Saturday, March 20, 2021

Superluminal spaceships vs common sense, special relativity

I was amazed by the number of people who are apparently "excited" by the – constantly recurring – claims that someone just made a big step towards spaceships that move faster than the speed of light. In the scheme of elementary science as I understand it, the failure to understand that superluminal objects are impossible in theory – and equally ludicrous in the engineering reality – represents the same proof of complete scientific illiteracy as the belief in the perpetuum mobile or omnipresent deadly geopathogenic zones, among many other things. Why are so many people not getting these basics – and returning to this stuff, often as if it were one of the greatest trends in physics?

It has been known since the 1905 discovery of the special theory of relativity by Albert Einstein that the localized objects in this world can never move faster than the speed of light (in the vacuum: 299,792,458 m/s). Massive objects can't quite reach it (although the LHC protons get extremely close, 99.999999% of the maximum speed, just 3.1 m/s below the limit); the photons (particles of light) and other massless particles are obliged to move exactly by the speed of light.

OK, so one of the parts of science that the proponents of the "warp drives" (a popular "brand" synonymous with the superluminal spaceships) are completely denying is the special theory of relativity. They don't really care and if you ask why they are denying this pillar of modern science, they may either tell you that 1) they don't trust it because of Einstein's ethnic origin, an explanation that is known as the "Aryan physics", or 2) they believe that Einstein's later theory, the 1915 general theory of relativity, allows us to suppress the basic conclusion of the special theory of relativity.

Concerning the "Aryan physics", well, it is just atrocious and atrociously dumb. The Jews are intelligent when it comes to most of the fancy things and that's why they have been (and still are) naturally important in theoretical physics. They covered my adviser, a later de facto boss, several triplets that invented the Standard Model, and many many others. Aside from the world, there also exists an antiworld where everything is anti- and that is perhaps where antiphysics is mostly studied by the anti-Semites. Not here.

You can be annoyed, you can protest but that's the only thing that you can do against these facts. The Jews are even much more "overrepresented" in theoretical physics than non-Jewish whites. That's simply how things have worked, due to both biological and cultural or historical reasons. Every modern physicist has to be an "honorary white" and also an "honorary Jew" to some extent. If you can't swallow the fact that you are often building small additions on the foundations that were largely built by whites and/or Jews, well, too bad, then you suffer from a condition that absolutely and totally prevents you from thinking like a physicist.

While Nazism was nominally defeated in 1945, many of the ideas – including the ethnic bans in science – are kicking and alive. Sometimes the reasons aren't clearly stated but the actual propaganda of the "Aryan physics" has been totally kept by the anti-scientific ideologues who have criticized supersymmetry, string theory, and other key areas of the contemporary research. The recent generations have brought absolutely nothing new to the deluded ramblings that the evil theoretical physics must be bad and the confusing mathematics must be removed so that the sociological arguments plus bare hands decide about everything. So sorry, if you think it's fair to have this ethnic bias in science, if you think that it's right to sling mud on relativity because Einstein was Jewish; or on Sputnik V because it's Russian, then you should stop reading because I consider you a dishonest pile of manure and further interactions can't bring anything good to anybody.

OK, the remaining 10% of us ;-) should realize something "less obvious" but still obvious. The claims that the general relativity allows us to circumvent special relativity is complete rubbish, too. The general relativity is a theory building on the assumption (GR Axiom 1) that you can choose any coordinate systems for the spacetime and any "apparent anomaly" in the local motion of anything must be attributable to the same "irregularities" of the spacetime that also explain all the gravitational forces. However, that is just the added assumption in GR. The general relativity is still a theory of relativity. It is "generalized special relativity" which means that it still has the axiom that
GR Axiom 2: All the laws of the special relativity apply whenever the spacetime curvature may be neglected.
It's because all the "new things in GR" which aren't present in the Minkowski-space-based special theory of relativity only arise once the curvature is nonzero. The new effects are proportional to a positive power of the curvature which means that they have to go away when the curvature is zero or negligible. The principle, GR Axiom 2, is often replaced with the claim
GR Axiom 2a: at very short distances (much shorter than the curvature radii), the spacetime looks flat, so locally, in the local inertial (e.g. freely falling) frames, we may use copies of special relativity as something embedded to general relativity.
Right, so special relativity must be OK at very short distances, even within GR. But the axioms 2 and 2a aren't quite equivalent because "short distances" aren't the only regime in which the the curvature becomes negligible. There is another one, another consequence of GR Axiom 2b:
GR Axiom 2b: The special theory of relativity is also OK for the majority of the Minkowski-like spacetime from which the highly curved vicinities of heavy objects were cut off.
In other words, the special relativity is also OK at very long distances – at distances much longer than the size of the objects that curve the spacetime. The most extremely curved example that is allowed by GR are black holes. They are objects defined by their event horizon that has some (Schwarzschild-like) radius \(R\). It is also the rough distance scales at which the curvature remains substantial – and indeed, it is massive curvature, with some coordinate singularities near the event horizon and the Riemann curvature components of the order \(1/R^2\) even at distances \(kR\) away from the black hole where \(k=O(1)\).

However, if you look at a black hole from distances much greater than its size \(R\), it is just another small, localized object, a point mass (and in perturbative string theory, you may even identify a black hole with a hugely excited fundamental string), and the motion of this point mass through the rest of the spacetime – which is approximately flat – must be consistent with the laws of the special theory of relativity. In particular, not even black holes can move faster than light. It is equally impossible for black holes and neutron stars as it is for spaceships. The arguments are still exactly the same as the usual arguments in special relativity; nothing has been revoked about them and nothing can be revoked about them in this regime. From the viewpoint of another inertial frame that must still be allowed (even in GR), the superluminal motion would look like the motion of backwards in time, and that is why there couldn't be a consistent identification of some causally linked events as causes, and others as their consequences.

The immense "order-100-percent" curvature near the black hole changes nothing about the arguments of special relativity whatsoever because this curvature is just some detail about the "internal structure" of this object, a black hole, that still looks like a point mass from the perspective of vastly longer distance scales (than the black hole radius). I don't need to know everything about the inner structure of an object. Special relativity still implies big consequences for the ways how objects can be or cannot be incorporated into (i.e. moving through) the spacetime. And the spacetime is almost exactly the Minkowski spacetime almost everywhere.

So black holes, neutron stars, spaceships, and all other localized objects (including solitons in a theory combining Einstein's, Maxwell's, and other things in a consistent way!) embedded within a surrounding Minkowski space still have some mass – which you may extract as the "ADM mass \(M\)" from the rules of GR because far enough from the localized objects, and you have enough space by the assumption, the spacetime may be considered the "asymptotic region" – and the corresponding 4-momentum \(P^\mu\) which obeys \(P^\mu P_\mu = M^2\). The internal structure of the objects (which may include some curvature) is a pure distraction from special relativity which is still the crucial theory here – and the reason why things can never move faster than the speed of light. If someone claims to have a paper that works with a theory obeying all energy conditions, causality, and it claims that a superluminal soliton may be created and moving within the surrounding Minkowski spacetime, you know that the paper is wrong and it is really a waste of time to localize the mistake. (And if some people propose self-accelerating gadgets, it's even worse. That self-acceleration would violate the conservation of the total energy-momentum vector, a law that is also guaranteed by Noether's theorem in asymptotically Minkowski [and some other] spacetimes. A pair of a negative-mass and positive-mass object could spontaneously accelerate but the negative-mass part is forbidden by the same laws that ban the tachyons or, almost equivalently, by the energy conditions.)

Practical man's arguments

But if you only care about some "practical superluminal spaceships", we are killing ants with cannons here. The first problem is that no spaceship has ever gotten close to the speed of light. According to the Guinness World Records, the fastest spaceship so far (in September 2020) was the Parker Solar Probe which moved by 466,592 km/h which is about 1/2,300 of the speed of light. The speed of light is still more than 2,000 times higher than the speed of our fastest cosmic probe.

In the real life of fast spaceships, people have trouble to get to 1/1,000 of the speed of light – which is needed before you could reach the speeds close to the speed of light or, if you're brainwashed by pseudoscience, higher than the speed of light. None of the "warp drive" would-be technologies is any helpful to solve the real problems of the rocket science such as the problem how to accelerate the probe from 1/2,300 to 1/1,000 of the speed of light. The experimental situation is nowhere near the speed of light so even if you misunderstood why the theory of relativity prohibits the superluminal motion, you should at least understand that we are nowhere close to testing probes at speeds comparable to \(c\).

Similarly, the whole talk about "the curvature inside the spaceship which forces us to switch from special relativity to GR" is a pure distraction for morons because in any realistic situation in the following centuries, the curvature will be absolutely negligible even inside any probe we can build. In the text above, I was cutting the small vicinities of the very heavy objects to regain the rules of special relativity but I don't even have to do it for objects we can ever realistically build! The curvatures around the Earth and all objects that will come from it in the following centuries will always be negligible which is why the special theory of relativity will always be an excellent approximation to understand the rough motion of anything we ever produce!

OK, how much can we curve things? The black hole curves its vicinity by ~100 percent or so. This red shift (well, the squared red shift but it is just a simple power law) is encoded in \(g_{00}\) which is\[ 1 - \frac{2GM}{rc^2} \] in a spherically symmetric solution with the mass \(R\) inside. How much does it deviate from \(1\) which is the flat, Minkowski space value? Well, it deviates by the second term. For a black hole, \(r\sim R\) and \(R \sim 2GM/c^2\). So the second term is of order \(1\) and at the horizon, it is actually exactly \(1\) which is where the coordinate singularity (near the event horizon) is produced by these coordinates. But all other objects – objects different than black holes – have the second term that is smaller and usually vastly smaller than the first one. So for neutron stars (which are the astrophysical objects that are closest to black holes' curvature), the red shift is typically by 20-25%. If you neglect the red shift (and, more generally, all the curvature produced by a neutron star), you no longer change things qualitatively. You only produce relative errors comparable to 20-25%.

What about the objects we can send to the space? The heaviest spacecraft so far is unsurprisingly the International Space Station and its mass is about 420,000 kg. Four hundred tons. The length and width are 73 and 109 meters, respectively. In the SI units, let us calculate the term \(-2GM/c^2\) with \(r\) around 100 meters. We will get\[ -\frac{2 \times 6.67 \times 10^{-11} \times 420,000}{100 \times 9 \times 10^{16}}. \] You will get less than \(10^{-23}\). This is a deviation from \(1\) so the square root \(\sqrt{g_{00}}\) that determines the red shift is still comparable to \(10^{-23}\) (the Taylor expansion for a square root!), not to \(10^{-11.5}\). So with the precision of some 23 digits, the International Space Station changes nothing about the almost precise flatness of the space inside and around itself. Qualitatively, this is true for the Earth itself and all objects we can produce out of the known matter by the known technologies and send to space. Even for the Earth which is larger than our spaceships, the induced curvature is tiny and can only affect some incredibly precise measurements of times and distances. The curvature from anything around the Earth including the Earth itself is surely absolutely unable to qualitatively change the motion of the objects.

For all practical purposes, all explanations of why and how things move on the surface of Earth and in the space research is totally given by laws compatible with the special theory of relativity.

The very suggestion that some complicated solutions in GR coupled to some other fields are relevant for the space program is another, elementary level of the stupidity in this whole pseudoscientific industry. NASA and astronomers still operate with objects within the Minkowski space and the Earth, the Sun, the Moon, planets, and a few more things only affect the motion subtly and by well-understood small corrections (things want to move on parabolae and other conics). The usage of GR or solitons in GR to argue that "something may be improved about the space research" is an absolute stupidity.

But again, don't get me wrong, the practical argument – which depends on some chosen level of technology, estimates for masses of spaceships, their speeds, dimensions, and other things, and all those things may evolve – isn't the only one. The theoretical argument which is totally robust and based on perfectly understood and verified principles of physics is also valid and guarantees that you can't build these things even theoretically – as long as your GR-like theory allows a consistent definition of causality and gets reduced to the special theory of relativity whenever it should! If someone claims to have a theory of GR coupled to matter and a soliton solution moving superluminally, just see that these claims imply that you may calculate the ADM mass \(M\) around the soliton and because the motion is superluminal, \(M^2\) is negative, a tachyon. You can't really get a tachyonic ADM mass from a soliton that obeys energy conditions inside but even if you couldn't prove this statement and even if it were wrong, it doesn't matter because a theory with localized tachyons may admit some condensation of them which self-evidently violates most energy conditions after some spatial averaging, anyway. The existence of superluminal localized solutions simply is an inconsistency of every theory with them, because of the causal special relativistic arguments, and pretending that you only need to to obey some technical energy conditions is to misunderstand relativity because the inconsistency of the superluminal movement within relativity is a much more clearly established argument or fact than the validity of any energy condition in GR! If some energy conditions fail to contradict self-evident inconsistencies such as the superluminal spaceships, then these conditions are just too weak to convey the restrictions that they should imply.

But I've understood that this text was just another waste of time (another hour in this case) because people are just brainwashed morons and almost all "journalists" are both morons and manipulators. So the elementary claim that "spaceships can't move faster than light" has become politically incorrect (again, like in Germany of the 1930s), just like the statement that a sane nation doesn't fight climate change, that you can distinguish men and women, and other totally elementary scientific facts. I am facing a whole industry of morons, corrupt liars, and they have acquired huge resources that they abuse to grow further. So it is like tilting at the wind turbines. If you are a randomly chosen reader, you have probably been utterly brainwashed by similar pseudoscience as well and the effect of this text on you will be at most temporary because you just fudging don't understand a single thing about modern science yourself. You have been reduced to – or you never cease to be – a moronic parrot and what these parrots believe is macroscopically determined by the resources that the two sides have accumulated (and the lying scum controls all the media). I can't change anything about the macroscopic trends of the growing human stupidity at some distance away from me – much like a "warp drive" cannot change the validity of the special relativity at distances much greater than the radius of the warp drive. ;-)

And that's the memo.

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