Backreaction on Superluminal Travel

Reasoning will never make a man correct an ill opinion, which by reasoning he never acquired.

                                                                           Jonathan Swift, 1721

A popular Youtuber named Sabine Hossenfelder has posted several videos promoting her belief that superluminal signaling and travel are compatible with the laws of physics. Her stated reasons are essentially the same as those voiced by many anti-relativity enthusiasts, on which we’ve commented previously, but she’s added a couple of new arguments, so it’s worth taking another look.  Despite the number of times she has addressed this topic, the precise content of Sabine’s thesis remains somewhat fuzzy, and her arguments in favor of it seem to fluctuate. She sometimes argues that superluminal travel is perfectly compatible with special relativity, while at other times she concedes that it isn’t, but that it is compatible with general relativity, and at still other times that it isn’t compatible with either of them, but that those theories are wrong, and superluminal travel will turn out to be compatible with whatever future theory eventually replaces them.

Before giving any rationale, Sabine’s latest discussion begins by acknowledging that her belief in superluminal travel is a personal commitment that has its origins outside of, and prior to, any mature scientific reasoning. In her own words:

I want to talk today about an issue that bothers me a lot, it’s that most physicists believe the speed of light is an ultimate, absolute, and impossible-to-overcome limit.  Indeed, I think it is the biggest mistake that physicists are making -- that our entire species is making.  It’s the reason we invest so little in space travel [because] as long as you’re bound by the speed of light, it would optimistically take several generations to travel to even the next closest solar system…  It’s also why we are unable to make contact with extraterrestrial civilizations, which I am convinced are out there, because if there is any way to message faster than the speed of light, obviously that’s what everyone else is using… I think it is possible to send signals faster than light. In some sense it’s why I went  into physics. You see, I thought the best way to make rapid progress on this planet was to make contact with extraterrestrials who have already solved the problems that we’re still working on. 

Sabine goes on to say that if extraterrestrials are sending messages exclusively superluminally, and we are listening exclusively for luminal messages, we will never hear from them, to which modern science answers “but they aren’t, because superluminal signaling is impossible”. Sabine then presents her latest summary of why she believes the physicists are wrong.

Sabine’s first argument is that we should return to the 19^th century concept of a unique local frame that is distinguished in terms of its local dynamics, meaning that the local laws of physics take a different form in terms of one inertial system than in terms of another.  Now, this is a blatant violation of Local Lorentz Invariance (LLI), which is among the most thoroughly and precisely verified principles of physics, and is a foundational element not just of special relativity, but also of general relativity and quantum field theory. It’s the very foundation of the crucial relation m² = E² – |p|². Sabine hints at two arguments here, one that says Lorentz invariance has no applicability because objects have rest frames (expressing an elementary misunderstanding of Lorentz invariance), and another that says Lorentz invariance may be empirically false. Of course, one can always argue that the next experiment (or the one after that…) will reveal a gross violation of LLI (as would be needed for macroscopic superluminal travel to be possible), but this is not scientific reasoning. If someone wants to fantasize about a universe in which special relativity is false and superluminal travel is possible, that’s fine, but it isn’t science, it’s science fiction.

In both special and general relativity, all causal effects from a given event propagate on or inside the forward light cone of that event. This is fundamental. Spacelike intervals – meaning intervals that point outside the light cone of the event -- would have imaginary “proper times”, which is incommensurate with actual elapsed proper time. This by itself suffices to prove that superluminal signaling and travel are incompatible with special and general relativity. To further emphasize this incompatibility, as first explained by Einstein in 1905, note that any possibility of superluminal signaling in this context would imply the ability to construct closed causal loops and logical contradictions, such as allowing for a message to be sent if and only if it is not sent. This is because, according to special relativity, all the local laws of physics take exactly the same form in terms of any local standard system of inertial coordinates, which are related to each other by Lorentz transformations, regardless of the velocity of those systems relative to any particular system, such as the local system in which the CMBR is maximally isotropic, or the rest frame of any given material entities. Hence if any degree of superluminal signaling were possible in terms of any system of inertial coordinates, exactly the same would necessarily be possible in terms of every such system, and hence (because they are related by Lorentz transformations) we would be able to send a signal backwards in time so it arrives at its point of origin before it was sent. This has been well understood since Einstein first discussed it in his 1905, 1907, and 1910 papers.

In her discussion of this topic, Sabine conflates the cosmological local CMBR isotropic frame, which singles out one unique temporal foliation at any location, with the dynamical concept of the “arrow of time”, which distinguishes between causal past and causal future, but which most definitely does not single out a unique temporal foliation.  All the laws of physics, including the laws of thermodynamics, take exactly the same form in terms of every local system of standard inertial coordinates, and there is a unique forwards and backwards light cone for each event, applicable to every inertial system. From this, Einstein’s argument follows unavoidably.

Sabine doesn’t appear to understand this, because after outlining her belief that LLI is grossly violated, she somehow still feels able to say “So we see that really there is no problem with faster than light signaling in Einstein’s theories”. As Einstein and countless other physicists have explained, that is simply false. Note that Sabine’s assertion here is not an empirical one, it’s purely theoretical, and unambiguously false for the reason explained above. Again, the proper time along a spacelike interval, if such a thing were possible, would have imaginary magnitude, which is simply not commensurate with proper time. The light cone isn’t just a barrier, it is a limit for any logically coherent causal propagation, and this clearly has nothing to do with the “arrow of time”, which refers to the distinction between the past and future light cones, not to the distinction between spacelike and timelike intervals.

Sabine’s assertions entail gross violations of local Lorentz invariance, which, as noted above, is a cornerstone of both special and general relativity as well as quantum field theory. It’s encouraging, though, that she recently acknowledged that the causality argument does indeed prove that superluminal signaling implies logical inconsistencies (closed causal loops) in the context of special relativity. However, she then simply jettisoned special relativity and continued to imagine that somehow (not invoking any extreme curvature or wormholes, etc., since all her discussions are stipulated to be in essentially flat spacetime) her posited violations of LLI would be viable in general relativity, even though general relativity too is founded on that principle, and closed time-like loops are no more benign in general relativity than in special relativity. Now, in still other expositions she has implicitly acknowledged that superluminal travel may be inconsistent with general relativity, but then she argues that we know general relativity can’t be right, because it isn’t a quantum theory, so it can be safely disregarded. This is the standard sophistry that until we know everything we don’t know anything. She feels confident that a future theory of quantum gravity will entail gross violations of local Lorentz invariance (despite the fact that violations of such a magnitude have long since been ruled out empirically), but with no rationale other than that it is her wish that it be so. Also, after admitting that superluminal signaling is indeed incompatible with special and general relativity, she immediately repeats the claim that superluminal signaling is compatible with “Einstein’s theories”.

Next, Sabine considers what quantum theory has to tell us about whether superluminal signaling or travel is possible. She begins by acknowledging that “quantum physics is often said to be non-local, and yet that non-locality somehow respects the speed  of light limit”, but then she immediately adds “If that doesn’t make sense to you, it’s because it actually doesn’t make sense.” Well, part of the problem here is that the word “locality” has different meanings in different contexts, and many authors conflate the different meanings. It would be better to use a word like “non-separability” rather than “non-locality” when referring to what is implied by the quantum correlations. Those correlations do not violate locality in the sense of Lorentz invariance and the fact that spacelike-separated variables commute. Entanglement in quantum theory refers to correlations between the results of measurements on (potentially far distant) entangled particles, but those non-classical correlations do not permit superluminal signaling. Indeed, this is one of the strongest confirmations of the inviolability of local Lorentz invariance – the very thing Sabine needs to deny – albeit while denying that she’s denying it.

At this point Sabine presents a lengthy digression about her frustrations in trying to convince people of the correctness of her ideas about the foundations of quantum mechanics.  She contends that quantum mechanics, in a so-called “superdeterministic” interpretation, can be explained by a “hidden variables” theory, and this, she says,

… strongly suggests that quantum physics is not fundamental. It suggests that there is an underlying, deeper layer that we  have not yet discovered… if you believe this, then quantum physics is really just an average description of some underlying deterministic theory. It’s a statistical theory… This is important because whenever you have some average theory,  you can get deviations from that average. And we know that deviations from that average, which is standard quantum mechanics, would allow us to send signals faster than light.

This is misleading, because there’s a well-known sense in which standard quantum electro-dynamics entails faster-than-light terms in certain approaches to the calculations. For example, the amplitude for a photon between two given events has the major term coming from the null interval, but there are other contributions, some along an interval with positive magnitude (subluminal) and some along an interval with negative magnitude (superluminal), but those cancel out over long distances. For an accessible discussion of this, see the text related to Figure 56 in Feynman’s “QED”.  These “deviations from the average” are well understood, similar to fluctuations in energy related to the uncertainty principle, and do not provide any means of signaling (let alone traveling) faster than light.

But these facts about standard quantum theory are not what Sabine is referring to. Indeed, she segways from discussing “deviations from the average” to discussing “deviations from quantum mechanics”.  She contends that superdeterminism entails measurable deviations from standard quantum mechanics, such that

…the outcome of the measurement depends on what you measure. And then, the measurement on one side can influence the measurement outcome on the other side.  It does so faster than light. That is still local because both of these properties were determined already when the particles became entangled…

This is a self-contradictory jumble, because it is saying that the correlations of entangled particles are (1) effectuated by faster than light signaling, and (2) already pre-programmed into the separate particles. Those are mutually exclusive propositions. Sabine summarizes this line of reasoning by saying “If quantum mechanics is not actually the fundamental theory of nature, if hidden variables are real, then we can almost certainly signal faster than light”. So, after jettisoning special and general relativity, she rejects standard quantum theory, but her attempt to replace these pillars of modern science with something else, something that supports superluminal signaling and travel, are incoherent and self-contradictory. In particular, note that John Bell’s whole purpose in introducing the notion of superdeterminism was as an alternative to superluminal action. Recall that the two possible explanations of the correlation inequalities that Bell articulated were (1) there are influences going faster than light, so we should return to a distinguished frame and jettison local Lorentz invariance (which he favored), or (2) we could adopt superdeterminism to pre-arrange the correlations without needing to invoke superluminal influence. In other words, the whole purpose of superdeterminism was to obviate superluminal influence and thereby preserve local Lorentz invariance, and yet Sabine claims that superdeterminism necessitates superluminal influence and the rejection of local Lorentz invariance.

It’s difficult to make any sense of her claim, but if we take her statements literally, the concept of “superluminal signaling” she has in mind is not actually superluminal signaling at all, but is based on the notion that superdeterminism implies that the message Mr A is sending to Mr B is pre-determined by the initial conditions of the universe, and those initial conditions are also in the causal past of B, so B is in a position to already know the message that A is going to send to him. According to this view, there is no free choice or new information at any event subsequent to the initial conditions of the universe.  Everything is pre-determined, and every event has access to all those initial conditions, so this would explain why Sabine believes B can “receive” (meaning B can infer from his causal past) A’s message when spacelike-separated from the transmission event. This would apply even to a message in which A tells B who just won the Kentucky Derby. Mr B is able to already know what A’s message will say, even before A sends it, and indeed even before the Derby is run, because the outcome of the Derby (like everything else) was pre-established in the initial conditions of the universe. Notice that, according to this notion, every event must have access to the initial conditions of the entire (and necessarily closed) universe, because two scientists at opposite ends of an EPR entanglement experiment could select their measurement angles based on, say, the incoming light from quasars viewed in opposite sides of the cosmos.

Regardless of whether anyone wants to take all this seriously, it is highly misleading to say that it entails superluminal signaling. If this were really what Sabine had in mind, she should not say that superluminal signaling is possible (which it isn’t in this model), but rather that superluminal signaling is pointless and unnecessary, because every receiver can deduce the content of every message that will ever be sent to him (or anyone else, even before it is sent), because everything is pre-determined and encoded in the initial conditions of the universe, to which every receiver necessarily has efficacious access (because it determines all his out-going messages as well). This is indeed what John Bell had in mind for what he called the “superdeterminism” loophole, which he did not embrace. Since Sabine routinely discusses the actual transmission of signals along localized trajectories in spacetime, her reasoning really isn’t compatible with this loophole, even though she is (perhaps unwittingly) invoking it by appealing to superdeterminism as a mechanism for superluminal communication. Overall, I don’t see any logically coherent interpretation of her statements.

At the risk of digressing into total silliness, we could also mention that, under this construal of Sabine’s statements, there would really be no concern about things like “grandfather paradoxes”, because she’s arguing that everything was pre-determined in the initial conditions of the universe, including any instances of “closed causal loops” in which people infer the “future” from those conditions, and we can/must stipulate that those initial conditions not only give all the necessary quantum correlations and measurement pseudo-choices, etc., but also ensure against any contradictory “effects” of closed causal loops. This elevates superdeterminism to an even higher level, that we might call superduperdeterminism. On this basis, we can determine all the messages that any aliens ever have or ever will send, since they are all contained in the initial conditions accessible to us in our past light cone. Also, all the information necessary to re-construct a duplicate Sabine (including all her thoughts and memories) in the Andromeda galaxy is available to any Andromedeans who wish to take advantage of that, and our earthbound Sabine can learn all the experiences of her double just by examining the initial conditions of the universe.

I hope and suspect that Sabine would not endorse any of this if she thought it through carefully… but I’m honestly not entirely certain. Ultimately, the real basis for Sabine’s unshakable belief in superluminal travel may be nothing other than her conviction that “extraterrestrial civilizations are out there”, and (tacitly) that it’s possible to travel to and from, or at least have two-way communication with, the aliens within a small part of the normal life span of an individual homo sapiens on earth (disregarding the fact that we can make the proper time of the traveler as short as we like). If that were true, it would tautologically imply that superluminal travel is possible. Sabine may feel that a vast universe in which we are the only living beings, or in which other beings exist but are so far away that we can never have two-way communication with them on the timescale of a human life span, is simply unacceptable, and that such a universe would be ugly and pointless. For someone who feels that way, there is a certain kind of logic in adopting that belief as a matter of faith, a sine qua non. The reasoning is somewhat reminiscent of Pascal’s famous advice

Let us weigh the gain and the loss in wagering that God is. If you gain, you gain all; if you lose, you lose nothing. Wager, then, without hesitation that He is.

However, rationally speaking, there’s no particular reason to believe, a priori, that it must be possible to signal superluminally, especially since there is abundant evidence that superluminal signaling is impossible. In any case, superluminal signaling is unambiguously incompatible with special and general relativity, not to mention quantum field theory, so this reasoning doesn’t excuse Sabine’s claims that superluminal travel is entirely compatible with “Einstein’s theories”.

As an aside, many modern physicists have taken something akin to Pascal’s attitude toward notions such as “naturalness” and super-symmetry, i.e., they feel that a universe in which these do not hold would be ugly and pointless, so we might as well simply assume they hold. Ironically, Sabine has been critical of this approach, scolding physicists for trying to impose what are actually just subjective aesthetic preferences onto scientific reasoning… and yet she herself is in the thrall of a subjective aesthetic commitment. She may think that a universe in which science fiction dreams can come true would be beautiful, whereas one in which they can never be true would be unbearably ugly and pointless, so she simply chooses to believe. This could be (somewhat) understandable if she acknowledged that her belief violates special and general relativity, since that would be an empirical claim, but it doesn’t excuse the claim that superluminal travel is consistent with special and general relativity… which it clearly is not.

An earlier video posted by Sabine, expounding her thesis on superluminal travel, has been viewed 3.7 million times, with thousands of enthusiastic comments from viewers, thanking her for confirming their long-held belief that superluminal travel is possible, and that the only thing keeping us from zipping around the galaxy in our superluminal spaceships right now is the hide-bound scientists who stubbornly refuse to listen to reason. So it goes.

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