A part of relativistic dynamics is axiomatized by simple and purely geometrical axioms formulated within first-order logic. A geometrical proof of the formula connecting relativistic and rest masses of bodies is presented, leading up to a geometric explanation of Einstein's famous E = mc² . The connection of our geometrical axioms and the usual axioms on the conservation of mass, momentum and four-momentum is also investigated.

We present a streamlined axiom system of special relativity in first-order logic. From this axiom system we "derive" an axiom system of general relativity in two natural steps. We will also see how the axioms of special relativity transform into those of general relativity. This way we hope to make general relativity more accessible for the non-specialist.

The experimental evidence for electromagnetic signals propagating with superluminal group velocity is recalled. Transformations of space and time depending on a synchronization parameter, e1, indicate the existence of a privileged inertial system. The Lorentz transformations are obtained for a particular e1≠0. No standard experiment on relativity depends on e1, but if accelerations are considered only e1=0 remains possible. The causal paradox generated by superluminal signals (SLS) in the theory of relativity does not exist in the theory with e1=0. The irrelevance (...) of SLS for the Einstein, Podolsky and Rosen paradox is pointed out. (shrink)

The chronological order of the events along a spacelike path is not invariant under Lorentz transformations, as is well known. This led to an early conviction that tachyons would give rise to causal anomalies. A relativistic version of the Stückelberg-Feynman “switching procedure” (SWP) has been invoked as the suitable tool to eliminate those anomalies. The application of the SWP does eliminate the motions backwards in time, but interchanges the roles ofsource anddetector. This fact triggered the proposal of a host of (...) causal “paradoxes.” Till now, however, it has not been recognized that such paradoxes can be sensibly discussed (and completely solved, at least “in microphysics”)only after the tachyon relativistic mechanics has been properly developed. We start by showing how to apply the SWP, both in the case ofordinary special relativity and in the case with tachyons. Then we carefully exploit the kinematics of the tachyon exchange between to (ordinary) bodies. Being finally able to tackle the tachyon causality problem, we successively solve the paradoxes of : (i) Tolman-Regge, (ii) Pirani, (iii) Edmonds, and (iv) Bell. Finally, we discuss a further, new paradox associated with the transmission of signals by modulated tachyon beams. (shrink)

It continues to be alleged that superluminal in uences of any sort would be inconsistent with special relativity for the following three reasons: they would imply the existence of a ‘distinguished’ frame; they would allow the detection of absolute motion; and they would violate the relativity of simultaneity. This paper shows that the first two objections rest upon very elementary misunderstandings of Minkowski geometry and on lingering Newtonian intuitions about instantaneity. The third objection has a basis, but rather than invalidating (...) the notion of faster-than-light influences it points the way to more general conceptions of simultaneity that could allow for quantum nonlocality in a natural way. (shrink)

As it is well known, classical special relativity allows the existence of three different kinds of particles: bradyons, luxons and tachyons. Bradyons have non-zero mass and hence always travel slower than light. Luxons are particles with zero mass, like the photon, and they always travel with invariant velocity. Tachyons are hypothetical superluminal particles that always move faster than light. The existence of bradyons and luxons is firmly established, while the tachyons were never reliably observed. In quantum field theory, the appearance (...) of tachyonic degrees of freedom indicates vacuum instability rather than a real existence of the faster-than-light particles. However, recent controversial claims of the OPERA experiment about superluminal neutrinos triggered a renewed interest in superluminal particles. Driven by a striking analogy of the old Frenkel-Kontorova model of a dislocation dynamics to the theory of relativity, we conjecture in this note a remarkable possibility of existence of the forth type of particles, elvisebrions, which can be superluminal. The characteristic feature of elvisebrions, distinguishing them from tachyons, is that they are outside the realm of special relativity and their energy remains finite when the elvisebrion velocity approaches the light velocity. (shrink)

A part of relativistic dynamics is axiomatized by simple and purely geometrical axioms formulated within first-order logic. A geometrical proof of the formula connecting relativistic and rest masses of bodies is presented, leading up to a geometric explanation of Einstein’s famous E = mc 2. The connection of our geometrical axioms and the usual axioms on the conservation of mass, momentum and four-momentum is also investigated.