There are theories everywhere, and the more ingrained they are, the more suspiciously they should be looked at. From the basic equations of relativity it is clear that if one adds speeds less than the speed of light, one will get a speed less than the speed of light. It is also clear that adding impulse to a mass will make it more massive, while its speed will asymptotically approach that of light (and, as I explained, the reason is intuitive, from Time Dilation).

The subject is not all sci-fi: modern cosmology brazenly assumes that space itself, after the alleged Big Bang, expanded at a speed at least 10^23 c (something like one hundred thousand billion billions time the speed of light c). The grossest, yet simplest, proof of that is simple: the observable universe is roughly 100 billion light years across, and it is ten billion years old. Thus it expanded at the minimum average clip of ten billion light years, every billion years. 100c/10 = 10c, according to standard cosmology. One could furiously imagine a spaceship somehow surfing on a wave of warped space, expanding for the same obscure reason.

The question naturally arises whether velocities which are greater than that of light could ever possibly be obtained in other ways. For example, are there communication speeds faster than light? (Throwing some material across will not work: its mass will increase, while its speed stays less than c.)

Textbooks say it’s not possible. There is actually a “proof” of that alleged impossibility, dating all the way back to Einstein (1907) and Tolman (1917). The mathematics are trivial (they are reproduced in my picture below). But the interpretation is apparently less so. Wikipedia weirdly claims that** faster than light communications would allow to travel back in time. No. One could synchronize all clocks on all planets in the galaxies, and having faster than light communications would not change anything. Why? Time is local, faster than light data travel is nonlocal**.

The problem of faster than light communications can be attacked in the following manner.

Consider two points A and B on the X axis of the system S, and suppose that some impulse originates at A, travels to B with the velocity u and at B produces some observable phenomenon, the starting of the impulse at A and the resulting phenomenon at B thus being connected by the relation of cause and effect. The time elapsing between the cause and its effect as measured in the units of system S will evidently be as follows in the calligraphy below. Then I use the usual Relativity formula (due to Lorentz) of time as it elapses in S’:

**Equations help, but they are neither the beginning, nor the end of a story. Just an abstraction of it. The cult of equations is naive, interpretation is everything. The same thing, more generally, holds for models**.

As Tolman put it in 1917: *“Let us suppose now that there are no limits to the possible magnitude of the velocities u and V, and in particular that the causal impulse can travel from A to B with a velocity u greater than that of light. It is evident that we could then take a velocity u great enough uV/C^2 will be greater than one.*

* so that Delta(t) would become negative. In other words, for an observer in system S’ the effect which occurs at B would precede in time its cause which originates at A.”*

I quote Tolman, because he is generally viewed as the one having definitively established the impossibility of faster than light communications. Tolman, though is not so sure; in his next sentence he turns out wishy washy:* “Such a condition of affairs might not be a logical impossibility; nevertheless its extraordinary nature might incline us to believe that no causal impulse can travel with a velocity greater than that of light.”*

Actually it is an effect those who have seen movies running in reverse are familiar with. Causality apparently running in reverse is no more surprising than the fact that two events at x1 and x2 which are simultaneous in S are separated by: (x1-x2) (V/square root (1-VV/CC)). That introduces a sort of fake, or apparent causality, sometimes this before that, sometimes that before this.

(The computation is straightforward and found in Tolman’s own textbook;* it originated with Henri Poincaré. ^{[9]}^{[10]} In 1898 Poincaré argued that the postulate of light speed constancy in all directions is useful to formulate physical laws in a simple way. He also showed that the definition of simultaneity of events at different places is only a convention.^{[11]}*) . Notice that, in the case of simultaneity, the signs of V and (x1-x2) matter. Basically, depending upon how V moves, light in S going to S’ takes more time to catch up with the moving frame, and the more so, the further it is, the same exact effect which explains the nil result in the Michelson-Morley interferometer; there is an underlying logic below all of this, and it’s always the same).

Tolman’s argumentation about the **impossibility of faster than light communications is, in the end, purely philosophical and fully inconsistent with the closely related, and fully mainstream, relativity of simultaneousness**.

Poincaré in 1900 proposed the following convention for defining clock synchronisation: 2 observers A and B, which are moving in space (which Poincaré called the aether), synchronise their clocks by means of optical signals. They believe to be at rest in space (“the aether”) from not moving relative to distant galaxies or the Cosmic Radiation Background and assume that the speed of light is constant in all directions. Therefore, they have to consider only the transmission time of the signals and then crossing their observations to examine whether their clocks are synchronous.

“Let us suppose that there are some observers placed at various points, and they synchronize their clocks using light signals. They attempt to adjust the measured transmission time of the signals, but they are not aware of their common motion, and consequently believe that the signals travel equally fast in both directions. They perform observations of crossing signals, one traveling from A to B, followed by another traveling from B to A.”^{}

In 1904 Poincaré illustrated the same procedure in the following way:

“Imagine two observers who wish to adjust their timepieces by optical signals; they exchange signals, but as they know that the transmission of light is not instantaneous, they are careful to cross them. When station B perceives the signal from station A, its clock should not mark the same hour as that of station A at the moment of sending the signal, but this hour augmented by a constant representing the duration of the transmission. Suppose, for example, that station A sends its signal when its clock marks the hour 0, and that station B perceives it when its clock marks the hour t. The clocks are adjusted if the slowness equal to t represents the duration of the transmission, and to verify it, station B sends in its turn a signal when its clock marks 0; then station A should perceive it when its clock marks t. The timepieces are then adjusted. And in fact they mark the same hour at the same physical instant, but on the one condition, that the two stations are fixed. Otherwise the duration of the transmission will not be the same in the two senses, since the station A, for example, moves forward to meet the optical perturbation emanating from B, whereas the station B flees before the perturbation emanating from A. The watches adjusted in that way will not mark, therefore, the true time; they will mark what may be called the local time, so that one of them will be slow of the other.^{[13]}“

This *Poincaré (“–Einstein”) synchronisation* was used by telegraphers as soon as the mid-nineteenth century. It would allow to cover the galaxy with synchronized clocks (although local times will differ a bit depending upon the motion of stars, and in particular where in the galactic rotation curve a star sits). Transmitting instantaneous signals in that networks would not affect causality. Ludicrously, Wikipedia asserts that faster than light signals would make “Bertha” rich (!!!). That comes simply from Wikipedia getting thoroughly confused, allowing faster than light signals for some data, and not for other data, thus giving an advantage to some, and not others.

***

*Quantum Entanglement (QE) enables at-a-distance changes of Quantum states:*

(It comes in at least three types of increasing strength.) Quantum Entanglement, as known today, is within Quantum state to within Quantum state, but we cannot control in which Quantum state the particle will be, to start with, so we cannot use QE for communicating faster than light (because we don’t control what we write, so to speak, as we write with states, so we send gibberish).

This argument is formalized in a “*No Faster Than Light Communication theorem*”. However, IMHO, the proof contains massive loopholes (the proof assumes that there is no Sub Quantum Reality, whatsoever, nor could there ever be some, ever, and thus that the unlikely QM axioms are forever absolutely true beyond all possible redshifts you could possibly imagine, inter alia). So this is not the final story here. QE enables, surprisingly, the ** Quantum Radar** (something I didn’t see coming). And it is not clear to me that we have absolutely no control on states statistically, thus that we can’t use what

*Schrödinger*, building on the EPR thought experiment, called “

**” to communicate at a distance. Quantum Radar and Quantum Steering are now enacted through real devices. They use faster-than-light in their inner machinery.**

*Quantum Steering*As the preceding showed, the supposed contradiction of faster-than-light communications with Relativity is just an urban legend. It makes the tribe of physicists more priestly, as they evoke a taboo nobody can understand, for the good reason that it makes no sense, and it is intellectually comfortable, as it simplifies brainwork, taboos always do, but it is a lie. And **it is high time this civilization switches to the no more lies theorem, lest it wants to finish roasted, poisoned, flooded, weaponized and demonized.**

Patrice Ayme’

Technical addendum:

https://en.wikipedia.org/wiki/Relativity_of_simultaneity

As Wikipedia itself puts it, weasel-style, to try to insinuate that Einstein brought something very significant to the debate, the eradication of the aether (but the aether came back soon after, and there are now several “reasons” for it; the point being that, as *Poincaré* suspected, there is a notion of absolute rest, and now we know this for several reasons: CRB, Unruh effect, etc.):

“In 1892 and 1895,Hendrik Lorentzused a mathematical method called “local time” t’ = t – v x/c2for explaining the negativeaetherdrift experiments.[5]However, Lorentz gave no physical explanation of this effect. This was done byHenri Poincaréwho already emphasized in 1898 the conventional nature of simultaneity and who argued that it is convenient to postulate the constancy of the speed of light in all directions. However, this paper does not contain any discussion of Lorentz’s theory or the possible difference in defining simultaneity for observers in different states of motion.[6][7]This was done in 1900, when Poincaré derived local time by assuming that the speed of light is invariant within the aether. Due to the “principle of relative motion”, moving observers within the aether also assume that they are at rest and that the speed of light is constant in all directions (only to first order in v/c). Therefore, if they synchronize their clocks by using light signals, they will only consider the transit time for the signals, but not their motion in respect to the aether. So the moving clocks are not synchronous and do not indicate the “true” time. Poincaré calculated that this synchronization error corresponds to Lorentz’s local time.[8][9]In 1904, Poincaré emphasized the connection between the principle of relativity, “local time”, and light speed invariance; however, the reasoning in that paper was presented in a qualitative and conjectural manner.[10][11]

Albert Einsteinused a similar method in 1905 to derive the time transformation for all orders in v/c, i.e., the complete Lorentz transformation. Poincaré obtained the full transformation earlier in 1905 but in the papers of that year he did not mention his synchronization procedure. This derivation was completely based on light speed invariance and the relativity principle, so Einstein noted that for the electrodynamics of moving bodies the aether is superfluous. Thus, the separation into “true” and “local” times of Lorentz and Poincaré vanishes – all times are equally valid and therefore the relativity of length and time is a natural consequence.[12][13][14]“

… Except of course, absolute relativity of length and time is not really true: everywhere in the universe, locally at rest frames can be defined, in several manner (optical, mechanical, gravitational, and even using a variant of the Quantum Field Theory Casimir Effect). All other frames are in trouble, so absolute motion can be detected. The hope of Einstein, in devising General Relativity was to explain inertia, but he ended down with just a modification of the *1800 CE Bullialdus-Newton-Laplace theory*… (Newton knew his instantaneous gravitation made no sense, and condemned it severely, so Laplace introduced a gravitation speed, thus the gravitational waves, and Poincaré made them relativistic in 1905… Einstein got the applause…)