# Sabine Hossenfelder's argument to rule FTL paradoxes out

I have recently seen Sabine Hossenfelder's video on faster-than-light travel, in which she argues no paradoxes would arise if we had something like a FTL warp device, because the trajectories leading to paradoxes are not permitted in the first place. Since I didn't really understand her argument, I also checked her blogpost.

I am not convinced, and while I have some knowledge of SR and GR I am certainly no expert so it is possible that I simply did not understand. The way I understand what she is saying is as follow: It is indeed mathematically possible to go "back in time" with FTL and create paradoxes, but such a reverse motion would violate thermodynamics 2nd law and is thus physically nonsensical. However, it is possible to find a frame of reference in which the passage of time is not reversed which still leads to a closed time loop. Such an example is presented here. So to me, her explanation isn't convincing and it stills looks like FTL would break the principle of relativity (one observer seeing a violation of the 2nd law, another seeing a perfectly normal situation).

• Transcript of the video May 21, 2021 at 18:34
• What should I do with that? The video was not clear to me, the transcript, which is a word-for-word transcription isn't either. May 21, 2021 at 20:08
• I'm just posting the link for the benefit of people who don't want to watch the video. May 21, 2021 at 20:44
• I think she means that FTL travel is not excluded by paradoxes because you could just conclude that if you travelled FTL or back in time you would just have to end up far enough away from your world line that you couldn’t reach it before you left. So let’s say you make a worm hole time machine, paradoxes could be avoided if physics sets a necessary distance of the mouths such that you couldn’t get back to your starting point before you went in. May 21, 2021 at 21:53

Yes, I think she's basically saying that if you accept that there's some preferred frame (e.g. in which the cosmic microwave background is most isotropic) and have your FTL travel be relative to that frame, then no actual paradoxes can occur, only apparent ones. Your ship may appear to go backwards in time in some frames, but since it never goes backwards in time in the preferred frame, no closed timelike curves can occur.

Of course, this gives up the principle of relativity, which is a pretty heavy cost. But the violation of relativity is only apparent in the new (FTL) physics, so it's not impossible -- just (IMHO) extremely unlikely.

This blog post is a transcript of the video, and also has a long comments section. While most of the comments aren't worth reading, there's at least one where Hossenfelder clarifies her position. The singly-indented paragraphs are her and the doubly-indented paragraphs are a commenter named Amos.

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.

Her position, then, is that Lorentz symmetry isn't violated in vacuum, but the matter distribution implicitly defines an arrow of time and that's enough to avoid causality violation.

I'm 98% sure that this can never work. Here's a thought experiment to show that it can't work. Suppose you have a tachyonic radio transmitter and receiver. You speak into a microphone attached to the transmitter and your words come out of a speaker attached to the receiver at a spacelike separated point. Put the lab into a rocket ship and repeat the experiment at different speeds. There are three things that could happen:

1. The spacetime separation between transmission and reception, relative to the lab frame, depends on the speed.

2. The separation doesn't depend on the speed, but at some speeds the experiment just doesn't work because the "transmission" point is later in entropic time than the "reception" point.

3. The experiment works identically at all speeds.

1 and 2 give you a way to distinguish different speeds, violating the principle of relativity, while 3 means that you can send a message into your own past using two copies of the transmitter and receiver moving at different speeds.

For 1 or 2 to happen, there has to be some sort of background that's visible to the tachyons but that can't be accelerated along with the rest of the lab or evacuated from it, which is a de facto violation of Lorentz invariance even if the (unattainable) true vacuum is theoretically symmetric.

I suppose there is also option 0: the radio never works. But if there's no way to build a FTL radio from the tachyons then I wonder in what sense they are FTL themselves. Even if they interact only gravitationally with ordinary matter, the radio could be made to work in principle, though it would be difficult in practice.

• I also think it would be really easy to construct otherwise smooth spacetimes where any "surface stationary relative to a matter distribution" would end up having various caustics and singularities as you go toward "backward time" May 21, 2021 at 21:25
• I 100% agree... For the argument in the comments section to work, it would have to be the case that if you boosted all of the matter then the "preferred frame" would change. So it would still be possible (just practically hard) to build a closed timelike curve, by sending an FTL signal in one frame, boosting all the matter to change the absolute notion of time, and having the second signal sent in this boosted frame. May 21, 2021 at 21:27

I do think that she kind of glosses over the problems with hyperbolicitiy of surfaces that you get from GR in spacetimes that have closed timelike curves in them. Most of the framework for the initial value boundary problem in GR breaks down once you allow these things, and you'd have to do a lot of careful work to guarantee consistency, if it is possible at all.

The following is from an email I sent to Sabine (which she didn't reply to):

In your video "Is faster-than-light travel possible?", you say that the causality-violation,
grandfather paradox objection to such travel is nonsense, rubbish, since it is based on a
confusion about the direction of time, that if we have a consistent direction of time, there is no such paradox. You claimed the confusion is that the paradox says that by traveling FTL you are going backward in time in some inertial coordinate frame IF, but nevertheless are getting older, so your entropy is increasing. As far as I can tell, your argument involves this Claim: By traveling backward in time in any inertial frame IF you would be going in the time direction of decreasing entropy in IF, since entropy decreases in the backwards time direction in each IF. This Claim is self-contradictory, for somewhat the same reason that if you are traveling FTL in some frame IF1, you are, according to special relativity, traveling backward in time in some other frame IF2. Specifically, if at point p1 along your FTL path you are, in frame IF1's time, earlier than you are at point p2, so the entropy (of some closed subsystem S) at p1 would be, according to Claim, less than it is at p2, in some other frame IF2's time, p1 will be later than p2, so the entropy of S at p1 would be, according to Claim, greater than it would be at p2 (contradiction).

While, as shown above, the entropy (of S), or any other (single-valued) scalar function of
all space-time points cannot be an increasing function of (frame) time everywhere in each
inertial frame, and so it wouldn't be true for all inertial frames IF that travel backward in time in IF would be travel in the direction of decreasing entropy everywhere (at the same frame time) in IF, it is true, assuming that the 2nd law of thermodynamics holds
everywhere and always along each time-like curve, and so entropy of S in a past light
cone would be less than the entropy of S in the corresponding forward light cone, that
travel into your own past light cone would involve travel to a s-t region where your own
entropy would be lower than before reaching the past light cone. However, this no more
shows that travel into the past with FTL travel would be impossible than does the fact that in such FTL travel one's own proper time is going in the opposite direction to the frame time of each frame in which one is traveling backward in time. It is assumed that along your FTL path going backward in time in some frame, if you could travel such a path, in your own proper time, as your mental time increased, i.e., as the time seemed to get later, according to a popular theory of the relation of mental time direction to the temporal direction of entropy increase, your own entropy would increase, while the entropy of most other things, those not traveling with you, would decrease. This is just one of the peculiar aspects of time travel into the past, but is not a strict contradiction of natural law even if the 2nd law applies with the time it refers to being the external frame's time, since, as Maxwell emphasized, the 2nd law is only a statistical law, holding only almost all the time, for large systems, but not always. More importantly, with FTL travel into the past, the time to use in the application of the 2nd law to the time traveler would clearly be her/his own proper time, not the time of the frame wrt which he/she was traveling backward in time, so his/her-her/his entropy could increase while the entropy of the things wrt whoever was traveling FTL was decreasing, without contradicting the 2nd law.

Your 2nd law argument that I just, I think, demonstrated to be faulty was an argument
against the causality-violation/grandfather paradox's showing that FTL travel would result
in time travel into the past in some inertial frame, so could lead to causal contradictions, and so FTL travel is impossible. The causality-violation/grandfather paradox does involve travel by something into the past light cone of something, neither necessarily a person, but the argument for it is based more-or-less rigorously on the generally agreed-upon local causal structure of space-time. It shows that FTL travel could result in travel into the past. If the argument conflicts with the 2nd law of thermodynamics, which it doesn't, so much the worse for the 2nd law.

The causality objection assumes a time-orientable (that there exists a continuous choice
of light-cones to be the future light-cone) universe, which I think you would agree this
universe is, at least locally. Also, it is stated for a region U of space-time which is causally iseomorphic (bicontinuously isomorphic) to a convex open region of Minkowski s-t. This could be time-oriented by the local temporal direction of the increase of entropy if one of the 2 Minkowski light-cone orientations is everywhere in U the same as that of the local entropy increase orientation. The causality-violation argument against FTL travel applies to FTL travel of any controllable signal, including sending a person, which could be sent; it doesn't apply to the signal sent by a spin or polarization measurement of one of the pair to the location of the other of the pair for an entangled pair which is in the singlet state used in tests of locality via the Bell inequality, since these signals are uncontrollable by the sender. (Many people deny that a signal is sent in this situation, even though there is a correlation between the results of the distant measurements which cannot be explained by a local theory (either deterministic or probabilistic). They are wrong. What signal is sent is decided by inanimate nature, however, rather than the experimenter. Probably relevant to this is a Japanese conference paper titled approximately "Controllable and uncontrollable signaling", by Abner Shimony, which I haven't been able to obtain, but might yet if I try harder.) All this is gone into in greater detail in my unpublished paper "A possible severe conflict between quantum mechanics and special relativity", available at https://www.logic-physics-settheory-math.com/conflict-between-qm-and-sr.

The causality argument against the possibility of FTL travel doesn't depend on any
judgement of which of 2 spacelike separated s-t points a or b is earlier, except for using a time-oriented region U, or on whether in traveling a s-t path in one path-direction something is going forward or backward in time. According to special relativity, if a & b are 2 s-t points, whether a or b occurs earlier is not physically significant. The causality argument against FTL travel uses only the assumption that for some pair of spacelike separated s-t points, a controllable action at one of them guarantees a specified response at the other. This is what is meant by being able to send a controllable signal FTL. The argument proceeds as follows:

Suppose, for some inertial frame IF, signaling FTL wrt IF from one s-t point to some other
space-like related s-t point were possible. Then, by the principle of special relativity & the Lorentz transformations, it would be possible, for each inertial frame IF, to signal
instantaneously wrt IF from each s-t point to every other space-like related s-t point. In
such a case, signaling from some s-t point (x,t) into the past of (x,t), & next preventing that signaling, could be arranged as follows: Send a signal instantaneously, in some inertial frame IF, from (x,t) to some (y,t), with y =/ x, from (y,t) send, instantaneously in frame IF' moving away from x, a signal to some (z,t') in the past light cone of (x,t), which is possible since a simultaneity slice in IF' thru (y,t) intersects the past light cone of (x,t), next from (z,t'), by slower-than-light signaling, send a signal to a mechanism that will prevent the initial sending of the signal from (x,t) to (y,t).

There is an assumption that the possibility of time travel would allow for paradoxes because a return to the past would allow changes to be made to the conditions that then existed- the famous example being that one might kill one's grandfather.

The scope for such paradoxes disappears if one adopts the presentist view of time, which crudely can be defined as stating that all particles exist as points in spacetime. In the presentist view, if you were to go back to 6:47 PM on 3 June 1930, say, you would not be able to kill your grandfather, because all the particles that comprised your grandfather then are no longer at that t coordinate- they are here in 2021 where you left them behind. Indeed, you would find that entire region of spacetime to be an empty void when you visited it, as the universe has since moved on to a later region of t.

• The problem with presentism is that it doesn't work with general relativity in the first place. It has trouble enough with special relativity, but it demands that physicists replace GR - a well tested theory - with something else that uses a lower-dimensional manifold. May 21, 2021 at 23:34
• I disagree. That depends upon how you interpret the meaning of the word 'present'. If you and I are at different heights in a gravitational field we experience time at different rates, but the present is the same for each of us. We might disagree about the time and the date but we both agree that now is the present. May 22, 2021 at 5:26
• General GR spacetimes do not allow a consistent foliation of presents (consider ones with CTCs for a starter). A presentist may claim such spacetimes are ruled out, but then they need to introduce extra elements to the theory to explain why they cannot occur. Presentism also runs into problems when we have different reference frames in SR, since it claims that things in my past should not exist despite you (present in my frame but moving) seeing them in your present. May 23, 2021 at 15:44
• Again, that view of presentism, which many presentist share, is erroneous. Consider the Andromeda paradox in reverse. Say two frames of reference moving relative to each other at 1m/s have their origin at some time t=t' in Andromeda, and one is stationary relative to you so is also your rest frame. If you start walking at 1m/s, you join the other frame. According to the frame you have just joined, your time coordinate is now very different. Does that mean you have moved from the present? No, it just means you have assigned a different t coordinate to it... May 23, 2021 at 17:45