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 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.  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 steadfast 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 reject special relativity, i.e., local Lorentz invariance (LLI), and return to the 19th century concept of a unique local frame that is distinguished in terms of its local dynamics, meaning the local laws of physics take a different form in terms of one inertial system than in terms of another.  Now, LLI is among the most thoroughly and precisely verified principles of physics, and it is a foundational element not just of special relativity, but also of general relativity and quantum field theory. It is the very foundation of the crucial relation m2 = E2 – |p|2. 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, it’s just asking “what would things be like if they weren’t the way they are?” 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.

 

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 pointing outside the light cone of the event -- would have imaginary “proper times”, which is incommensurate with actual elapsed proper time. This 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 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 and 1907 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. Based on her videos, it’s difficult to avoid the conclusion that Sabine misunderstands the meaning of Lorentz invariance. 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 this isn’t an empirical assertion, it’s a theoretical assertion, and it is unambiguously false for the reason explained above.  Spacelike intervals 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 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. (The reader would be astonished at the amount of patient discussion it took to bring her to even that admission.) 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 said that even though superluminal travel may be inconsistent with general relativity, 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 sophism 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, actually, it does make sense, because it can be shown that the phenomena related to quantum entanglement do not permit superluminal signaling. The entanglement 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. 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, 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, 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. Her views seem hopelessly muddled and confused.

 

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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