Cedric and Alcubierre

Some years ago an internet personality – let’s call him Cedric – posted an explanation of why he believes faster-than-light travel is possible, even within the context of special relativity. He offered a number of justifications for his belief, none of which made any sense, as discussed in another article. Now he’s returned with another presentation on the subject, acknowledging that he himself cannot now understand his previous statements.

Despite the fact that all the reasons he previously adduced for his belief in the possibility of faster-than-light travel were thoroughly debunked, his belief has not wavered. He has simply formulated a new batch of (equally invalid) pseudo-arguments. This is reminiscent of Jonathan Swift’s remark that “Reasoning will never make a man correct an ill opinion, which by reasoning he never acquired.” Sometimes this is rendered as “You cannot reason someone out of something they were not reasoned into.” Cedric’s belief in faster-than-light travel is obviously prior to any rational reasoning. It’s essential for him to believe it, because without faster-than-light travel (or at least communication), he knows that his dreams of interacting with extra-terrestrial life in a way that even remotely resembles the depictions in popular fiction would be impossible. Indeed he begins his latest presentation with

I believe there’s intelligent life on other planets. And the most plausible reason why they haven’t contacted  us is that … we haven’t even figured out how to send  information faster than light… Maybe some of those aerial phenomena really are space probes from alien species. And if we want to properly evaluate how likely that is, we need to talk about the possibility of travelling faster than light, or at least sending information  faster than light. Because if it’s possible at all, then that’s what the aliens are doing.

In this, Cedric resembles many anti-relativity enthusiasts, a surprising number of whom are motivated by a romantic devotion to the possibility of superluminal travel. The problem they perceive is that whenever they try to talk about the exciting future of interstellar travel, some know-it-all professor says “No, you can’t do that”, and when they ask why, they are told “Because Einstein said so”. Naturally this enrages them, and thus is born their determination to tear down both Einstein and special relativity.

One might think that Cedric doesn’t fall into this category, because he routinely speaks approvingly of Einstein (“yes, that guy again”) and relativity, but this is actually not unusual for anti-relativityists, many of whom insist that they are actually espousing relativity as properly understood, but they have their own private understanding that differs very significantly from the understanding of actual theoretical physicists and presented in text books. Furthermore, they claim Einstein held their views, but he has been misunderstood. For example, one of the claims made by Cedric in his previous presentation was that, “Contrary to common belief, Einstein never said superluminal velocity for material objects was incompatible with special relativity”. Cedric was then provided with numerous and well-known quotes from Einstein’s papers in which he says (and proves) this very thing, so the “common belief” is correct.  In his recent presentation, Cedric has somewhat muted his earlier claims about what Einstein did and didn’t say on the subject.

Cedric doesn’t enumerate each of the notions from his earlier presentation that he now admits were nonsense, so to some extent we can only judge by what he leaves out of the latest presentation. Gone is the clearly erroneous insistence that the thermodynamic “arrow of time” singles out a unique temporal foliation, although he can’t help briefly alluding to thermodynamics again, but now disconnected from any coherent claim of relevance. In addition, he briefly mentions his misconception about the speed of light being just a barrier rather than a boundary, a notion that was also thoroughly debunked previously. Special relativity doesn’t just imply that a material object can’t propagate precisely at the speed of light, it implies that a material object can’t propagate at or above the speed of light in terms of any standard system of inertial coordinates, and neither energy nor signals can propagate above the speed of light.

Also notably missing is his previous denial that he was advocating a preferred frame. In the latest presentation he actually embraces the rejection of local Lorentz invariance, claiming now that the local frame in which the galaxies and CMBR are maximally isotropic constitutes a physical preferred frame, violating local Lorentz invariance, and thereby rejecting special relativity entirely… while being oblivious to the fact that this is the implication of what he is saying. This is precisely what his earlier presentation tacitly assumed, as was explained to him in detail, but at that time he vociferously denied that his belief relies on adopting a distinguished local frame and rejecting local Lorentz invariance. Now at least he acknowledges that this is indeed what his beliefs imply. He has conquered his embarrassment about holding this abundantly falsified belief.

His latest presentation consists largely of an attempt to summarize elementary special relativity, although he does a terrible job. For example, he describes an elaborate scenario in which he claims that the composition of velocities at low speeds is purely additive (which of course it is not), and then makes the false and very misleading claim that things are qualitatively different when dealing with light, for which velocity composition is not additive. The correct distinction is not between material entities and light, but between entities at different speeds. The very same composition relation (u+v)/(1+uv) applies to the water from the fire hose and to a beam of light, a fact that is essential for students to clearly understand.

He then acknowledges that it would take infinite energy to accelerate a fixed material object to the speed of light, and repeats his nonsense that this doesn’t imply a material object can’t move (in terms of a standard system of inertial coordinates) at a speed exceeding the speed of light. He gives no support of that claim in his latest presentation, and the claim was thoroughly debunked in a review of his previous presentation.

Cedric then makes the bizarre claim that when “a quantity goes to infinity”, physicists generally say that singularity is unphysical, and therefore the fact that special relativity says it would require infinite energy to accelerate a material object to the speed of light should also be regarded as unphysical. He omits any comment on the fact that highly energetic particles asymptotically approach the speed c, and that this is a direct consequence and manifestation of the fact that standard inertial coordinate systems are related by Lorentz transformations, which itself is a direct consequence of the fact that every bounded quantity of energy E has inertia E/c². The mass-energy equivalence on which special relativity is founded is not a singularity at all, but it has the consequence that no amount of energy would be sufficient to accelerate a material object to the speed of light, because as the object is accelerated it acquires more energy and hence more inertia, and so on. Cedric’s rejection of this is, again, nothing but a denial of local Lorentz invariance, which is the cornerstone of both special and general relativity.

He then goes on to make a truly bizarre argument, namely, he argues that it is wrong to say a material object can’t be accelerated to the speed of light, because a material object with a certain “rest mass” can decay into massless energy which propagates away at the speed of light.  Hence (he argues) we have succeeded in accelerating the object to the speed of light!  Ha!  Take that, science!  Well, this is the kind of confusion that troubles beginners when they first learn about special relativity, and they have to work through exercises to show that, for example, individual photons have no rest mass, but an aggregate of photons collectively has a rest mass, and so on. Needless to say (or so one would have thought), the fact that all “rest mass” is ultimately relativistic mass, i.e., energy, does not invalidate local Lorentz invariance, and provides no support at all for the belief in superluminal travel or signaling. No one disputes that luminal signaling is possible.

Cedric tries to connect this to his claim about superluminal travel by saying that the relativistic energy equation might be mis-construed to imply that infinite energy would be involved in a transition from massless particles to configurations with rest mass. However, he then admits that this reasoning is invalid (because numerator and denominator both go to zero), and then concludes that “This doesn’t help us at all to travel at the speed of light.” True enough… so why devote a sizeable portion of a presentation on reasons for believing in superluminal travel to this topic, when it self-admittedly does not support that belief?

By the way, Cedric’s attempted exposition of how the Higgs mechanism imparts rest mass to

otherwise massless energy is very misleading, as it follows the usual senseless popularization approach of treating the Higgs field.  He says

The particles of light, the photons, are massless, which means they don’t feel the Higgs field at all. But other particles do feel it. When the field condenses, it sticks to the particles. That slows them down and it looks to us like they have a mass.

This obviously is not a Lorentz invariant description, so it gives students only an illusion of understanding, not even mentioning the internal degrees of freedom (e.g., the zig-zagging components of the Dirac representation of a particle). Nevertheless, to his credit, Cedric does at least acknowledge that, despite his description, the Higgs field is locally Lorentz invariant (to distinguish it from the 19th century aether), but of course this contradicts his denial of local Lorentz invariance, which he apparently is willing to accept when convenient.

As an aside, it’s noteworthy that Cedric seems never to have considered the elapsed proper time of a traveler going from Earth to some distant star, which approaches zero as his speed approaches c. Thus the elapsed proper time for the traveler can be made arbitrarily close to zero.  Does Cedric deny this? Or does he contend that the elapsed time for a traveler can be made less than zero? As explained in the earlier article, the “elapsed time” along a spacelike interval would be imaginary… but what would this mean? Would the traveler’s wrist watch indicate imaginary time? How would that differ from real time? Would the traveler have imaginary heart beats? How would those differ from real heart beats? And if a timelike entity can follow a spacelike interval, is it also possible for spacelike entities to subtend timelike intervals?

At this point Cedric tackles the subject that proved to be his un-doing in the previous presentation, and he shows that although he learned a lot from that discussion, and on some level now realizes that his previous reasoning was completely invalid and all the criticisms (which he haughtily dismissed at the time) were completely correct, he nevertheless (in the characteristic manner of all anti-relativity cranks) continues to maintain his thoroughly falsified beliefs. In the previous presentation he insisted that special relativity combined with thermodynamics enabled us to single out a locally preferred temporal foliation. He insisted that special relativity did not imply that all the laws of physics take the same form in terms of every standard system of inertial coordinates – despite the fact that this is essentially the definition of the principle of special relativity. Now he says

Physicists do have a reason to assume that time on the space-ship could go this way, but it’s not a good reason. It’s because in special relativity all observers [sic] must be treated the same. In Special Relativity, if you think that something is physically possible [in terms of one standard system of inertial coordinates], then it must also be possible [in terms of any other]. But Special Relativity is special because it doesn’t contain gravity and this means  it doesn’t actually describe reality. For this, we need general relativity. And while the time-travel  argument is correct in special relativity, it is not correct in general relativity.

So, finally we have an admission that the critics of his previous presentation, which was entirely in the context of special relativity, were indeed correct. But instead of reacting rationally by discarding his falsified beliefs, he says, well, so much the worse for special relativity, I hereby reject special relativity (i.e., local Lorentz invariance), and henceforth claim that general relativity (not special relativity) is consistent with superluminal travel. Of course, the problem is that one of the cornerstones of general relativity is local Lorentz invariance, which is precisely what Cedric needs to deny in order to claim superluminal propagation of matter or energy or information. Now, within general relativity, one can explore theoretical topologies and distributions of curvature, and (by violating basic energy conditions) even imagine closed timelike curves, but (1) establishing such configurations would only be propagated through the essentially flat background of interstellar space at the speed of light, and (2) any closed timelike curves lead to logical inconsistencies (a signal is sent if and only if it is not sent), just as in special relativity, so this evasion tactic fails.

Cedric concludes with a defense of his rejection of local Lorentz invariance, by claiming that the local laws of physics take a special form in terms of a global system of coordinates (and unique temporal foliation) in which the distribution of the galaxies on the cosmological scale, and the CMBR, are maximally isotropic. It was pointed out to Cedric in the criticisms of his previous presentation that this must be what he was assuming, and he denied it, but now he has apparently realized that this is indeed what he is claiming. He says the local inertial coordinates at rest in this isotropic cosmological system are called the “co-moving frame”, although in physics the term is actually applied to the inertial coordinates in which any specific entity is instantaneously at rest. In other words, the phrase “co-moving frame” isn’t ordinarily restricted to just co-moving with the local frame in which the CMBR is maximally isotropic. This was a point of Cedric’s confusion in the previous presentation, and he still appears to be confused about it, although he at least realizes now that he is talking about the isotropic CMBR frame and denying local Lorentz invariance.

After all this build-up, Cedric confesses that his thesis (as was explained to him previously) consists of saying “Assume that faster than light travel is only allowed forward in time in this particular frame… [so] you can’t make loops in time…”  Right, and this is a flagrant denial of local Lorentz invariance, according to which the local equations of physics take the same simple homogeneous and isotropic form in terms of any local system of standard inertial coordinates (as given by, e.g., a grid of standard rulers and clocks at rest and inertially synchronized in any given frame), regardless of its state of motion relative to the CMBR isotropic frame. Local Lorentz invariance is the cornerstone, not just of both special and general relativity, but of quantum field theory as well, and it is among the most thoroughly tested principles of physics. All of modern physics is based on this principle. Indeed the Dirac equation for the electron (crucial to the understanding of the Higgs mechanism touted by Cedric) was founded explicitly to make quantum mechanics locally Lorentz invariant.

So, Cedric’s unwavering belief in superluminal travel, which he spreads to his many gullible online acolytes, is based on nothing less than the complete rejection of local Lorentz invariance, which is the very foundation of modern science, including special and general relativity and quantum field theory. He exhibits a remarkable lack of understanding of this principle, and complete disregard for the vast array of empirical and theoretical support for it.

He concludes the defense of his thesis with the standard sophistry that unless we know everything we don’t know anything.  He says

To add one final reason why you shouldn’t trust [modern science]… General Relativity can’t be correct because it doesn’t work together with quantum theory. This is why we need a theory  of quantum gravity, and we still don’t have one. We know however that causality and locality become really screwed up in quantum mechanics, and the same is probably the case in quantum gravity. This is why I think it’s extremely implausible that any argument about faster-than-light travel would survive in the to-be-found theory of quantum gravity.

One final reason? Not a single rational “reason” for denying local Lorentz invariance has been put forward previously, so it all comes down to this:  Cedric believes “causality and locality” [sic] become really screwed up in quantum mechanics (a term that normally refers to non-relativistic quantum mechanics, as distinct from relativistic, i.e., locally Lorentz invariant, quantum field theory), and on this misguided basis he “thinks” it is extremely implausible that local Lorentz invariance is valid.  That is an astonishingly silly and non-serious “reason”, not actually a reason at all, but merely a statement of a completely baseless prejudice in favor of a science-fiction fantasy belief.

On a related topic, one occasionally reads about a so called “warp drive”, often with reference to an individual named Alcubierre, but what Alcubierre wrote on this subject had no rational basis. He presented a metric line element, and verbally discussed it as if this line element entails a “bubble” that propagates superluminally through a flat space-time background, but that is clearly fallacious, since the leading edge of any variation in the background spacetime metric cannot propagate (in terms of that background) faster than light. This is true regardless of whether we posit some unrealistic “negative energy”. The self-contradictory consequences of closed timelike loops can’t be evaded, regardless of how one fantasizes that they are produced.

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