“Relativity”, first named and defined by Henri *Poincaré* (1904) is a local theory of LOCAL TIME. Einstein was aware of this and thus contributed later to what he called “GENERAL Relativity”, by incorporating accelerations of the gravitational type (Relativity as defined by *Poincaré* is all about uniform motions, as in Galilean Relativity). The main contribution of Einstein in his Relativity paper of 1905 was to derive the (already derived) equations of Relativity without referring to a state of rest (Einstein’s work is mostly a slick mathematical trick with the axiomatic system, because the state of rest is there nevertheless… as Einstein himself admitted much later).

Einstein has awed generations of physicists. Einstein had a world picture in his head, partly from his mastery of differential calculus at young age (from a helping uncle), friendly to fields and slick math. A famous conclusion from Einstein’s exposition of Relativity is that communications Faster Than Light (FTL) are impossible, because they violate CAUSALITY. Most theoretical physicists have to repeat this lest they lose their good standing. The source is Einstein. Here is Einstein’s reasoning:

**Einstein’s logical mistake in his demonstration of the impossibility of FTL communications is that the addition of velocity formula has been demonstrated ONLY when adding speeds LESS THAN c**. So Einstein should not have applied something demonstrated for W<c and ONLY FOR W<c, to W>c.

To see that relativistic speed addition applies only for speeds less than c, one has to go through the derivation of the relativistic addition of velocities step by step, as Einstein does in this Relativity-recapitulation paper of 1907, from which the impossibility of FTL com comes from, and extracted above.

***

Let’s acquire some philosophical altitude: Relativity is a type of logical cooking which applies only locally. Its main ingredient is LOCAL LIGHT CLOCK THEORY. Local light clock is, admittedly a pleonasm, as it turns out that the universe, considered to be a differential manifold U with metric given by light, is curved… So non-local light clock are impossible (at any point their size would be bounded by the exponential radius). The Michelson-Morley experiment shows that the time given by a light clock doesn’t depend upon its orientation relative to its speed… Now causality is a different concept, independent of time (it is not because something happened before, or after, that it is causally related to something else). There is a causality category CC, independent a priori from the Universe U, a differential manifold.

The conflict between CC and U is the problem of nonlocality. Amusingly we now know that the resolution of this conflict requires some FTL mechanism, or FTL causality. Could there be no FTL mechanism, and no FTL causality? Yes, but at an even higher logical and counter-intuitive price: namely the Universe, far from being just a differential manifold equipped by light metric (which has T2, Hausdorff separability, topologically)… Would not be topologically separable… Instead in my own SQPR, separability is maintained, time delayed causality is maintained, and Dark Matter blossoms [1]…

A lot of the hang-ups of all too many physicists about causality and Faster Than Light and Quantum Nonlocality have been caused by the erroneous feeling that it has been demonstrated beyond a reasonable doubt that Faster Than Light is impossible, no matter what, in all and any way.

A meta objection could be made, trying to supersede my logical refinements above: that all and any communication require momentum transfer and that momentum augments as 1/(1-vv/cc)… Right, but there again, an assumption is made which is unproven: that all communications require momentum transfer. This is precisely what, ironically enough, the Pandora box Einstein-Podolski-Rosen (EPR) paper of 1935 showed not to be necessarily true. The EPR opened for all of humanity to be thereafter tormented, or delighted with, ever after… EPR should have made manifest that Einstein 1907 had slipped on a slick mathematical banana… But no… [2]

Patrice Ayme

***

[1] Global time can still be maintained as a concept, but it is path dependent (and this is true in GR). In SQPR, U is embedded in a larger Euclidean space of dimension at least 2n+1 (Whitney and Nash theorems). However all this, including how many dimensions there really are, belong to the experimental realm.

***

[2] An example of something completely obvious which was then completely lost for ever and ever: Non-Euclidean geometry. At the same time as Euclid made his geometry all the geometry which could be had. Pytheas of Marseilles, Πυθέας ὁ Μασσαλιώτης *Pythéas ho Massaliōtēs*; *Pytheas Massiliensis*; c.350 BC-c.285 BC and then Eratosthenes, used Non-Euclidean geometry to measure the Earth and universe.

It took 21 centuries for eminent mathematicians, philosophers, physicists and thinkers to rediscover all this… Notice though that **János Bolyai, **Gauss, and Riemann were not professional physicists (the latter two were paid as mathematicians…).

Bolyai became so obsessed with Euclid‘s parallel postulate that his father, who pursued the same quandary for many years, wrote to him in 1820: *“You must not attempt this approach to parallels. I know this way to the very end. I have traversed this bottomless night, which extinguished all light and joy in my life. I entreat you, leave the science of parallels alone…Learn from my example.” ^{[4]}*

János, however, persisted (*perseverare diabolicum*) and eventually concluded that the postulate is independent of the other axioms of geometry and that different consistent geometries can be constructed on negating and modifying it. In 1823, he wrote to his father:* “I have discovered such wonderful things that I was amazed…out of nothing I have created a strange new universe.*

Gauss, contacted, replied by glorifying himself and pretending that he had published nothing for fear of the “*cries of the Boeotians*“…. Gauss wrote: “*To praise it would amount to praising myself. For the entire content of the work…coincides almost exactly with my own meditations which have occupied my mind for the past thirty or thirty-five years….” *Never mind that Gauss said to some other friend: “*I regard this young geometer Bolyai as a genius of the first order.*“

Disgusted **János Bolyai left mathematics, all too often, a most poisonous church full of autistic navel gazers with mountainous egos dissolvable FTL… **