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  10. Just a thought. In a big bang universe space is expanding faster than light, but in a situation where our observations of expansion, could be simulated by repulsive gravity, then it would just be matter being pushed apart from other matter inside a static universe. In this case it seems that matter could never exceed the speed of light.

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  11. Hi Sabine,

    You state in your article: "Imagine you have a particle that goes right to left backwards in time, what would it look like? It would look like a particle going left to right forward in time. These two descriptions are mathematically just entirely identical. A particle does not know which direction of time is forward. "

    It seems to me that you are making a pretty big assumption here.

    How do you know particles don't understand the direction of timeflow? Perhaps the individual particles are "the things that DO know" the forward direction of time flow. All the evidence suggests that they do, the mathematical equations of motion give a physical forward timeflow, and the result is the universe that we observe.

    Also, the statement is technically incorrect. The one symmetry that has never been observed to be violated is the CPT symmetry (Charge/Parity/TimeReverse). A particle moving backwards in spacetime must also be charge-conjugated to be identically equivalent to a particle moving forward in spacetime. Thus, an anti-matter particle (C) going backward in space & time (P&T) is equivalent to its normal-matter partner moving forward in spacetime.

    I am also looking at Intro to SR, 2nd Ed., Wolfgang Rindler, pg. 17-18.
    He lays out the argument about a "Relativistic Speed Limit", which leads to the causal-paradox problem.
    Essentially, if you have that ability to send messages at FTL, you can send a message into your own past, which could then change events such that you wouldn't send out the message. To my knowledge, no one has yet observed a causal paradox.

    Can you please point out more specifically his mathematics mistake and how this is "complete nonsense"?

    John Wilson

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    1. John,

      I am not making an "assumption" I am merely telling you how it is in the theories that we currently use.

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  12. Dear Sabine,

    You've really made me think with this one.

    By weaving Boltzmann time into your analysis of time travel, I think you are at least indirectly making an argument for the existence of a canonical frame.

    That's because Boltzmann time is always local. Entanglement influences local Boltzmann time, but only in ways that are undetectable. By adding transfers of real data, though, every local Boltzmann time metric can message and thus record itself in every other local Boltzmann in the universe. That is... yes, that is very hard to get around. Thus you have unavoidably created a truly universal Boltzmann time metric, and thus a canonical frame for that metric.

    But am I reading you correctly on that point? From the above argument... well, I don't think it matters. You did it, even if unintentionally.

    Unlike many, I have no problem with the concept of a canonical frame, but only as long as the Poincaré-Lorentz-Einstein-Minkowski (call it Gang of Four) symmetries are absolutely conserved.

    I've gone through Gang of Four symmetries in enough detail, looking for holes for entanglement. From that I am at this point deeply convinced that the Gang of Four got it exactly right: Their symmetries are never broken, not by any effect known, and not even by quantum entanglement. Direction-asymmetric time dilation always ensures that each frame sees its own space-like view as the one that drives all causality in the universe, even though all other frames will see that same frame as half in their past and half in their future. But after you apply the asymmetric, direction-dependent time dilations, it doesn't matter: every frame ends up seeing itself as fully and self-consistently causal.

    I like to explicitly label this equality as "causal symmetry", but it's hardly profound, since it is implicit in every assertion that "physics is the same in all frames". You cannot have same-physics without same-causality, duh! The result is delightful in any case: A single canonical frame is all you need to keep the universe and all of its many frames evolving. However, no one in any frame can perform any classical or quantum experiment that can tell whose frame is the canonical one! There are times when the universe is perverse in a delightfully ego-satisfying way: We are all at its center!

    What I've never attempted to analyze is whether information transfers in a canonical frame can maintain Gang of Four symmetries. I always assumed that would be a flat violation, but dang it, now you've gone and opened up a can of worms by pointing out (at least in my reading of it) that as long as your canonical frame maintains statistically irreversible Boltzmann time direction and causality, who cares if real information is also transferred? Wow. Hmm!

    So, I do already have one insufficiently examined hypothesis:

    If superluminal transfer of true information — not just of entanglement wave function resets — really is experimentally possible, then it will be possible to use such effects to determine which is the canonical frame of the universe, the single frame that drives all of causality. (It would necessarily be a CMB-ish frame, incidentally, since that is the only one that minimizes total relativistic energy in its space-like view.)

    So... yes, I think your concept of superluminal real-data transfer must necessarily violate Gang of Four symmetries, but in a narrow and very specific way: A non-canonical frame traveler will be able to see "future predictions" arriving from their trailing edge (relative to canonical frame and the real past), but will never see prophesies coming from their leading edge (again relative to canonical, and thus the genuinely undetermined Boltzmann future).

    And again... wow, dunno, gotta think about that. But I think it can be made Boltzmann compatible. True prophecy... but only for really fast movers!

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    1. And to answer my own hypothesis:

      Yes: If superluminal transfers of true, causality-impacting data are possible, it would necessarily collapse the entire universe into a single universe-spanning fabric of Boltzmann time. It would also make identification of that frame trivial: It would be the frame with the fastest clocks.

      Imagine that observers in every frame had such instantaneous communication ansibles (the Le Guin term), and could broadcast to anyone else. The resulting enforcement of shared Boltzmann local causality — the resulting Boltzmann fabric — would still follow special relativity symmetries, making all non-canonical frames appear slower. However, since the canonical frame defines causality, all of those other frames would be slower in real clock rates, not just relative clock rates. They would become fast-moving, slow-clock subunits of the canonical fabric, rather than independent fabrics. Yet as long as these subunits rely only on speed-of-light communications, they would continue to see the special relativity symmetries that make them think they are the fastest-clock frame.

      The moment such non-canonical frames turn on their own ansibles, however, they will discover it was an illusion: They are not the fastest-clock frames after all. Also, what appeared to be ansible “prophesies” would simply be them being held back in time. The Boltzmann “now” of the slower-clock travelers would be just as real as that of any other faster frame, so those frames would have no more control over the future of the travelers than they do over their own futures.

      What you with ansibles is not causality, but full adherence to special relativity. Once the ansibles begin broadcasting, the temporal illusions of special relativity will be shattered and the fastest-clock canonical frame revealed.

      To phrase that as an experiment: Launch an ansible with an atomic clock towards Pisces/Pegasus at about 370 km/s, which will place it roughly in the CMB frame that is mostly likely to be characteristic of the canonical frame When the probe uses its ansible, its atomic clock should be running about 0.76 millionths faster than the same atomic clock here on earth.

      I am personally very reluctant to abandon the Gang of Four symmetries, since I suspect they are more fundamental to the existence of classical physics than we realize. But who knows? If a superluminal true-data transmission mechanism is someday found, wouldn’t that be extraordinary? Pragmatic applications aside, such a find would necessarily reduce the universe into a single Boltzmann state space. Accelerated frames would become nothing more than fast-moving, slow-ticking subunits of that Boltzmann fabric, and gravity its long-range topology. But causality would remain undamaged, which is remarkable!

      This brings up my final point: Given that there is still entanglement to explain, why not just “go canonical” anyway, even in the absence of ansibles?

      One of the important lessons of modern computers is that a single state space is capable of sustaining an indefinitely number of virtual worlds — virtual frames — that seem just as real as the primary world. We do this kind of context-based virtualization all the time on smart phones. For the universe version, the only catch is that virtualization would have a resource cost. But it already does! In the real universe the cost of creating a frame for an object would be the energy required to accelerate that object to a higher velocity.

      So: If a canonical frame with Boltzmann time enables all of known physics without paradox, why shouldn’t the real universe be just as efficient?

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    2. Erratum to my immediately previous post, start of paragraph 5:
      "What you with ansibles"
      --> "What you lose with ansibles"

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  13. Traveling really fast has its own peril. If you encounter just a grain of sand while cruising at say 10% of the speed of light, that encounter is equivalent to a Hiroshima nuke going off on your vessel. That's why we will never go anywhere far away unless we get star trek warpspace going.

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  14. A few points on this seem odd. There is some difference between traveling faster than light and multiply connected spacetimes or spacetimes with closed timelike curves. In Minkowski flat spacetime the energy momentum interval m^2 = E^2 - p^2, here taking c = 1, for faster then light interval is such that m^2 < 1, or that the mass m is imaginary valued. This is called the tachyon. Now for the Klein-Gordon equation with □φ - m^2φ = 0, then m^2, or with units restored (mc/ħ)^2 [1/Compton wavelength squared], is a sort of potential and this is negative. This is one way to see that the vacuum is unstable. This is a bit like a spring that pushes outwards more the greater it is distended, not an ordinary spring, and where with even the slightest distention will then accelerate away.

    The tachyon and the negative energy vacuum are then related. A tachyon is an odd beast. It is not hard to draw a 2-dimensional spacetime diagram with 45-deg lines being null rays, vertical a local time direction and horizontal space. A timelike straight path is more vertical and the spacelike or faster than light path more horizonal. Now draw 45-deg line from the spacelike path to the timelike one. It is not hard to see that an observer on the timelike curve would see the tachyon appear at a point and split off in opposite directions. The bosonic string has a negative energy vacuum plus tachyon, Since all the other string theories are related to the bosonic string by STU duality or transformations this is one reason string theory loves the anti-de Sitter spacetime, which has a negative vacuum energy or equivalently a negative cosmological constant. The universe we observe is more de Sitter-like or FLRW with positive vacuum and cosmological constant.

    It the AdS spacetime is related to black hole Boulware vacuum with negative vacuum energy seen in wormholes. I recently got a paper published on the energy condition between two near colliding black holes and this is locally AdS-like. This is a sort of gravitational form of the Casimir effect, and this has been suggested as a way to make a wormhole. The point of this paper is quantum hair in this Casimir effect will have subtle quantum graviton physics in gravitational waves. Kip Thorne has been a big exponent of wormholes, where he was the science advisor for the 2014 film Interstellar that featured a wormhole as a tunnel to a region with a giant black hole. However, in order to do this it requires the vacuum energy be negative over a large distance, or for there to be some quantum fluctuation of negative energy across a vast distance, This would mean changing the structure of maybe the entire universe
    The AdS and dS spacetimes can be thought of as hyperboloid sheets around a double cone. The AdS is one of two sheets inside the two cones, and the dS is a single sheet hyperboloid on the outside of the double cone. This though has two distinct patches with a boundary that is spacelike if the spatial surface is a sphere, lightlike or null if the spacelike surface is a flat R^3 space and timelike if the spatial surface is hyperbolic or “saddle shaped.” It is possible the inflationary manifold is a dS. Is there then a relationship between the dS and AdS? They are curiously related in a way not too different from Dirac cone conditions on a Haldane chain. This then again might suggest that if we were to really make wormholes and the like we could flip the vacuum structure of the universe, or some expanding bubble in this universe. If you think about it, we will not want to go there even if we can do this.

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  15. Continued from above post due to space limitations:

    This holds I think for other exotic spacetimes such as the Alcubierre warp drive. If we think about it on a very elementary level a particle that moves through space has v’ = v + at, for v velocity and a acceleration. Similarly the distance this particle travels is easily found with the average velocity d = (v’ + v)t/2. Then it is easy to see ½(v’^2 - v^2) = ad, which is an equation we teach freshman students. Multiplying this by mass gives kinetic energy and work = force times displacement. We then have with the first of these equations the transformation of momentum by acceleration and this results in an equation for kinetic energy. This in turn is conserved, or homogeneity of time gives a Nöther theorem result energy is conserved. This means energy conservation, at least as we know it, requires the transformation of momentum etc in a singly connected topology. There are not two different displacements that connect two points that can’t be diffeomorphically mapped into each other. I would then argue the spacetime we are in is the topologically obstructed from permitting multiply connected topology such as wormholes.

    Again, this is not the same as logically impossible. The AdS can be said to exist, or more likely at least the CFT it is dual to on the conformal boundary. We just are not in that sort of spacetime. I would then argue that while faster than light motion is not prohibited in relativity, we are blocked from it, at last locally. The question of course is where does the AdS and all this string/M-theory fit into things, Well, that is the knotty problem, or is it naughty? This is where we meet the barrier to our understanding. David Deutsche suggested a way out of the so called grandfather paradox if we assume the time traveler path is a quantum amplitude. If there are dual or quantum correlated states between say AdS and dS this might be a way of addressing this problem

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  16. This blog text was a disappointment, I think.

    Let me explain. In science miracles are banned.

    You can ask if a human can birth a fish. In common language there could be stories that it can happen or maybe an odd religious tell to wait this kinda miracle and then heavens will be open.

    In science a fish-like human baby is a bad prediction -> no science at all, but a miracle.

    There are two answers to the question of the blog subject:
    - yes, there are routes where light spend more time than in the most optimal route (but wormholes are miracles)
    - no, the local speed of light over vacuum is defined to be maximum speed of causal information change AND this idea gives brilliant predictions (the speed limit for information is science)

    By the theory of relativity there is the concept of proper speed; the speed of observer in respect of the supposed isotropic environment. This speed can limit arbitarily near to infinity and light speed in these kind of frame can be said to be infinite.

    For science sake, don't touch infinity with physicality or especially don't imagine the speed over infinite being physical!

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  17. I think wormholes offered as a way for normal-matter particles to go superluminally is not really satisfying, because for a wormhole metric to be a solution to GR, it has to be supported by matter which is not normal (ie, violates energy conditions.) So even if your test particle falling through the wormhole is totally reasonable, somewhere else you've got to have a pile of exotic matter.

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    1. That's right, as I previously explained here.

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    2. That article of yours was definitely no disappointment :)

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  18. I think it is not correct to refer to causal considerations as "rubbish". Rather I would say, "incomplete". The real problem is that tachyons cannot ever go *slower* than C. Therefore they cannot interact with bradyons. And since we live in the causal world of bradyons, there is really nothing you can say about the non-causal world of tachyons except that it is inaccessible and unknowable. Which is equivalent to saying, it doesn't exist.

    The geometry of spacetime is definitely tied to causal order through the light cone. One way to think of spacetime is as a projective metric geometry with a degenerate ideal domain (the light cone). Euclidean geometry is the same thing, with a different degenerate ideal domain. In each case the degeneracy brings in affine physical features.

    -drl

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  19. Dr. Hossenfelder,

    Thank you so much for this post as your timing for me is impeccable. For about the last week I have been contemplating "time" as it relates to faster than light travel. CERN accelerates protons, which have mass, to 99.9999991 percent the speed of light without creating proton mass greatly approaching infinite so it seems that the speed of light is not as big an obstacle that it can be made out to be with respect to mass. Similarly, there are other theories associated with the speed of light from tachyon particles, variable light speed, gamma ray bursts and cosmic inflation to name a few. But for me time seems to be a bit of a sticking point.

    Consider a traveler from the Andromeda coming to earth for a visit. He is here for a year, our time, and looks up to the night sky to see his galaxy shining back at him so he gets home sick and decides to go home. However, because it takes the light from the Andromeda galaxy 2.5 million years to get here he does not know his home world in Andromeda was destroyed by a supernova 3 weeks ago, our time. And he could not know that this has occurred for 2.5 million years our time. Just a bit of a conundrum.

    For me we are missing something with respect to time and its passage, not with respect to travel speed. This belief is also indicated by your wormhole example. I believe that we could also say that the various options for faster than light or great distance travel is showing us that we are missing something with respect to time.

    Thank you Dr. Hossenfelder, I have a been more to add to my thinking now.

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    1. Steve,

      The mass of the proton is invariant. It does not change if you speed up the proton. What changes is the energy.

      This is a very common confusion and it comes about because historically physicists used something called the relativistic mass which does change with speed. No one uses this today any more, so the best is to just forget about it. The masses of elementary particles are constants of nature.

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    2. The relativistic gamma factor γ = 1/√(1 - β^2) for β = v/c is such that for β = .99999999 is γ = 7071. This means that Andromeda at 2.5 million light years will be reached by a traveler at this speed in 354 years. This assume the acceleration time is rather brief. The velocity of an accelerated body is v = c tanh(gs/c), for s the proper time on the accelerated frame. For g = 1g or 9.8m/s^2. The proper time required to reach a terminal velocity is s = (g/c)atanh(v/c). for β = .99999999 is about 30,000 seconds or about 21 days. The same would hold for acceleration or deceleration upon reaching the Milky Way. That is a bit of time still to travel between galaxies, and this time 354 years ago is around the time of the Great London Fire and plague and when Newton went home, sort of the 17th century lockdown, and contemplated ideas that went into his De Motu.

      What Sabine says about relativistic mass is the modern idea or maybe better put usage. Momentum is p = γmv and energy is E = γmc^2. This means for (mc^2)^2 = E^2 - (pc)^2 the mass is invariant and energy is E^2 = m^2(γ^2v^2 + c^2) = K^2 + (mc^2)^2, or kinetic energy plus rest mass energy. The difference between relativistic energy and relativistic mass is the little matter of c^2, so the issue is a bit of a trifle. However, the notion of relativistic mass was used less because it caused people, often with elementary level students, confusion that somehow on the frame of a moving mass that the mass would increase.

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    3. Sabine, you say:

      “The mass of the proton is invariant. It does not change if you speed up the proton. What changes is the energy.”

      My question here: do you distinguish between mass and inertia as different entities? You should do it in this case, because for a fast proton the inertia is increased, which means that its acceleration needs a higher force than the acceleration of a slow or resting one. That is an experimental fact.

      And what describes the Higgs mechanism? Does it describe the mass of a particle or its inertia? The Higgs mechanism is a dynamical process, i.e. the interaction between the particle in view and the virtual particles of the Higgs field. Should we assume that this dynamical process is not affected by relativistic influences? That would sound unphysical to me.

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    4. antooneo,

      It seems you have some rather basic problems of comprehension. Please put these questions forward in a forum and not here.

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    5. Antooneo: In thinking about physics it is important to think in a certain domain, or in a sense to wear different hats depending upon the domain you are talking about. Here really, we are talking about special relativity. A crucial aspect of this is the interval or length s given by a proper time τ as s = cτ. This is an invariant and given by coordinates x, y, z and coordinate time t according to a modified form of the Pythagorean formula as

      s^2 = (cτ)^2 = (ct)^2 – x^2 – y^2 – z^2

      Here the proper time τ is the time a clock on a path measures on that path, In mechanics there is a big dualism between coordinates and momenta, and classical mechanics is framed by Hamiltonian formalism this way. With wave mechanics there is a dualism between time and frequency. Frequency is also directly proportional to energy. So the above length of a path in special relativity has a dual form with momentum p and energy E as

      (mc^2)^2 = E^2 – (pc)^2,

      where now just as the proper time is the invariant in coordinates of space and time, now mass or mc^2 is the invariant. This is what is meant by the mass of a particle is the invariant.

      Now, if we change hats and think of the Higgs field things becomes a bit more subtle. The Higgs field has Goldstone bosons H^± or a doublet (H^+, H^-) and (H^0, h) where the H^± Goldstone bosons couple to the charged flavor changing weak gauge bosons and the H^0 Goldstone boson couples to the neutral current weak boson. The h boson is free, and this is what the LHC detected. This also couples to fermion particles in Yukawa Lagrangians of the form ℒ = gψ-barHψ, which if H is H_0 couples a fermion to itself, and the charged H^± flips different flavors of fermion doublets, such as leptons to their neutrinos or between quarks. This then defines a fermion mass ~ m^2|ψ|^2.

      What does this have to do with the invariant mass of special relativity? At very high energy the invariant momentum-energy interval is

      0 = E^2 – (pc)^2,

      which applies to the massless photon. The weak gauge fields and fermions are massless when they interact at TeV high energy. These Goldstone bosons are a sort of quantum condensate that form a “goo: that particles couple to at low energy, but at higher energy those particles decouple from this Higgs condensate. The two domains of physics occur at different vacua, where the high energy physics is called a false vacuum that is not stable, and then the lower energy vacuum is stable where the Higgs field gives mass to particles. This high vs low energy has to do with the energy of interactions. A proton moving at TeV kinetic energy is on its frame the same as a particle sitting still. Things becomes more complicated when there are interactions.

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    6. Sabine,

      What is the problem here? You have stated that Energy increases at particle’s motion but mass does not. But we know the formula ..
      E = m * c^2, where c is a constant. So I was surprised about your statement and wanted to say this in a polite way.

      Maybe the use of this notion has changed with time, but I have worked for a big electron accelerator for several years and our everyday wording was that “mass increases at motion”. Is it really so bad to say this?


      Lawrence Crowell,

      thank you for your explanation. I am working on relativity since
      > 20 years and I am quite familiar with it; even though I do not follow Einstein in any detail. I also give talks at conferences, so it is not so strange to me.

      The point with the Higgs mechanism is that it depends on the Higgs field, whereas astronomy tells us that this Higgs field does not exist. This is one of the problems of present physics which seem to be accepted by the community. Anyway, also this assumed mechanism has to reflect relativity, and it should do it quantitatively.

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    7. Antooneo,

      This is the special case for p=0 as Lawrence correctly says. Again, could you please keep off-topic questions out of my comment section, thank you.

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    9. Antooneo,

      Where did you get the idea astronomy indicates the Higgs field does not exist? Astronomy says almost nothing about that.

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    10. Lawrence Crowell,

      Astronomy says that the Higgs field is incompatible with the cosmological constant by at least 56 orders of magnitude.
      Please see as a reference:
      Steven D. Brass, The cosmological constant puzzle, Journal of Physics G, Nuclear and Particle Physics 38, 4(2011) 43201

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    11. Antooneo,

      No, astronomy does not say anything about the vacuum expectation values of the Higgs field because the cosmological constant is a free parameter in GR. I explained this here. As I have said several time, if the cosmological constant was such a terrible prediction that what theory was ruled out by it? None. And why is that? Because it wasn't a prediction in the first place.

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    12. Lawrence Crowell said >The proper time required to reach a terminal velocity is s = (g/c)atanh(v/c). for β = .99999999 is about 30,000 seconds or about 21 days.<

      Hmmm, when I accelerate at 1g, after 30 thousand seconds my speed is still three magnitude orders below c, so relativistic effects are not significant, yet. Perhaps to approach c, 30 million seconds was meant (and BTW s/h conversion is 60^2, not 60)? Still it’s only about 1 year each for ±accelerated departure/arrival, so still not very significant relative to the proposed relativistic coasting in between for 354 years, which itself is however quite arbitrarily based on an eight nines approach to c. Why not six nines for a more leisurely 3536 years; or ten nines for intergalactic travel in decades?

      Nonetheless, given FLT and the equivalence principle, I find classic travel (say in a windowless vessel) at 1g for the duration rather more comfortable (except for the flip-over maneuver made midway), which makes my return to Andromeda precisely 3109 years.* However, my round trip (plus whatever time I’ve dallied here) must be added to the 5 million light-year roundtrip in order to tally the local time that’ll have passed there since I left.

      Alas I won’t be able to tell them anything they hadn’t already seen, as the arrow of time won’t be denied; the effect indeed manifests everywhere, even when I work up to a roundtrip stroll to the grocery, as excess energies are dissipated via blue-shift (just a bit less noticeably). But that I suspect is what Sabine will be talking about next time.

      *e.g. 2 ( ½•9.81 (3109/2)² •365.246 •24 •60² /3E8 ) = 2.5E6 light-years traveled in 3109 years. Thus FTL travel time to Proxima Centauri is 4.05 years; Sirius 5.77 years; Betelgeuse 49.8 years; Sagittarius A* 315 years.

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    13. I guess I did something wrong with the calculator. I wrote s = (g/c)atanh(v/c), which is from v = c tanh(sc/g) for s the proper time. It is easy to see that for v = .99999999c my get with my calculator 2.52×10^8sec, where for some reason I am now getting a larger number. That is 8 years. It is still a smaller percentage of 350 or so years.

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    14. Sabine,

      I have looked into your referenced blog.
      Why is a comparison of influences (“ratio”) not possible? As far as I know, the cosmological models which are about the development of the universe have the pressure of it as an essential argument. There are positive and negative contributions to this pressure by the different fields and processes. These contributions can be summed up, why not? And so a comparison of these influences should be possible.

      As an explanation of the actual observation with respect to the cosmological constant (measurements of Riess, Permutter) there is a certain ‘dark energy’ assumed as we know. Is this a bad idea in the scope of present main stream? And if this question of a specific energy is investigated, what is wrong about the way to look at all energies which exist here? The vacuum fluctuations mean an energy. And the Higgs field as well.

      I have given above a reference to a paper about this. I can give another one about the topic:
      Frank J. Tipler, Genesis: How the Universe Began, arXiv:astro-ph/0111520v1 28 Nov 2001.

      Are those totally wrong? And apart from this, I know several professors of particle physics who still say that this is an unresolved problem. If your consideration is the solution for this problem, why do they not follow? Nobody wants unresolved problems. - At least you have a special minority position here (which I am quite familiar with).

      The Higgs model on the other hand is anyway unsatisfying as it does no give us any answer to the mass of a specific particle. I know another model which yields results which are correct by better than 10^-5. And it does not contain any adaptable parameters, only known constants. But not main stream, unfortunately.

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    15. Yes, a relativistic vessel (one with windows to observe its speed against the stars) takes 2.92E8 seconds (almost ten years) at g to arbitrarily attain eight nines approach to c, in order to coast wide voids in mere centuries (or for arbitrary less time: arbitrarily more nines - so the theory goes). However β = 0.761 as classically fixed by s = c/g = 30.6 million seconds (about a year, as I said) offers a threshold into all this FTL arbitrariness, one that’s both unattainable and imperceptible when it’s fallen through (which is why my vessel has no windows).

      The universe is quite tolerant of (perhaps even built to encourage) blissfully ignorant rule-breakers, as everything tends to work itself out. It’s a very important thing to re-member, so I talk about it.

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    16. antooneo asked:
      >I have given above a reference to a paper about this. I can give another one about the topic:
      > Frank J. Tipler, Genesis: How the Universe Began, arXiv:astro-ph/0111520v1 28 Nov 2001.

      >Are those totally wrong?

      Well... let's be polite and just say that Tipler has long been known for work that might be called "speculative."

      And, in a similar spirit of courtesy, let's just say that parts of Frank's paper are "flawed." Consider, for example, his argument on p.8: "FRW Universe does NOT admit a U(1) gauge field, like electromagnetism" in which he claims to prove that the CMB cannot be electromagnetic radiation.

      His argument is "in FRW there can be no momentum flow." and that therefore "The fact that the FRW universe cannot admit an electromagnetic field is ignored in standard cosmology texts."

      This "fact" is indeed ignored because it is false. There can be momentum flow in FLRW: it is called "pressure."

      In the local cosmic frame, the momentum itself must average out to be zero, but it does not have to be exactly zero at a single point and at a single time.

      I could go on, but that would be unkind.

      Let's just say it is a mistake to take that paper seriously.

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  20. Dr. Hossenfelder, thank you very much for your videos and articles. They are always very thought provoking. However, I am struggling with interpreting a thought experiment about FTL communication:

    Alice and Bob are moving apart with velocity v=0.8c; at some point T=0 they were very close to each other in space and both reset their clocks to 0 at that point. Both are equipped with "hyperwaves" able to send messages at, say, 4 times the speed of light.

    At time T=10, Alice sends the message "Hi this is Alice, my clock says 10" to Bob. Bob will receive this at time T=12.5 in Alice's frame, when he is X=10 units away (in Alice's frame). Using the Lorentz transformation with v=.8 we see that (12.5, 10) transforms to (7.5, 0); that is, Bob receives the message when his own clock reads 7.5. He now waits until his clock reads 10, and sends the message "Hi this is Bob, I'm replying to your message at T=10" back to Alice, again at 4x the speed of light. But by the same reasoning, Alice's clock will read 7.5 when she receives Bob's message. That is, Alice receives Bob's reply before she sent her original message.

    Now, this doesn't necessarily imply a paradox will occur, but it seems mighty hard to avoid in general. Are you suggesting that we should "invert the causality" and interpret the events "message leaves Alice's hyperwave" and "message is received at Bob's hyperwave" in the other order, so that the message "Hi I'm Alice at time T=10" appears to go from Bob to Alice instead?

    Thank you,
    Eric

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  21. I should have mentioned if there were repulsive gravity to explain the observation of expansion, there would probably be a limit to the size of the universe, otherwise matter would eventually be exceeding the speed of light, or all bunched up in one spot. If the universe was continually pushing matter apart, then we would need a mechanism for the creation of new matter.

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    1. Michael John Sarnowski,

      You raise several interesting questions: you caused me to do some calculations to get the answers, and I think many physicists are unaware how this works (hopefully, cosmologists already know these answers!).

      The basic point is that dealing with your questions involves which coordinate system you choose to use.

      In cosmology, we usually use "cosmic time," roughly speaking the time measured in each galaxy since the Big Bang. Then “all of space right now” is everywhere that has the same cosmic time.

      But this coordinate system has some weird features: basically, the "straight line" from here to a distant galaxy is curved in spacetime (in technical terms, it is not a geodesic).

      It is also hard to compare speeds at different points in space: if you use "cosmic time," there is a natural way to do this, but there are other reasonable coordinate systems in which the manner of comparing velocities at different points gives different answers.

      So... suppose you have an expanding infinite universe with zero cosmological constant: that means the expansion speed cannot be accelerating. Now, if you consider a galaxy far enough away, the distance between us and that galaxy will be increasing at faster than the speed of light. And, yet, bizarrely, if you shoot a light ray towards that galaxy, the light ray will eventually catch up with that galaxy! (Physicists: I sketch the proof below.) To simplify, as the light ray goes away from us, it starts to get a kick itself from the expansion of the universe.

      Furthermore, one of the other reasonable coordinate systems takes your infinite universe and turns it into a finite universe. In that coordinate system, almost all of the matter is piled up against the edge of the universe! (Physicists: no, I am not pulling some trick with conformal transformations! The distance I am talking about as finite is plain old distance.)

      As I said, your comment induced me to work through the math on all this, so thanks for raising these issues (I sort of vaguely knew how this works, but the math is the bottom line).

      All the best,

      Dave

      P.S. Note to physicists: to prove the point about the light ray, express the FLRW metric in the form:

      ds^2 = dt^2 - R(t)^2 dχ^2

      (I suppress the angular variables.)

      Then just write down the differential version for a luminal path in the radial direction and integrate. If R(t)/t is positive and bounded above for t>= t0, where t0 is the time at which the light ray is sent, the result follows.

      For the simplest example of the “infinite universe becomes finite” issue, compare the Milne coordinates vs. the standard coordinates on Minkowski space: the result is then obvious. The general case is a bit messier: see Wolfgang Rindler's “Finite foliations of open FRW universes and the point-like big bang” in  Physics Letters A 276:52-58.

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  22. This article was very interesting, however, the comments were much more amusing.

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  23. I can't find any reason in physics either why anything can go faster than light ceteris paribus.

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  24. Faster than light travel is impossible because matter is, in essence, "made of light". It's like Schrodinger said on page 26 of his 1926 paper Quantization as a problem of proper values, part II. He said “let us think of a wave group of the nature described above, which in some way gets into a small closed ‘path’, whose dimensions are of the order of the wave length”. Also see What is spin? by Hans Ohanian. Then think of gamma-gamma pair production as a process that converts the path from linear to closed, and annihilation as the opposite process.

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    1. Look up zitterbewegung. This the physics of a massive particle according to a massless particle that is scattered by a field. The mass m is a scattering field of sorts. The two Weyl equation for a spin-½ particle is given by

      ∇^{AA’}ψ_A = √½mψ^{A’}

      and the conjugate field obeys

      ∇^{AA’}ψ_{A’} = √½mψ^A.

      These two fields, which are themselves 2-spinors, define the Dirac spinor in the Dirac field. In this picture however we see this mass is a sort of potential that scatters the field into its conjugate.

      What sort of field does that? The obvious field is the Goldstone boson of the Higgs field. These keep the two Weyl fields transforming into each other. This then corresponds to the orbit of the massless particle, remaining on a path tangent to a local light cone, that is a spiral in spacetime, or circle when mapped into 3-space. This zitterbewegung or trembling motion describes the motion of a massless particle “forced” into a region with spatial dimension of its Compton wavelength λ_c = ħ/mc. At higher energy if this field is decoupled from the massless Dirac or Weyl field pair then it is free to move on a null path of a light cone.

      I worked some numerical computations of zitterbewegung. In two dimensions a wave function swishes back and forth, while in 3 spatial dimensions it moves on a circle. I tried publishing this in a journal for physics education, but it was not accepted as being not entirely relevant.

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    2. Lawrence: I’m familiar with zitterbewegung. I’m not comfortable with the Goldstone bosons though. In gamma-gamma pair production two 511keV photons interact with each other, as per the Breit-Wheeler process. We have clear evidence that photons really do interact with photons. So it seems reasonable to me that each 511keV photon interacts with itself to stay in a spin-½ configuration. Meanwhile E=mc² and the mass of a body is a measure of its energy content. See Light is Heavy by van der Mark and (not the Nobel) ‘t Hooft which talks about a photon in a mirror-box: https://arxiv.org/abs/1508.06478. I think it’s a shame your paper wasn’t accepted. If you ever revisit it, you might like to consider the situation wherein a photon is confined in a small region akin to the electron Compton wavelength because displacement current is real.

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    3. The Breit-Wheeler process γ γ′ → e^+ e^− is really just the time reverse of electron-positron annihilation e^+ e^− → γ γ′. What makes this difficult to realize is that getting two single photons to annihilate this way is hard because the cross-section is small. So one must employ a coherent state of many photons, such as a laser. Then a multiphoton state with a summation of energy can accomplish this. Recently though using high energy electrons incident on a target that produce gamma rays the production of electron-positron pairs was found.

      A photon in a box or high-Q cavity does in a sense increase the mass of the box. It takes a lot of photons to make it significant. It does seem to me though that the photon is purely massless. A Proca equation description is possible, but by various means the mass of the electron is as I recall now below 10^{-16}eV.

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  25. What about quantum entanglement?

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    1. I'll talk about that next week.

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    2. Negate OPM: I think it's all down to mundane things like conservation of angular momentum. I do think it's possible that we could discover some kind of wave that propagates through space faster than light. After all, longitudinal seismic P waves travel faster than the transverse seismic S waves, and shock waves travel faster still. But I don't think we'll ever discover any kind of instant propagation through space that qualifies as "spooky action at a distance".

      PS: Louis de Broglie and David Bohm also thought of matter as energy in a closed path.

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    3. It sounds as if Sabine is going to go into this, but to give a small spoiler, quantum entanglement is not about something propagating faster than light. The Einstein-Podolsky-Rosen paper of 1935 made a point that something was not right with the idea of reality and the locality of interactions and light speed. However, various results illustrate that entanglement is not about some signal propagation faster than light.

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    1. "Just to clarify this, Einstein's special relativity actually forbids (based on the relativistic expression) faster-than-light (u < c). The math say this not me."

      This is wrong. Maybe actually look at the math. Also, you presumably meant u>c.

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    3. I am not kidding. And of course as I said particles that travel faster than light can have negative energy. Look, I have studied this stuff. I have a PhD in the field. Dealing with the math is what I do for a living. Why is it so hard for guys like you to consider that maybe I know what I am talking about?

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    5. John,

      a) It is not my theory, the theory is Special Relativity, it is Albert Einstein's. I do not know what it means to "solve a discontinuity" and in any case, I never said that the discontinuity is absent. In fact, if you would maybe, just maybe, care to listen what I said, I said that there is a discontinuity. I even have a graph with a discontinuity in my video. Point is, this tells you nothing about the existence of particles that travel faster than light.

      b) No, I do not talk about some "wider framework". Your misunderstanding is the reason I made this video. Why can you not at least think about what I am saying?

      c) It is not my theory.

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    7. "It is not me who misunderstood what you are saying."

      Well, yes, actually it was you who misunderstood what I said, as the rest of your comment makes very clear. That is unless I have confused some John's here, in which case I apologize.

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  27. This comment has been removed by the author.

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    1. This is the last time I approve a comment from you that promotes your self-made theories.

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  28. For me, I don't think that any known physical field can be associated with a particle that travels at a speed greater than the speed of light; the particle would move as if it did not exist or the physical fields would be pointing to a place where there is no longer anything; I suppose. How independent are energy, time, space, speed, and physical fields from each other? I suppose there are limits.

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  29. Another way faster than light particles (tachyons) could avoid causal contradictions is to expand to such a large size compared with conventional sub-light-speed particles (bradyons) that their scale and diffuseness make any interaction between the two kinds impossible.

    Both bradyons and (if they exist) tachyons gain energy as they approach light speed. So if ultra-high energy tachyons can exit a black hole at a whisker above light speed, like water bubbling over the sides of a boiling pot (and having arrived from the future inside, so the Black hole need not change mass!), then their high energy could itself gravitate (energy equals mass, right? ), and thus they might manifest as Dark Mass. Is this detected anywhere but centred on black holes? I've no idea, and perhaps nobody yet has, but I suspect not.

    Furthermore, as the tachyons accelerate, losing energy all the while, then their collective increasingly uniform presence permeating space and expanding ever faster in all directions could manifest itself as cosmic expansion. One could even take that a stage further, in that as they are travelling back in time then at the Big Bang they could be, at the limit of increasing speed, the causative retrospective agents of inflation.

    Regards

    John R Ramsden

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  30. "So, faster than light travel is a problem because it can lead to causal inconsistencies."

    Your whole conclusions are mistaken: the effect of the movement backwards in time is a pure optical effect, comparable with the sonic boom effect: If a flashing light wave is coming towards you, you will receive all flashes at the same time. If a superluminal object is approaching you, the signals which are sent later by the object will reach you earlier, in inverse order. But this is optical, there is no time reversal and no change of direction of the object.

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    1. No, it is not. Seriously where do all you guys suddenly come from who know nothing about special relativity but believe you do?

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    2. If a particle is moving faster than light from A to B, that means simply that it is getting earlier to B than a light ray, but it does not mean that it will reach B before A. No special relativity required.

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    3. You do not even know that time-order is observer-dependent in special relativity but you come here to bless us all with your great insights.

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    4. Time dilation is a real, physical phenomenon that has been experimentally verified. It's not an "optical illusion", Ralph!

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  31. "Imagine you have a particle that goes right to left backwards in time, what would it look like? It would look like a particle going left to right forward in time."

    But a spaceship is not a particle, and has its own arrow of time determined by which way its entropy is increasing for it. So a faster than light spaceship has a thermodynamic arrow of time that points the "wrong way" relative to the coordinate arrow of time of objects at rest in some intertial reference frames.

    If we allow the spaceship to interact with them, then it can cause temporal paradoxes *for those objects* (the ones at rest). The spaceship may be free of paradox, but the rest of the universe isn't.

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  32. No great insight, it is very banal: If a supersonic aircraft is moving towards you, you will hear it arrive first and afterwards you will here it start. But this is observation only, it does not mean that there is a causal issue. Please check.

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    1. Once upon a time, there was a great physicist by name Albert Einstein. He understood that the speed of light (or, to be more precise, the speed of massless particles) plays a special role in physics. It is not like the speed of sound!

      Also, you clearly do not want to even consider that what I say may be correct, so I will not approve further comments from you. I have neither the time nor the patience to debate people who refuse to learn. Bye.

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    2. Sabine,I must apologize, it was not my intention to be offensive. In the meanwhile, I learned that the problem seems to be linked to the so-called Tolman paradox, I did not know about this theory before.

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  33. Ah. But wouldn't causing temporal paradoxes (actual ones, not apparent ones) be sufficient reason to rule out FTL in principle? Perhaps I misunderstood your argument.

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    1. If they did, then yes, that's what they would do, but they don't, by the very argument that you yourself gave.

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    2. But I specifically pointed out that an FTL spaceship could cause paradoxes for third parties (not "apparent" paradoxes, real paradoxes in the same sense that time dilation is real).

      My Ph.D. is in mathematics rather than Physics, so my physical intuition may be poor, but mathematically it seems inescapable that if time dilation is real, the laws of physics are the same in all inertial frames, and FTL signalling is possible, then it is possible for an observer to cause a signal to be sent back to their own past light cone. Note that this does require the assistance of a third party who also has access to an FTL signalling device. I posted an example earlier, but I'll try to pare it down to its essence.

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    3. Eric,

      Sorry about that, I seem to have misunderstood your original comment. No, the space-ship does not have an arrow of time that can be inconsistent with the universal arrow of time. The whole point of what I am saying is that it is assuming that this can happen which leads to paradoxa, not the fact that the space-ship goes faster than light. In brief: Consistent arrow of time => No paradoxa, regardless of whether ftl. Re-reading your comment, I think you say: If inconsistent arrow of time => possible paradoxa, which is correct, but not what I said.

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    4. "No, the space-ship does not have an arrow of time that can be inconsistent with the universal arrow of time."

      OK, but what is the "universal arrow of time"? I guess it's the direction in which entropy is increasing. But entropy is a property of an individual system, not of spacetime as a whole, no? So the direction is system dependent, not a universal feature of spacetime. Or have I misunderstood entropy? It's certainly possible.

      Thanks

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    5. Ah, I'm sorry, I posted some nonsense a while back, namely that spacetime had no entropy. Of course in GR it is a dynamical system, I was too narrowly focused on treating flat spacetime as a background.

      So a unique arrow of time does make sense. I still wonder about its relation to coordinate time. Are there any inertial frames in which the two are always aligned even for spacelike separated events? One would speculate that there is one such preferred frame but it isn't obvious to me.

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    6. Hi Eric,

      How the arrow of time relates to coordinate time is a good question. I am guessing you probably refer not to any coordinate time, but to cosmological time in particular. I don't think anyone knows. It's a difficult question because these cosmological coordinate systems works with some average distribution of matter and not the local one.

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    7. I was thinking of specific coordinate times and whether they are all "equally valid", i.e. aligned with the thermodynamic arrow of time. If there are FTL influences it seems this won't be the case. For example, consider events A "the rocket leaves Earth" and B "the rocket crashes into Mars and explodes". If A and B are timelike separated then all observers agree on the coordinate times to assign to these two events, that t_A < t_B. If A and B are spacelike separated (the rocket went FTL for part of its trip from Earth to Mars) then there is no unique time coordinate ordering for these events. This implies that some observers will record B as before A in their coordinate times: in coordinate time the rocket exploded at Mars before it left Earth. This isn't necessarily a paradox in and of itself, but at the least it creates a privileged class of observers, namely those for whom the arrow of coordinate time agrees with the arrow of causality (for whom A comes before B in coordinate time as well as causally).

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  34. Yes, if you look at the Lorentz-Fitzgerald formula alone, you only see a principle that puts apparently insuperable difficulties in accelerating a mass to the speed of light, which does seem to leave room for negative masses etc.

    But thinking about c as a fundamental constant, a property of nature, it seems to say that there is a constant, built-in so to speak, relationship between spatial distance and time. And talking about anything traveling faster is another example of talking about north of the north pole.

    There is the question of spacetime interval being the proper formulation. And there is the current (last time I looked, at least,) issue of the theoretical possibility of closed timelike curves in general relativity. But pretty much everyone reject GR as science, as wrong, merely useful for commercial purposes, like calculations for GPS etc.

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    1. This is incorrect. Speaking about speeds faster than light is entirely well-defined and such speeds can easily accommodated in special relativity. As I explained in my blogpost.

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    2. S. Johnson wrote:
      >But pretty much everyone reject GR as science, as wrong, merely useful for commercial purposes, like calculations for GPS etc.

      You are just joking? Right?

      SJ also wrote:
      >But thinking about c as a fundamental constant, a property of nature, it seems to say that there is a constant, built-in so to speak, relationship between spatial distance and time. And talking about anything traveling faster is another example of talking about north of the north pole.

      In QFT, virtual particles travel faster than light. In technical terms the VEV of φ(x) φ*(y) is non-zero when (x-y) is spacelike. Tom Banks discusses this in detail in his his book Modern Quantum Field Theory : A Concise Introduction. As Banks explains, everything works out (no violation of Lorentz invariance, causality, etc.) because of the existence of antiparticles.

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    3. In special relativity then, an object traveling faster than light does not lose energy when it emits radiation, nor does it absorb radiation as it travels. That this sort of thing is well-defined is surprising. That's why I thought FTL was, to put it in other words, a matter of going from *here* to *there* without a path in-between, at least not in a frame of reference that can define a proper time for the object.

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  35. Bee wrote: "So, faster than light travel is a problem because it can lead to causal inconsistencies. At least that’s what most physicists will tell you or maybe have already told you. I will now explain why this is complete nonsense."

    It would help if you illustrate it with the timeline of a tachyon on a space-time diagram.

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  36. Einstein did not rule out faster than light motion, he just said, no idea how to get there.

    Einstein discussed this topic several times, such as when he wrote in 1907 that, if superluminal motion or signalling were possible “we would have to consider as possible a transfer mechanism whereby the achieved effect would precede the cause. Even though this result, in my opinion, does not contain any contradiction from a purely logical point of view, it conflicts with the character of all our experience to such an extent that this seems sufficient to prove the impossibility.”

    Imagine you have a particle that goes right to left backwards in time, what would it look like? It would look like a particle going left to right forward in time.

    In either case the particle is following a timelike (or, if you prefer, a reverse timelike) interval. Granted the fundamental laws of physics are (more or less) time-symmetrical, but they aren’t symmetrical between time and space. The particle will never be moving along a spacelike interval, regardless of which direction of time we choose. Swapping past and future light cones (advanced and retarded potentials, entropy increasing or decreasing, etc.) is one thing, but swapping timelike with spacelike intervals is quite another. If we etch the name of the winner of the Kentucky Derby on a particle after the race and send it leftward or rightward to some other location, in neither case will it arrive prior to the Derby. That would require either that the particle propagates along a spacelike interval (which is forward in coordinate time for some inertial frames and backward for others), or else a jiutterbug along alternating forward and reverse timelike intervals. And either alternative leads to an effect preceding the cause, which “conflicts with the character of all our experience”.

    The reason for the grandfather paradox is *not faster than light travel, but it’s that these stories screw up the direction of the arrow of time. You are going back in time, yet you are getting older. *That is the inconsistency.

    I think the meaning of "superluminal travel" is to proceed in a directed sense from origin to destination, i.e., from one event to some space-like separated event, and according to special relativity this unavoidably entails “going back in time” in terms of some inertial coordinate system while you are proceding from origin to destination, i.e., getting older. (Of course, it’s problematic to even define elapsed proper time along a spacelike interval, but it is forward in coordinate time in at least some inertial frames, and backwards in others. The laws of physics are not invariant under exchange of time and space.) What you call “screwing up the direction of time” is precisely the reductio ad absurdum that leads to the conclusion that superluminal travel or signalling is not possible, because such screwed up time is unavoidable under the assumption of superluminal propagation in special relativity, and this “conflicts with the character of all our experience”. That’s why Einstein wrote (in a 1912 exposition) that “according to the theory of relativity, one will have to consider it out of the question that there is a kind of signal (i.e. a propagation usable in principle for telegraphy) whose velocity exceeds c.”

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    1. @Amos
      Bravo, you put it very well! Can you give us a pointer to the source of the Einstein quote, please?

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    2. Amos: Does information have any aging process? Do photons get younger or older?

      I can screw up cause and effect just by transmitting a single bit (for a True/False binary decision) back in time. I could get very rich Sending Tomorrow's outcomes to myself Today without me physically doing the time travel. And it screws up cause and effect, the outcome of stocks, sporting games and games of chance determine my bets (or lack of) on them. As long as long as the answer to my question is unequivocally binary, I can formulate as complex a question about tomorrow as I like, and receive the answer immediately.

      I don't see that, hypothetically speaking, detecting a spin-up or spin-down on an entangled particle that is the engineered result of a future interaction would be an age-dependent process. (Hypothetical because it presumes some way of controlling the outcome will be invented).

      It seems to me "conflicting with the character of all our experience" is a useless criterion. So does superposition, wave-particle duality, quantum foam, Inflation, quantum jumps, Black Holes and on and on.

      “conflicts with the character of all our experience” sounds like a rephrasing of "I can't imagine it so it can't be true."



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  37. Dr. Hossenfelder: A question, not a theory -- It seems to me that wavefunction collapse provides an arrow of time; information (eigenstates) is lost that cannot be recovered. It is a discontinuity in the evolution of the system. We can't take the new Schrodinger equation and recover the state from before the collapse. In that sense, quantum physics does not work equally well in both time-forward and time-backward formulations. Forward we can evolve forever but don't know when we will experience a collapse. Backward evolution cannot recover the eigenstates states discarded by the most recent collapse.

    But I've never heard any mention of collapse as an arrow of time by physicists. Why not? Am I failing to understand something?

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    1. Re Dr. A.M. Castaldo 1:38 PM, May 23, 2020:

      Time is a controversial issue. Different physicists (e.g. Carlo Rovelli, Julian Barbour) have different views about the nature of time, including the view that time doesn’t exist. I would think that time cannot exist in the same [i]simple[/i] sense that (e.g.) relative position and mass might be said to exist. I would think that a one-way time can only be generated when a system or a subject detects a discontinuous change in number in another variable (e.g. relative position), and that this can only possibly be triggered by the one-way discontinuous change in number that comes from quantum events. I.e. the generation of a time variable can only be represented as an algorithmic step (as opposed to other variables like relative mass and position, that can only be represented via equations).

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    2. Lorraine Ford: Just seems to make sense to me. I assume time travel is impossible because quantum collapse is an irreversible loss of information, returning to a previous state conjures back lost information from nothing.

      I don't buy the argument that time's arrow aligns with increased entropy; I think order is in the eye of the beholder.

      For example, the lossless compression of a digital movie into a self-extracting file produces billions of bits that under statistical analysis appear to be uncorrelated. Because that's the job of the lossless compressor, to encode and eliminate as many of the redundancies and original data correlations as possible. But obviously these bits have no more entropy than the original bits, to which they can be restored.

      Like Schrodinger's equation, it can evolve the system in either time direction. So the system at time X has exactly the same 'disorder' as it does at time Y, no information or relationships or lost, all future and past states are recoverable. Except as fenced in, in the past and in the future, by quantum collapse.

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    3. Dr. A.M. Castaldo,

      I agree. Like time, quantum collapse seems to be another irreversible aspect of the world. Irreversibility seems to be unusual: it would be strange if quantum collapse events and the time variable, number and direction weren’t somehow connected.

      As far as I know, the entropy variable assumes that a pre-existing arrow of time exists in the universe; and local entropy doesn’t always “travel in one direction” anyway.

      The issue seems to be something like: how do you extract a time variable, number and inherent direction from a system in which time is seemingly not a fundamental, foundational aspect of the system. Quantum collapse events seem to be connected to the time variable.

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    4. Rather than a Time dimension existing, the time variable seems to represent information about other information, and the information might be (e.g.) “position number has changed”. Position can go from 1 to 2, and then back to 1 again. But you can’t undo the information that change has occurred. Detecting that number change has occurred can only be represented algorithmically.

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  38. Instantaneous communications at a distance do not necessarily lead to closed time loops if there is a unic preferred frame for such processes. This violates the spirit of special relativity but would not necessarily require to give up the structure of space-time (Lorentz transformations and so on). Also this would not necessarily involve particles: the wave packet collaŝe coud be such process : of course in QM this is not allowed but if QM is not the last word there might be a more fundamental theory beyond QM involving processes such as an instantaneous wave packet collapse really allowing information exchanges.

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  39. Not sure how "physical" this might actually be, but acceleration as we know it may not be the only way to increase speed. I am specifically referring to the negative absolute temperatures related to laser beams. You don't achieve that state by steady cooling, the mechanism of going there is entirely different. So perhaps what the theory really says is that we cannot get to v>c by crossing c at some point in time. But maybe we can jump through it somehow. If this line of thinking is entirely wrong, please spare a minute to explain why.

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  40. In this example:

    https://en.wikipedia.org/wiki/Tachyonic_antitelephone#Two-way_example

    Alice sends a message using tachyons moving at speed a > c to Bob and Bob sends the message back to Alice. Bob moves at a speed of v < c away from Alice. If v > 2a/[1+a^2/c^2] then Alice will receive the message back from Bob before she sent the original message to Bob.
    How should the causal paradox in this case be resolved (Alice could decide to not send the message to Bob is she receives a message back from Bob)? And whether the message is actually received before it was sent, depends on the speed at which Bob is moving. One can then consider a quantum mechanical version of the thought experiment where the speed is a superposition of being above and below the threshold value of 2a/[1+a^2/c^2].

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    1. As I said, the reason you have this paradox is that the arrow of time is inconsistent. Just go and draw it.

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    2. Count Iblis ,It seems to me that if I flip the light switch, no matter how fast the light emitted by the bulb is, it will never reach my hand before I flip the switch; the action of operating the switch is in the absolute past.

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    3. seems you think that this entropy related arrow of time you are talking about is really the fundamental concept.
      It seems to me rather that the arrow of time just requires a preferred origin of time to start with plus the so extremely natural condition that there is no miraculous fine tuning in the initial state insuring that no such thing will occur as the egg separating from the mayonnaise. This way the arrow of time is not an emergent concept , it is already there from the begining and is as fundamental as the lorentz transformations ... and then the second principle of thermodynamics could follow as a consequence of there being no fine tuning in the initial state...hopefully!

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    4. The paradox appears because you assume that both Bob and alice can send tachyons with arbitrary speeds relative to their respective restframes... Actually for each of these tachyons there exists a frame in which it flies instantaneously (Delta t=0). And the paradox arises because you assume that these two instantaneity frames could be different. But if for some fundamental reason there actually exists only a single frame of instantaneity in the universe, then both Bob and Alice cannot help but sending their instantaneous tachyons in this frame and then of course the journey time round trip is zero in this preferred frame and so it is zero in all other frames as well : (Deltax=0= Delta t is Lorentz invariant) : No backward in time signaling then: you can at most send instantaneously the signal to yourself.

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    5. I think the difficulty is that it's not possible to construct sensible arrows (consistent with both causality and coordinate time) if the message speed a exceeds a certain value M(v) = 1/v + sqrt(1/v^2 - 1) (such that v > 2a/[1+a^2]).

      Another way of thinking of it is to ask "what is the maximum possible (two way) speed of communication for two observers moving apart with speed v"? Either this value is frame independent (in which case it must be the speed of light; special relativity only allows for one invariant speed) or else it must depend upon v. If the latter case is allowed then the physics of FTL interaction with ordinary matter is not frame independent. This is not logically impossible, but does seem unlikely.

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    6. Eric,

      Of course it's frame dependent. The arrow of time is equivalent to a foliation, which is a preferred frame. Note that this is consistent with SR (or GR in general) because the frame is generated by matter and transforms covariantly.

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    7. We violently agree that FTL travel only with respect to a preferred rest frame is logically consistent. I disagree that it's "consistent with SR" since one of the postulates of SR (as it's usually presented) is that the laws of physics have the same form in all inertial reference frames, whereas this hypothetical FTL mechanism does not. For example the 2nd law of thermodynamics will be violated in some reference frames by objects moving faster than light.

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    8. Eric,

      First, to say the obvious, we don't live in Minkowski-space, we live to some approximation in FRW space which has a preferred foliation, whether you like that or not.

      Having said that, you are misunderstanding the principles of SR. There is nothing whatsoever wrong with having a preferred frame in SR if that frame is defined by matter (or fields). Eg, if you put a single particle into Minkowski space, that defines a preferred frame which is the only frame in which the particle is in rest. This, needless to say, is not in conflict with SR. SR merely postulates that there is no *fundamental* frame that is preferred.

      "For example the 2nd law of thermodynamics will be violated in some reference frames by objects moving faster than light."

      No, it won't, that's the whole point. The arrow of time will be consistent with entropy increase because that's where it comes from in the first place.

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    9. Sabine,

      Thank you for your patience; as I mentioned, I'm a mathematician and so my intutions about physics are nowhere near as good as yours. I think we may be talking past one another in some way though.

      I said: "For example the 2nd law of thermodynamics will be violated in some reference frames by objects moving faster than light."

      You replied: "No, it won't, that's the whole point. The arrow of time will be consistent with entropy increase because that's where it comes from in the first place."

      There isn't an issue for single particles moving FTL, as you pointed out so well in your video; different observers simply disagree about which end "emitted" the particle. It's a problem for macroscopic systems which have their own internal entropy.

      For example if event A "rocket leaves Earth" and event B "rocket crashes and explodes in a million pieces" are spacelike separated, an observer whose coordinate time has B before A will not be able to create consistent laws of physics in terms of their coordinate time. Even kinematics seems difficult: the rocket can be in two (spacelike separated) places at the same coordinate time.

      The laws work only in "absolute" time, the time of the preferred frame. Perhaps this is a semantic quibble, but it seems that this no longer qualifies as consistent with "relativity".

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  41. In Dr Hossenfelder's example, negative energy could be avoided if we consider that space has a minimum of energy and the particle has a lower energy; Of course, this could be absurd; Another thing, I would like someone more capable to make a corollary from the perspective of different observers for the example of Dr. Hossenfelder; Could one of the observers see the phenomenon as two different particles? Please, just ask.

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    1. No. That is one of the bonkers things about GR though, the absolute value of the components of the stress tensor matters. Everywhere else in physics we just have relative differences in energy to care about, so you can avoid negative numbers by re-zeroing, but in GR, this has physical consequences.

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  42. A few words from the great theorist E.C.G. Sudarshan:
    (1) "Tachyons, in a sense, re-introduce the concept of rigid bodies into relativistic quantum mechanics." and " In a vacuum, only tachyons can travel faster-than-light, hence they emit Cerenkov radiation. Thus, an unambiguous identification of electrically charged superluminal particles should be possible." (page 50, Physics Today, May 1969).
    (2) "The imaginary result for the rest-mass of Tachyons offends only the traditional way of thinking and not observable physics."
    (Meta-Relativity,page 720, American Journal of Physics, 1962).
    (3) "The factorization of a transition amplitude into initial and final states cannot be relativistically invariant if Tachyons are included." and "...a particle which is stable 'at rest' may emit a Tachyon when the particle is moving with sufficient speed." and, "If Tachyons exist, they are probably neutral. If we do not find them, then we ought to be able to find out why they could not exist. So far we have found no reason why they could not exist." (Quantum Field Theory of Interacting Tachyons, Physical Review, Vol 174, No. 5, October 1968). Conclusion: the experimental search for superluminal particles has been ongoing since roughly 1962, along with requisite theoretical research. Apparently, the experimental evidence in support of Tachyons is as robust as the experimental evidence in support of supersymmetric particles and superstrings.

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    1. If I may politely disagree...

      1. You state, "Tachyons, in a sense, re-introduce the concept of rigid bodies into relativistic quantum mechanics."

      This cannot be, else you agree with Billy Pilgrim (Vonnegut, Slaughterhouse 5) that "Among the things Billy Pilgrim could not change were the past, the present or the future".
      2. Unless I am on the dreaded "Dr. Hossenfelder's S-List", there is a Post awaiting Moderation. In it I get to the problem: "What is the Mechanism that allows Interaction between the Superluminal and the Luminal?
      3. If Tachyons are flitting around from place to place with no Interaction Mechanism with "our" Universe, there are no reasons for Tachyons.
      4. There must be a way of mapping from the Tachyonic Side onto our side.
      5. Keys: The Classical Language leads one astray. There is no "Infinitely Fast in Zero Time" Tachyon that Interacts with our Universe. Therefore, any Tachyon that Interacts must have a "Non-Zero Momentum Structure" if no Mass yet.

      THE Key is that the Lower Momentum Tachyon is the Faster Tachyon. Therefore, a faster Tachyon may displace a slower Tachyon in any Interaction Mapping onto our Universe. Therefore, the "Next Tachyon" in any Interaction with the slow Universe may come from almost any other Location in the Universe.

      This disposes of the "Rigid Universe". In fact, one may be able to build Quantum Probability from First Principles.

      CW

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    2. Sudarshan quotes a derivation by Sommerfeld which concerns a charged superluminal particle utilizing Maxwell's classical electrodynamics (such a particle would spontaneously emit electromagnetic waves). A more serious objection to Tachyons arises here: "except for spin-zero Tachyons, all other Tachyons must have an infinite number of polarization states." (Phys Rev, V 174, No 5, 1968). There is a 1969 article by Aharonov, Komar and Susskind where they introduce a model where "Tachyon-like behavior is introduced without one's having to introduce negative energies." (Superluminal Behavior, Causality, and Instability, Phys. Rev. 182, 1400).
      I have not seen the later article.

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    3. Thank you, Gary Alan! More material to learn!
      Edward Kapuscik has done much work on this (See: https://arxiv.org/pdf/1412.6010.pdf ).
      His Conclusions:
      1. "First, [the equations given] rigorously follow from the general principles of special theory of relativity and therefore are well justified..."
      2. "This fact eliminates all troubles in constructing quantum field theory of tachyons. In particular, tachyons may exist with arbitrary spins contrary to the Feinberg tachyon which can be only spinless..."
      3. "Third, for infinite velocities momentum of tachyons vanishes while their energy remains finite..."

      Here is where we disagree. I believe it is possible to prove that the "Infinite Velocity Tachyon" either doesn't exist or has no conceivable Interaction in our Universe. If you eliminate this "Infinite Tachyon", You may then construct a Consistent Metric with Tachyons. Tachyons are not Particles but Map onto our "Slow Universe". At worst,for those who still don't like the smell of Tachyons, their Role may be reduced to a "Technical Location". There are some subtle hints that Tachyons in this sense do in fact function in our Universe.
      4. "[A given equation] supports the Feinberg argumentation that in order to determine the tachyon velocity it is sufficient to measure momentum and energy of tachyons..."
      ***
      Thank you Gary.
      Especially, thank you SH for providing me space to post about this exciting Topic.

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  43. I don’t know if it’ll help to understand the »faster-than-light-issue« but for what it’s worth, the main »understanding problem« is a real one. Theoretical physicists are used to discuss abstract objects based on mathematics. A thought experiment will not tell you if you made useful assumptions. Right or wrong is not an issue. If something math-based makes real sense the “best proof” would be an application based on ones “thinking how it could be done”.

    Physically speaking, the »faster-than-light-issue« is strongly related to the »energy-issue«. But – to quote Richard Feynman - "It is important to realize that in physics today, we have no knowledge of what energy is."

    The use of »secondary terms« like energy, mass, ... in physics is not only widespread within the framework of (theoretical) basic research, there are only secondary terms in this field existing.

    »Preachers and understanders« of »secondary terms« believe in the suggestive radiance. They somehow have a “good feeling” of scientific closeness, for example when they hear about electric charge, photons, mass, electric field or gravitational field, talk about them and insert these terms or sizes into formalisms.

    Reminder (for example what a »secondary term« stands for): Quarks are not particles, neither in the phenomenological nor in the quantum-theoretical sense, since they do not appear as isolable particles or states. The physical particles, on the other hand, can be thought of as bound states composed of quarks. No physical objects correspond to the elementary quantities of quantum field theory. The desired, different types of postulated elementary particles in the standard model (SM) differ in the quantum numbers of dynamic properties such as charge or isospin. Some are massless by postulate, others are not. The electron is postulated as a mass- and charge-point, as desired in theory. This simply means that one takes results-oriented mathematical elements that somehow fit with or without mass. This arbitrary procedure is possible because from a mathemtical point of view “anything goes along with the theory”.

    However, quantized properties are characterized by inner symmetries and have nothing in common with properties in the usual sense that can be understood as physical qualities inherent in things. The isospin of the nucleons or the "color" of the quarks no longer express any qualities in this sense, but only arbitrarily defined basic states or directions in an abstract space that are related to each other through symmetry transformations. Almost all previously known symbol systems are cited. Sometimes it is the colors (red, blue, green), sometimes letters (u, d, s, c, b, t), sometimes symbolic properties (strange, charm, beauty, ...) and furthermore flavors. The terms 'tohu' and 'wabohu' from the story of creation in the Old Testament were proposed for a structure still below the quarks.

    So, would could it phenomenologically mean if one refers to an accelerated high energy proton postulated made of Quarks, gluons, virtual seaquarks (that means mostly binding energy and “relativistic energy”)? Further more: Compare this accelerated composite particle to a postulated »elementary one« like an accelerated electron.

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  44. Sabine wrote: Speaking about speeds faster than light is entirely well-defined and such speeds can easily accommodated in special relativity. As I explained in my blogpost.

    It’s true that speeds greater than c are well-defined in special relativity, but the question is whether a material body or signal can move (propagate) at such speeds. The standard answer is no, and several reasons can be given, one of which is that superluminal signaling would imply the ability to send signals into our causal past, which conflicts with all our experience. You seem to be disputing this reasoning, but it isn’t clear (to me) from your blogpost what your counter-argument is. To clarify, given an inertial coordinate system x,t, suppose a putative superluminal traveler moves directly from the event A at x=0, t=0 to the event B at x=L, t=0. If the traveler’s watch is set to 0 at A, what does it read at B?

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    Replies
    1. Amos,

      The watch will read whatever time coordinate you chose that it represents.

      "The standard answer is no, and several reasons can be given, one of which is that superluminal signaling would imply the ability to send signals into our causal past, which conflicts with all our experience."

      This crucially depends on what you mean by "signaling". What I am saying is simply that as long as you have a consistent arrow of time, you cannot "signal" in any meaningful sense of the word. The only way you can "signal" to the past (against the arrow of time) is identical to "signaling" to the future (with the arrow of time).

      Look, just draw the supposed paradox in a space-time diagram and put a time-like slicing over it. Then read off the directions of time in your closed loop. You will find that if you previously thought you were able to create a paradox, then necessarily one of the directions of time in your "signalling" (or traveling) diagram disagrees with the arrow of time.

      I have drawn some examples here, but the argument doesn't depend on the exact shape of the curve.

      Delete
  45. I've been under the impression that FTL travel would put one in a part of the universe with which you have no causal connection in the ordinary sense (thinking in terms of causal influences confined to one's backward light cone). One could imagine a causal connection from the origin of an FTL trip to the destination: construction of the spaceship, enter and strap in, put the key in the ignition, fire the stern jet, and off we go... this would create a kind of causal "thread" into a part of the universe with which you have no other connection. The folks you leave behind might have to wait many years to see your destination. Only at that time would they have your destination in their backward light cone, and be causally connected to that region of the universe-- in the ordinary way. But by returning via FTL you could provide information about your destination and in this way establish a sort of causal link, outside the normal channels, so to speak. Very confusing. I guess not impossible in principle but it would force us to think about how causality actually works. If you wanted to prevent this sort of tourism some sort of cosmic censorship would have to be at work. Star Trek universes might have to be constructed differently.

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  46. Hi Sabine,
    I totally agree with you that traveling faster-than-light will not lead to travel in to the past or future (=entropy). You cannot go back to the time where the dinosaurs lives, because most of the atoms where the dinosaurs made of are in the present. So if you go back to the past or future, you will find a more or less empty space. BTW: Wouldn't one then have to assume that slower-than-light particle are moving into the past? Or shouldn't we even think of it that way?*
    But would an electron that exceeds the speed of light not “just” become a positron?
    The positron is an electron “running backwards in time” – In the Feynman's interpretation. I Think.
    And negative energy in form of a particle – could be seen as an imaginary mass. So a positron could be a kind of a tachyon particle with nevertheless positive Energy (~ minus x minus).
    *If you look at e.g. Quantum correlations with no causal order (https://www.nature.com/articles/ncomms2076) they are talking about “past and future”. But maybe should talk about faster-than-light and slower-than-light particle.
    I “believe” that the present is a kind of a mirror (made out of fast-as-light particle), were faster-than-light particle and slower-than-light particle actualize.
    But this is of course an immature view on this.

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  47. If you believe in relativity, then faster-than-light communication in one reference frame implies backwards-in-time communication in another reference frame. This second possibility brings up the "grandfather paradox" — what happens when you go back in time and kill your grandfather? So either (a) relativity is wrong or (b) maybe some particles can travel faster than light, but if you try it, you won't remember your departure when you arrive at your destination.

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    1. "If you believe in relativity, then faster-than-light communication in one reference frame implies backwards-in-time communication in another reference frame. "

      No, it does not. Just because you have a space-like curve does not mean you can actually communicate across it. If you could actually communicate back in time, that would be in conflict with the arrow of time, so you can't. There is no paradox as long as you realize that we do, for better or worse, have an arrow of time. As I explained in my blogpost and in my video.

      Delete
    2. @Sabine

      Your statement here:
      >If you could actually communicate back in time, that would be in conflict with the arrow of time, >so you can't.

      and your statement in the blog text:
      >there is no reason in principle why ... faster than light communication is impossible.

      are in direct contradiction, because faster than light communicaiton allows to communicate back in time. Your statement here is the correct one.

      Delete
    3. Franzi,

      "@Sabine

      Your statement here:
      >If you could actually communicate back in time, that would be in conflict with the arrow of time, >so you can't.

      and your statement in the blog text:
      >there is no reason in principle why ... faster than light communication is impossible.

      are in direct contradiction, because faster than light communicaiton allows to communicate back in time. Your statement here is the correct one."


      No, faster than light communication does NOT allow you to communicate back in time. This is what I am saying all the time. If you could do that, it would conflict with the arrow of time, so you cannot. There is nothing contradictory about these statements, you just still do not understand this simple point: YOU CANNOT BEAT THE ARROW OF TIME. Nothing can. Faster than light communication can't either. The supposed problems with faster than light travel or communication arise because people who ignore the existence of an arrow of time.

      Delete
    4. @Sabine

      Violating causality and going against the arrow of time is the same. Therefore what you are saying now is correct, but in contradiction to what you said in the blog post. You are now making the standard argument, that you deemed "complete nonsense" in your blog post.

      Delete
    5. If you can communicate from point A to point B for any two points A and B that are spacelike separated, then you can communicate from point A to point B to point C, where C is in A's past light cone. And if you assign a "real time" to every point and are only able to communicate forward in "real time," this violates relativity. So either relativity is wrong or communicating faster than light is impossible (this is what I said). Or maybe there's a third possibility, but I've failed to grasp it from your explanation.

      Delete
    6. An interpretation of QM(quantum state)+SR(metric by caysality) can be so that if lightlike particle "ecceed" the speed c, it changes into the opposite state of motion, i.e. reflection of direction AND creates a timelike event.

      "YOU CANNOT BEAT THE ARROW OF TIME" - that's true.

      Delete
    7. Franzi,

      No, what you say is wrong. I am saying the same thing here and in all comments as I have said in my blogpost. It is complete nonsense to claim that faster than light travel leads to causal inconsistencies. What leads to causal inconsistencies is ignoring the existence of an arrow of time. Yes, of course violating causality is the same as ignoring an arrow of time, which is why I say it isn't hard to see. Congratulations, Franzi. It wasn't that hard, was it?

      Delete
    8. Peter,

      "And if you assign a "real time" to every point and are only able to communicate forward in "real time," this violates relativity. "

      This is where your argument goes wrong. An arrow of time is, needless to say, not incompatible with relativity. Relativity works just fine, yet we have an arrow of time. What is incompatible with relativity is a fundamentally preferred frame. There is nothing whatsoever wrong with a foliation that is created by matter. To put this in simpler terms, each time you look at a table that table has a preferred frame that is its restframe. Needless to say, this is not in conflict with relativity. Frankly I didn't think that this is so little known.

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    9. @Sabine @Peter

      >This is where your argument goes wrong. An arrow of time is, needless to say, not incompatible >with relativity.

      Why do you contradict Peter? What he was saying is not "an arrow of time is imcompatible with relativity" but "an arrow of time + superluminal signaling is".
      And we this you agree now. And that what Peter wrote was contra your blogpost shows that you changed your mind. And that's fine, why don't you admit it?

      @Peter
      Do you agree?

      Delete
    10. Franzi,

      I have no idea what you think I "changed my mind about". This is a simple argument, and I have merely repeated it over and over again.

      Re Peter, he wrote (see above) "So either relativity is wrong or communicating faster than light is impossible (this is what I said)."

      which is wrong. Let me say it once again: There is nothing wrong with communicating faster than light as long as you keep in mind that our universe has an arrow of time. Peter is confused because he erroneously thinks that an arrow of time is in conflict with relativity. Which it is, of course, not.

      As to what your problem is I have no idea, but you are once again wasting my time.

      Delete
    11. Sabine: this is where you disagree. I assume your definition of "special relativity" involves the Lorentz contraction, time dilation, etc. My definition also includes the statement that physics looks the same from all inertial frames. It's this last statement that is violated by an arrow of time between spacelike separated points.

      Delete
    12. Peter Shor,

      You can "disagree" with me all you want that matter always defines a reference frame, even in special relativity, but then you are just wrong.

      Delete
    13. I argued at this link

      http://backreaction.blogspot.com/2020/05/is-faster-than-light-travel-possible.html?showComment=1590487682892#c5727969112872128162

      there is an ambiguity in time ordering for a spacelike interval. Also, a timelike observer detecting light emitted from the spacelike interval in regular proper intervals witnesses the tachyon appear at a point and take off in two directions. I tried to include a link of a picture of this, which I got off Google images, and Sabine objected to that. It did turn out to be Fred Wolf’s stuff, where he has a dubious track record.

      I think one can set an arrow of time in either direction equally well on a spacelike interval. With a timelike interval there is a clear ± sign to the direction. With a spacelike interval there is only a ± sign with respect to a spatial direction.

      Delete
    14. Exactly how does matter define a reference frame? Suppose we have one galaxy moving very fast relative to the rest of the universe. Is the reference frame in that galaxy defined by that galaxy itself, or by the matter very, very far away from it in the rest of the universe?

      Delete
    15. Peter,

      Matter defines a reference frame because it has a rest frame. That's a local thing. You are in rest relative to the center of planet earth (or so, I assume, to good accuracy). How to average over these local frames in GR is a long-standing and unsolved problem, so, with apologies, but I don't know how to define it.

      In any case, do you seriously want to question the existence of an arrow of time? If so, I assume the logical next step is that you will build us a perpetuum mobile. That would solve a lot of problems indeed. Looking forward to it!

      Delete
    16. Peter Shor: "It's this last statement that is violated by an arrow of time between spacelike separated points."

      I think this whole discussion would become much clearer if we avoided the unqualified use of the word "time".

      I believe you are saying "there is no unambiguous assignment of coordinate time between spacelike separated points". This is not at all the same as saying "there is no unambiguous assignment of causality (or entropy) between spacelike separated points".

      Delete
  48. The watch will read whatever time coordinate you chose that it represents.

    I don't understand that. I'm talking about an ordinary clock, i.e., a device that ticks out the proper time along its world line. Like a crystal-based wrist watch or a cesium clock or whatever. The ticks would be in proportion to the normal heart beats of the traveler, etc. The question is, if you believe a traveler can proceed directly along the spacelike interval from x=0,t=0 to x=L,t=0, what is the difference in his wrist watch readings at those two events? In other words, what is the elapsed proper time for the traveler between those events? This is an invariant.

    The only way you can "signal" to the past (against the arrow of time) is identical to "signaling" to the future (with the arrow of time).

    I still can't figure out what you mean by that. The definition of superluminal signaling (if it were possible) is sending a signal from some event A to a spacelike-separated event B. If you reject this premise, then we're in agreement that superluminal signaling is impossible. On the other hand, if you're willing to entertain the premise, then we proceed with the reductio ad absurdum: We note that (according to special relativity) there exist inertial coordinate systems in terms of which tAtB. (This is true regardless of which direction of the time coordinate you take to be the causal positive direction.) By putting two such signals together, we would be able to send a signal to our causal past (in whichever direction that is), something which we know is contrary to all our experience. Hence we conclude that superluminal signaling is not possible.

    If someone denies any meaningful causal sense at all, and/or they contend that causal effects actually can flow equally well in either direction, then this argument will not impress them, but for people who distinguish between the causal past and the causal future the conclusion is unavoidable.

    You will find that if you previously thought you were able to create a paradox, then necessarily one of the directions of time in your "signaling" diagram disagrees with the arrow of time.

    Of course it does. That's he point. According to special relativity, if it were possible to send signals superluminally, it would be possible to send signals "backwards" in time, and since we reject this "backward" possibility, we must reject he possibility of superluminal signaling.

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    1. In ordinary communication signals must propagate forward in time relative to all coordinate times. I believe Sabine's proposal is to relax this so that signals need only propagate forward in time relative to some particular preferred frame. In this case it is impossible to construct a closed timelike loop. So there are no "grandfather" paradoxes. It does make coordinate time useless for some purposes though, which seems to me to create other issues.

      Delete
  49. Dr Hossenfelder,

    First off thanks to you and Lawrence Crowell (Dr.Crowell????) for your responses to my post. However, I must confess that I now have more questions. This is a good thing because I now have more concepts to ponder and research. I hope that you will allow me to make a few observations as I have read through most of this blog thread a couple of times. First and foremost, Dr. H I think you should be proud of the discussions you start in your blogs. I have found the open and honest discussion you illicit to be fascinating, right, wrong or indifferent. You have provide a place where people can come and for the most part have open discussions about a critical and complex topic(s).

    Next, your topic was FTL travel which quickly moved to discussions regarding time. This is interesting to me because this shows how strong "time" plays out in this kind of discussion.

    Lastly, almost all comments centered around currently known and/or discussed concepts resulting in unique and well discussed disagreements. Isn't a little imagination necessary in theoretical topic discussions such as this?

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  50. Correct me please if wrong: Bob traveling faster than light could appear in two places at once according to Alice and effectively exert doubly the gravitational force because there would be two Bob's exerting a force on Alice(if timed correctly for awhile). According to Bob there is just him speeding about although he could look back and see himself in his prior position. What happens if the sun explodes? We continue to feel its gravity for 8 minutes. So Bob can leave his position and move to another before Alice can detect that he is gone and be able to exert a second gravitational force for a awhile before Alice is able to detect an absence of gravity from the first position. Obviously this effectively violates a whole bunch of conservation laws too.

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  51. Lawrence,

    Please do not post links to researchgate. A lot of cranks park their pamphlets there and I don't have time to check each link individually. If you are referring to a published paper, please refer to the journal.

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  52. Hello Sabine,

    I would like to formulate some remarks.

    "Our observation that forward in time is different than backward in time comes from entropy increase. It arises from the behavior of large numbers of particles together. If you have many particles together, you can still in principle reverse any particular process in time, but the reversed process will usually be extremely unlikely. Take the example of mixing dough. It’s very easy to get it mixed up and very difficult to unmix, though that is in principle possible.

    In any case, you probably don’t need convincing that we do have an arrow of time and that arrow of time points towards more wrinkles. One direction is forward, the other one is not. That’s pretty obvious."

    I find this entire paragraph seriously problematic.
    There is no such thing as an observation backward in time, unless perhaps our memories count, which they don't.

    So the comparison with forward in time makes a priori no sense I think.
    And if you were capable of perfectly unmixing dough, then this would still be happening while time is going forward. No process can be reversed in time, who makes up this stuff ?!

    The entire narrative is troublesome. And this stems from our understanding of time.

    Time in GR is what so called clocks measure. Except that they are devices measuring the frequency of an energylevel oscillation. Energy input is the key word here.

    Whereas the conventional meaning of time is time as a tool of the mind to structure the succession of events,, and the experience of duration. No device with an oscillation is measuring that.

    If you mix up those two notions of ti.e, you get all kinds of extrapolations which certainly do not stem from experimental evidence.

    The goal should be to scientifically establish and further understand how these oscillations take place, what are the causes of their fequency change. The search for a fysical process,which will objectify 'time' in GR. The key word is energy density.

    Have you been reporting a story here, or do you have a personal opinion which differs ?

    Best, Koen

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  53. As a biochemist/bioinformatician i have a different question:
    what would happen to our plain old usual organic matter IF we somehow made if travel at FTL speeds? Wouldn't it fall apart? The thing is, the chemical bonds which hold us together are in essence electromagnetic interactions and effects, so they are mediated by photons. If we for example had some photons emited from my back, they wouldn't they be unable to reach my front? I'd love to hear Your response to this Sabine :)

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  54. An isolated system that traverses a space-like curve could end up having less entropy than it started with per some observers. If the arrow of time is tangled up with the second law of thermodynamics, and the second law must hold for all observers, i.e., the arrow of time is consistent, then it must follow that one cannot assemble such a system. Or in other words, one cannot build a spaceship with tachyons.

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  55. Just because you have a space-like curve does not mean you can actually communicate across it.

    Right, and, in fact, we cannot communicate across a space-like interval, because every space-like interval goes backward in coordinate time in terms of some systems of inertial coordinates, so if communication across any such interval was possible we would have effects that precede their causes, enabling causality paradoxes. Of course, we could also violate the second law of thermodynamics, but that’s just one of the consequences of the complete violation of causality.

    If you could actually communicate back in time, that would be in conflict with the arrow of time, so you can't.

    There are various concepts of the “arrow of time”, and it is a subtle subject, whereas the proposition that effects should not precede their causes (in terms of any inertial coordinate system) strikes most people as more fundamental and incontrovertible. Ask someone if effects can precede their causes and they will probably say no, but ask them if the second law of thermodynamics could ever be violated in any circumstance, and they might hesitate.

    For any impossible thing, like superluminal travel, we can derive infinitely many different absurdities from assuming it is possible. One absurdity that's immediately apparent is effects that precede their causes (and the resulting causality paradoxes). Another may be violations of the second law of thermodynamics and the associated “arrow of time”, but to the extent that this directionality is inviolable it can be traced back to the fact that effects can’t precede their cause.

    The key point is that every space-like interval is backwards in time for some systems of inertial coordinates. So, if we stipulate that we can’t travel or signal backwards in time for any inertial coordinate system (effect can’t precede cause), it follows that superluminal travel and signaling are impossible.

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    1. Amos,

      "we cannot communicate across a space-like interval, because every space-like interval goes backward in coordinate time in terms of some systems of inertial coordinates, so if communication across any such interval was possible we would have effects that precede their causes, enabling causality paradoxes"

      No, this is wrong. It's a non sequitur. Just because you have signals that go faster than light does not imply you have causality violations. You get causality violations only if you ignore the existence of an arrow of time.

      Delete
    2. I write about the zitterbewegung as a process where a massless particle is scatter to traverse space in different directions by a process, likely the Higgs mechanism. In two dimensions this is a particle in a box sort of model. A tachyon is similar, but the massless particle on a light cone is scatter back and forth in time.

      There is some issue with expressing time with a tachyon. There is an ambiguity in assigning a past and future between two spacetime points or events on the path of a tachyon. Assigning an arrow of time along a tachyon worldline is not possible in an unambiguous way.

      https://backreaction.blogspot.com/2020/05/is-faster-than-light-travel-possible.html?showComment=1590315240828#c4635505264912300279

      Delete
  56. I went back to look at your 2015 blog post, and I think I can see the problem. You drew some triangles with two spacelike intervals and a timelike interval, and you say one of those spacelike legs is okay because it goes forward in time (in terms of this system of inertial coordinates) but the other spacelike leg you’ve drawn in red, and you say this one is bad because it goes backward in time, and hence (you argue) we just need to preclude the legs that go backward in time and we can keep the good spacelike legs (signals) that go forward in time.

    The problem is that the leg that goes forward in time on your drawing is also going backward in time in terms of other, equally valid, systems of inertial coordinates, and conversely the interval in red that goes backwards in your drawing is actually going forward in time in terms of other systems of inertial coordinates. Any spacelike leg can serves as the backward leg of a paradoxical loop, so you can only preclude paradoxical loops by prohibiting signaling along every spacelike interval. Hence superluminal travel and signaling is impossible.

    Then I noticed this startling statement: “…entropy increase is ultimately correlated with decoherence and thus probably also with the rest frame of the microwave background…” The only way I can interpret this is that you are invoking a preferred frame, which can serve as the basis for defining an absolute time coordinate, and you distinguish between allowed and disallowed spacelike signaling intervals based on whether it goes forward in terms of that absolute time, associated with the rest frame (or rather, the isotropic frame) of the microwave background. The problem with this is that it violates local Lorentz invariance and the principle of relativity. It would mean that we can distinguish by local physics between different systems of inertial coordinates. In one unique frame we would have isotropic superluminal signaling capability and in others we would have restricted non-isotropic superluminal signaling capability.

    The basic premise of the standard proofs that superluminal signaling is impossible is that special relativity (local Lorentz invariance) is correct. Obviously if special relativity is wrong, then the proof does not apply. By distinguishing absolutely between forward and backward spacelike intervals, and assigning different physical effects for them, you are positing a violation of local Lorentz invariance in favor of a preferred frame (the isotropic CMBR).

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    1. Amos,

      "The problem is that the leg that goes forward in time on your drawing is also going backward in time in terms of other, equally valid, systems of inertial coordinates"

      Yes, of course. Why the heck do you see the need to tell me an utterly trivial fact of special relativity, especially after I explicitly mentioned it in my video. Seriously, why can you not at least for a second consider that I have thought about what I am telling you. Of course you can change forward and backward in time relative to some ARBITRARY coordinate time.

      "The only way I can interpret this is that you are invoking a preferred frame,"

      Yes, the arrow of time is a preferred frame, congratulations!!

      " The problem with this is that it violates local Lorentz invariance and the principle of relativity."

      No, it does not. Any type of matter defines a preferred frames and this is not in conflict with relativity whatsoever. You seem to have a very basic misunderstanding about the meaning of relativity.

      Delete
  57. Its Memorial Day in the US as I write this. That's the day we honor those who died in past wars. It got me thinking about the past and going back in time which I do not believe is possible in any real sense.

    The very human feeling that we can go back in time and alter past events is fictional time. You can't go back and kill Hitler and prevent WWII. You can't go back and observe a child's birthday. Those sort of events are vaporware, they have evaporated in the mists of the past.

    They exist now in our memories, and in the permanence of objects we see around us, in pictures on the mantle of a child's birthday party or the graves from past wars.

    So live in the present but don't forget the past. Peace.
    Happy Memorial Day.

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  58. Thank you, Dr. Hossenfelder, for taking the time to explain this to us. I think I have a better understanding now. Correct me if I'm wrong, but I believe your point is that spacetime is curved, and hence in the real world any inertial reference frame is valid only locally, i.e. spacetime is flat only close to the observer. So it may not be a problem if the coordinate arrow of time disagrees with the causal arrow of time for spacelike separated events, it just shows that the time coordinate cannot be validly extended that far (just as "north" and "south" are only meaningful locally on a sphere).

    In all of this it's important to carefully distinguish between the coordinate arrow of time (valid only locally) and the thermodynamic arrow of time (valid globally). In flat spacetime without FTL these always point the same way, which is why it's easy to conflate them.

    I'm still a bit uncomfortable with disgreements about the arrow of time in nearly flat spacetime. But this may be explained by the FTL mechanism itself, if it warps spacetime.

    I'm also not quite convinced that there is a unique foliation giving a global thermodynamic arrow of time. Perhaps there are several equivalent ways of defining it. In any case this is my own lack of understanding and is the kind of thing that's established in a textbook or journal paper rather than in a youtube video.

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  59. Dear Sabine,

    Is instantaneous action-at-a-distance (IAD) possible, in principle? What do you think?

    IAD is there in the Fourier theory, and I know that the Fourier theory is at the base of the non-relativistic QM, and that's how, there is IAD also in the non-rel. QM.

    But I don't know about the relativity theory (except for some modern physics-level bit about SR). If GR allows for (in the sense, it doesn't rule out) FTL, does it also allow for (or remain silent about) IAD? What about QFT?

    Please see if you can address this cluster of ideas in simple enough terms; thanks in advance.

    Best,
    --Ajit

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  60. Recami, et.al. (2008) wrote a review (arXiv:0804.1502v1): "Homage to E.C.G.Sudarshan, Superluminal Objects and Waves (overview of the relevant experiments)." There, it is reiterated: "everything that was thinkable without meeting contradictions had to exist somewhere in the unlimited universe (attributed to Democritus)." Murray Gell-Mann re-worded it thus: "Anything not forbidden is compulsory." Recami also reminds us that "at the beginning of the 1970s our own papers on similar subjects were always rejected by the Physical Reviews— things have now changed a lot as to superluminal motions (footnote, page 14)." Among other things, the paper claims: "Superluminal electric charge is expected to behave as a magnetic monopole and a black-hole a priori can be the source of tachyonic matter (page 5)." The paper concludes: "...localized superluminal waves are probably unable to transmit information faster than c." (see pages 13 and 18). There is much food for thought. Ultimately, I revert to Sudarshan's lovely 1968 Physical Review paper: "If we do not find them we ought to be able to find out why they could not exist." That challenge should be looked into.
    One wonders how it is that Sudarshan's 1968 paper was accepted by the Physical Review, while, as Recami says " in the 1970s all our papers were rejected." Recami should inform the reader as to why 'all' of those papers were rejected by Physical Review.

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  61. Just because you have signals that go faster than light does not imply you have causality violations.

    It does if local Lorentz invariance (special relativity) is valid: The laws of physics take the same form when expressed in terms of any system of inertial coordinates, and any putative signal along a spacelike interval goes backward in time in terms of some system of inertial coordinates, so it would follow that we can signal backwards in time in terms of any system of inertial coordinates (including the local isotropic CMBR frame), which implies causality violations.

    You get causality violations only if you ignore the existence of an arrow of time.

    In the context of special relativity, any ability to signal along any spacelike intrerval implies the ability to signal into the past of any system of inertial coordinates (including whichever one you label as the absolute time, if you like). This is just the standard argument as given by Einstein, et al.

    Yes, the arrow of time is a preferred frame, congratulations!!

    In the context of special relativity the class of local inertial coordinate systems (in which all the laws of physics take the same form) all share the same light cone structure, i.e., the distinct regions of the causal future and causal past, so they all have the same “arrow of time” in the Lorentz invariant sense, but this doesn’t distinguish any particular frame within that class. Your statements imply that the local laws of physics are detectably different in terms of different systems of inertial coordinates (because you have isotropic superluminal signaling capability in one unique frame but not in others), which violates local Lorentz invariance. (Also there is no well-defined proper time along any spacelike interval, etc.)

    Any type of matter defines a preferred frame…

    In this context, “preferred frame” means that, according to your statements, the local laws of physics are not Lorentz invariant, they take a special isotropic form in terms of one particular frame: In that one unique frame we would have isotropic superluminal signaling capability and in others we would have restricted non-isotropic superluminal signaling capability. This is a direct violation of local Lorentz invariance and the principle of relativity.

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    1. You have just argued that if what you say is correct (namely: faster than light travel leads to causality paradoxes), then special relativity must be wrong just because particles have rest frames. That constitutes a reductio ad absurdum and proves your argument is wrong. Thanks for saving me the effort.

      Delete
    2. It seems to me one could look at it two different ways:

      1) In some frames faster-than-light signalling is possible and in others it is not possible, so the laws of physics are not the same in all frames.

      2) No, it is the laws of physics which say that FTL signalling is possible in some frames and not others, so the laws of physics have not changed from frame to frame, just their results.

      In either case it seems a lot conceptually simpler to me to just say, as far as we know, FTL signalling is impossible (in all frames), but we might (as almost always) be wrong. (I gave up on it long ago, but still like to read sf novels that use it.)

      Anyway, Dr. Hossenfelder certainly made us think, didn't she? (Ouch, it is hard sometimes!)

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    3. Perhaps faster than light signalling is not possible in a flat spacetime, because it leads to globally inconsistent coordinates. But inconsistent coordinates are not a problem in curved spacetime, they're expected. So relativity rules out some kinds of FTL, namely those which are not associated with some kind of warping effect on spacetime.

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    4. Eric,

      Well, yes, that's one way to look at it. The moment you put any matter into space-time it is strictly speaking no longer flat and it's the matter that defines the arrow of time. So you could say that the problem with the supposed causality paradoxa is requiring space to be flat which -- again, strictly speaking -- means it contains no matter. However, I do not find this answer particularly helpful because we deal with matter in special relativity all the time while leaving the space-time flat.

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    5. It is not entirely helpful, in fact none at all. As we do physics we acknowledge certain mathematical structures as ideal. A tiny particle in flat space does have some tiny gravitational influence, but it is negligible. The gravity field of an electron does not do much to change the flat space ideal.

      Traveling faster than light in curved space is more complicated to understand, but you run into the same issues. A tachyon in curved spacetime has an ambiguity to the ordering of the proper interval with any meaning as time. One observer would order it this way and another observer would order it the opposite way.

      Delete
  62. 26-MAY-2020

    Forgive me if this was already mentioned, but wouldn't FTL travel
    imply an ability to exceed the escape velocity of a black hole's
    horizon? Extragalactic jets are relativistic, but do we observe
    superluminal velocities? Either way, we don't see quasars or AGN
    getting younger, do we?

    Superluminal velocities implies stuff could actually leave the black
    hole interior. That seems dubious.

    An interesting new confusion.

    Cheers,
    mj horn

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    1. mj horn,

      Just because it's possible doesn't mean it actually happens.

      Delete
    2. Indeed so. A traversable wormhole connecting the exterior and interior of a black hole would permit one to access information about the interior. This runs into troubles with the Bekenstein bound. A tachyon probe that one might imagine could be scattered into and out of a black hole might also convey information about the interior.

      Delete
  63. Years ago I followed with intense interest claims by a ceramics engineer/physicist duo that were totally startling in their content, always mindful of Carl Sagan’s dictum: “Extraordinary claims require extraordinary proof”. In some sense corroborating evidence, at least in my non-physicist mind, for this duo’s experimental claims were provided by work conducted at a professional laboratory in Austria, which I won’t detail for brevity. The claim in question was that a kind of gravity-like ‘beam’ from a high temperature superconductor was able to physically displace a pendulum bob, through a small arc, a very considerable distance away. Not having remotely the knowledge depth of physics as Sabine, and many commentators on this blog, I certainly wasn’t qualified to judge if their alleged experimental results were totally outrageous, suitable only for the tabloids, or possibly legit.

    Then about 8 years ago the duo made the even more startling claim that the disturbance from their ‘beam’ propagated at just under 64 times the speed of light, as measured by piezoelectric sensors spaced a kilometer apart, and synchronized with atomic clocks. On reading that, the credibility of their research dropped to zero in my mind, as everyone knows that no influence between two points in space can occur sooner than it takes a light beam to traverse the two points. That thought was followed by a sudden epiphany: ‘but nobody informed the Universe’ – as it dawned on me that galaxies beyond the Hubble horizon are separating from us at ‘effective’ superluminal speeds due to the expansion of spacetime.

    According to the current Big Bang model points in space were separating from each other at something like an effective billion, billion, billion, etc., times light speed during the first second of the Inflationary Epoch. That made the duo’s claims seem rather modest in comparison, if it’s assumed that what was really happening in their experiment was a very-localized expansion due to some interaction occurring within their superconductor. In effect, the 50 gram pendulum-bob and superconductor were behaving like miniature galaxies, accelerating away from each other due to local spatial expansion. Of course this implies that the, (momentary), density of ‘dark energy’ in the duo’s experiment was orders of magnitude greater than is currently seen in our Universe. The Hubble Constant (H0), defining the expansion rate of our Universe, is about 67.6 (km/s)/Mpc, or about .225 c, over a span of 3.08 x 10^22 meters. By crude comparison, (the presumed), expansion of a, (10 cm. diameter), column of space in the duo’s (alleged) experiment was about 64 c, over a span of 1.5 x 10^2 meters, or 5.7 x 10^22 times greater than H0.

    This is all pretty weird, but back in the day it really intrigued me. Whether it’s true is another question.

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  64. I grew up on science fiction, love science fiction, and desperately would want faster than light to be possible, however being more pragmatic much of the speculation (mathematically possible but not proven by observation) is another reason to consider Einstein’s greatest theories are exceptional approximation’s that don’t exactly mimic space-time. It’s been reasonably apparent to me how the use of different fundamental assumptions and axioms could likely keep his proven observables intact while making much of the speculation not possible. I apologize for violating the rules but they should be considered; space and time are always concurrent (inseparable), and empirically are always a change of position in space (physics equations often contains many interpretables that are not observable that are necessary, but not always helpful in advancing science).

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  65. You have just argued that if what you say is correct (namely: faster than light travel leads to causality paradoxes), then special relativity must be wrong just because particles have rest frames.

    The fact that particles have rest frames does not imply that special relativity is wrong, nor does it invalidate Einstein’s explanation for why superluminal signaling in the context of special relativity would lead to causal paradoxes. Local Lorentz invariance does not deny the existence of objects with rest frames, it just asserts that the laws of physics take the same form when expressed in terms of any system of inertial coordinates, so none of those system is distinguished or preferred in that sense. (Note that they all share the same arrow of time, i.e., the same past and future light cones.) Einstein’s (and the standard text book) argument that superluminal signaling or travel unavoidably implies causal paradoxes is as follows:

    The premise of the argument is that special relativity is (locally) correct, meaning all the laws of physics take the same form in terms of any system of inertial coordinates, so whatever capability for superluminal signaling exists in terms of one inertial coordinate system must exist in terms of every other. This is just the principle of relativity. Now, any putative spacelike signal proceeds in the negative coordinate time direction of some inertial coordinate systems, so by the principle of relativity it would follow that signals can likewise propagate in the negative time direction of any system of inertial coordinates, and hence we can construct loops that violate causality. This argument does not imply that special relativity is wrong. Rather, it shows that if special relativity is correct, superluminal signaling implies causality paradoxes, from which we typically infer that superluminal signaling is impossible.

    In contrast, your argument is that the local laws of physics take a special form in terms of one particular frame (the CMBR frame), in which (according to your description) we have isotropic superluminal signaling capability, whereas in other inertial coordinate systems we would have restricted non-isotropic superluminal signaling capability. This is a direct violation of local Lorentz invariance and the principle of relativity. Again, this does not prove that special relativity is wrong, it simply shows that if special relativity (local Lorentz invariance) is correct then any superluminal signaling implies causality loops.

    The watch will read whatever time coordinate you chose that it represents.

    The question isn't about coordinate time, it's about proper time, e.g., the time showing on the wrist watch of a putative superluminal traveler. If you believe a traveler can proceed directly along the spacelike interval from x=0,t=0 to x=L,t=0, what is the difference in his wrist watch readings at those two events? If more information is needed to give an explicit answer, what additional information is needed? Or is the question inherently unanswerable?

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    1. Amos,

      "by the principle of relativity it would follow that signals can likewise propagate in the negative time direction of any system of inertial coordinates"

      As I said, what coordinates you chose is entirely irrelevant. Coordinates are merely labels. The question is whether you can signal along the direction that these coordinates identify as "forward". You simply assume you can. This is wrong. Because in some frames this forward-direction is not aligned with the arrow of time. In other words, you assume that you can send information against the arrow of time, which ignores the 2nd law of thermodynamics.

      This is where the erroneous conclusion comes from that grandfather paradoxes may happen. It is ignoring the existence of an arrow of time; not faster-than-light signalling.

      Delete
  66. As I said, what coordinates you chose is entirely irrelevant. Coordinates are merely labels.

    Coordinates are labels, but there is a special class of coordinate systems in terms of which the laws of physics take the very same simple homogeneous and isotropic form (principle of relativity), and these are called inertial coordinate systems, and, according to special relativity, inertial coordinate systems are related by Lorentz transformations.

    Since all the laws of physics take the same form in terms of any system of inertial coordinates (principle of relativity), it follows that whatever capability for superluminal signaling exists in terms of one inertial coordinate system must exist in terms of every other. Hence any putative spacelike signal implies the ability to construct loops that violate causality (effect precedes cause) as Einstein explained.

    The question is whether you can signal along the direction that these coordinates identify as "forward".

    To be precise, the question is whether, assuming special relativity is correct, any ability to signal (or travel) along a spacelike interval would imply that we could construct causal loops, and the answer is yes, for the reason Einstein explained (see above).

    You simply assume you can.

    The only assumption is special relativity (local Lorentz invariance), and then we examine the consequences of the possibility of signaling along spacelike intervals, and find that it implies the ability to construct causal loops, as Einstein explained.

    In some frames this forward-direction is not aligned with the arrow of time.

    According to special relativity, no spacelike interval is "aligned with the arrow of time". Only timelike intervals (all of them) are aligned with the arrow of time, which is why causal effects can proceed only along timelike intervals. To clarify your position, I keep asking you to tell me the elapsed proper time along a spacelike interval - any spacelike interval - and you keep not answering.

    In other words, you assume that you can send information against the arrow of time…

    Every spacelike interval is equally “against the arrow of time”, and if we could signal along one, and assuming special relativity is true, we could construct causal loops, as Einstein explained.

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    1. Amos,

      "Every spacelike interval is equally “against the arrow of time”"

      No, it is not. Because the universe has an arrow of time.

      Delete
    2. @Amos Can you please tell us the source of your Einstein quote?

      Delete
  67. Dr. H states:

    "This is where the erroneous conclusion comes from that grandfather paradoxes may happen. It is ignoring the existence of an arrow of time; not faster-than-light signalling."

    You are correct. If there are Tachyons AND there is an Interface between Lorentzian Sensibilities and the Superluminal, there is without doubt a very strict Arrow of Time - reversing Superluminal parts with Sub-Luminal parts will not "reverse time". Only at the shortest distances could there be such an exchange and that would not reverse time but would provide, for ex., a rationale for understanding CP violations. On this view, the Arrow of Time is VERY strict.

    Thanx,

    CW

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  68. There is a question about measuring the speed of light, which sounds simple but is not in my view. Any speed is related to space.

    The simple equation says
    v = d / t where d is distance and so related to space.

    Which space is meant in cosmology? Present physics says that the space of our universe is steadily expanding. If we now talk about the speed of light, to which space is c related? That is particularly important when we discuss the assumed constancy of c during the development of the universe.

    There are two relations to space possible:
    1) To the current state of the expanding space whichever it is during time
    2) A background space which is assumed not to change during the development of the universe

    Consequences for both cases:
    1) Any measurement of c will yield the same value at any time. But this understanding of a constant c is not able to solve cosmological horizon problem by the assumption of inflation, because the relation of c to space will never change and so the conflict remains.
    2) If we relate c to a background space, then inflation is in fact a solution for the horizon problem. But this denies Einstein’s relativity.

    So, what is the reality?

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    Replies
    1. It's 1, and you are misunderstanding what you say is a consequence.

      Delete
  69. Further reading:
    (1) Theorist Robert G. Sachs wrote a beautiful book entitled
    "The Physics of Time Reversal" (1987, Univ Chicago Press). Among other things, we read: "The irreversibility of the processes of the Universe is often said to define an 'Arrow-of-Time' that fixes the forward sense of time. This 'Arrow-of-Time' has little to do with the time variable as measured by physicists. In particular, it has no bearing on the physics of time reversal." (page 30).
    (2) In a fascinating paper, T. Padmanabhan attempts to relate Mach's Principle and the Notion of Time (pp. 424-430, 1994, Physical Origins of Time Asymmetry).
    (3) Matt Visser co-authored a paper "Faster-than-c signals, special relativity, and causality" where we read: "As far as causality is concerned, it is impossible to make statements of general validity, without specifying at least some features of the tachyonic propagation." (arXiv:gr-qc/0107091).

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  70. Amos wrote: "Every spacelike interval is equally “against the arrow of time”"

    Sabine replied: No, it is not. Because the universe has an arrow of time.

    The existence of an "arrow of time" does not imply that any spacelike interval is timelike. (What would be the elapsed proper time along a spacelike interval?) All local inertial frames share the same “arrow of time”, meaning they all have the same past and future light cones, which represent the Lorentz-invariant causal (partial) ordering of events, and all the laws of physics (including thermodynamics, etc.) take exactly the same form in terms of any of those inertial coordinate systems (principle of relativity), so you cannot maintain that the temporal foliation of one of those frames is consistent with the “arrow of time” and the foliations of all the other inertial frames are not. They are all equally compatible with the arrow of time. Yes, the CMBR is isotropic in terms of one frame and not in terms of others, but that doesn’t invalidate local Lorentz invariance, and hence does not invalidate Einstein’s explanation for why superluminal signaling in special relativity would imply causal loops.

    According to what you’ve said, within a sealed compartment in inertial motion we could perform local physical operations that would tell us our velocity relative to the isotropic frame of the CMBR. When asked how you reconcile this with local Lorentz invariance you’ve alluded to the fact that objects have rest frames, which suggests that you believe there is some kind of all-pervasive substantial ether at rest in the CMBR frame that permeates the universe (even inside “sealed” compartments) and establishes a locally detectable rest frame everywhere. But even such an all-pervasive medium would not invalidate special relativity (and hence not enable superluminal signaling) unless the effective spatio-temporal symmetry is also assumed to be Galilean rather than Lorentzian.

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  71. Hello Sabine
    You say "However, there is nothing in Einstein’s theory that forbids a particle to move faster than light. You just don’t know how to accelerate anything to such a speed. So really Einstein did not rule out faster than light motion, he just said, no idea how to get there."

    I am surprised. If i don'n mistake, the well proved Lorentz transformation (TL) imply that a massive particle would tend to a infinite energy when v tends to c, whatever the mean for accelerate it (*). And his proper frequency f tend to infinite, so also his energy E= hf. Now infinite energy is prohibited in physics, so no material thing cannot travel faster than light in a spacetime where TL apply . Where is the error ? And tachyons - those dubious speculations- , cannot travel at speed less than c.
    (*) And of course the well proved energy's conservation imply that you would need infinite energy to accelerate that massive particle whose energy would be infinite.

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  72. I thought I would, before this reaches 200 posts and become too inconvenient to access, give on small thumbs up for the tachyon. Cumrun Vafa wrote on how the singularity of a black hole is a condensate of tachyons. It is an interesting idea. The reduced Penrose diagram for the Schwarzschild black hole has the horizontal singularity continuous with the final appearance of the black hole due to Hawking radiation. So. it is not hard to think that quantum fields that reach the singularity are shot along a spacelike direction and expelled as Hawking radiation. This in part goes with Susskind’s ER = EPR as the nontraversable wormhole structure expands to some maximum.

    ReplyDelete

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