In this paper we explain why and how tachyons do not imply any causality violation within relativistic theories. Particular emphasis is given to the role of the Stückelberg-Feynman reinterpretation principle, both in ordinary physics and in tachyon physics.

Starting from the formal expressions of the hydrodynamical (or “local”) quantities employed in the applications of Clifford algebras to quantum mechanics, we introduce—in terms of the ordinary tensorial language—a new definition for the field of a generic quantity. By translating from Clifford into tensor algebra, we also propose a new (nonrelativistic) velocity operator for a spin- ${\frac{1}{2}}$ particle. This operator appears as the sum of the ordinary part p/m describing the mean motion (the motion of the center-of-mass), and of a (...) second part associated with the so-called Zitterbewegung, which is the spin “internal” motion observed in the center-of-mass frame (CMF). This spin component of the velocity operator is nonzero not only in the Pauli theoretical framework, i.e., in the presence of external electromagnetic fields with a nonconstant spin function, but also in the Schrödinger case, when the wavefunction is a spin eigenstate. Thus, one gets even in the latter case a decomposition of the velocity field for the Madelung fluid into two distinct parts, which constitutes the nonrelativistic analogue of the Gordon decomposition for the Dirac current. Explicit calculations are presented for the velocity field in the particular cases of the hydrogen atom, of a spherical well potential, and of an electron in a uniform magnetic field. We find, furthermore, that the Zitterbewegung motion involves a velocity field which is solenoidal, and that the local angular velocity is parallel to the spin vector. In the presence of a nonuniform spin vector (Pauli case) we have, besides the component of the local velocity normal to the spin (present even in the Schrödinger theory), also a component which is parallel to the curl of the spin vector. (shrink)

Special Relativity can be based on the whole proper group of both ortho- and antichronous Lorentz transformations, and a clear physical meaning can be given also to antichronous (i.e., nonorthochronous) Lorentz transformations. From the active point of view, the latter requires existence, for any particle, of its antiparticle within a purely relativistic, classical context. From the passive point of view, they give rise to frames “dual” to the ordinary ones, whose properties—here briefly discussed—are linked with the fact that in relativity (...) it is impossible to teach another, far observer (by transmitting only instructions, and no physical objects) our own conventions about the choices right/left, matter/antimatter, and positive/negative time direction. Interesting considerations follow, in particular, by considering—as it is the case—theCPT operation as an actual (even if antichronous) Lorentz transformation. (shrink)

In this article, after a theoretical introduction and a sketch of some related long-standing predictions, a bird's-eye view is presented—with the help of nine figures—of the various experimental sectors of physics in which Superluminal motions seem to appear (thus contributing support to those past predictions). In particular, a panorama is presented of the experiments with evanescent waves and/or tunnelling photons, and with the “localized Superluminal solutions” to the Maxwell equations (like the so-called X-shaped beams). The present review is brief, but (...) is followed by a large enough bibliography to allow the interested reader deepening the preferred topic. (shrink)

We prove that the classical theory with a discrete time (chronon) is a particular case of a more general theory in which spinning particles are associated with generalized Lagrangians containing time-derivatives of any order (a theory that has been called “Non-Newtonian Mechanics”). As a consequence, we get, for instance, a classical kinematical derivation of Hamiltonian and spin vector for the mentioned chronon theory (e.g., in Caldirola et al.’s formulation). Namely, we show that the extension of classical mechanics obtained by the (...) introduction of an elementary time-interval does actually entail the arising of an intrinsic angular momentum; so that it may constitute a possible alternative to string theory in order to account for the internal degrees of freedom of the microsystems. (shrink)

In this paper—dedicated to Prof. Asim O. Barut—we generalize the Diracnon-linear electrodynamics by introducing two potentials(namely, the vector potential A and the pseudo-vector potential γ5B of the electromagnetic theorywith charges and magnetic monopoles) and by imposing the pseudoscalar part of the product ωω* to be zero, with ω≡A+γ5B. We show that the field equations of such a theory possess a soliton-like solution which can representa priori a “charged particle,” since it is endowed with a Coulomb field plus the field of (...) a magneticdipole. The rest energy of the soliton is finite, and the angular momentum stored in its electromagnetic field can be identified—for suitable choices of the parameters—with the spin of the charged particle. Thus, this approach seems to yield a classical model for the charged (spinning) particle which does not encounter the problems met by earlier attempts in the same direction. (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)

We revisit the introduction of the Superluminal Lorentz transformations which carry from “bradyonic” inertial frames to “tachyonic” inertial frames, i.e., which transform time-like objects into space-like objects, andvice versa. It has long been known that special relativity can be extended to Superluminal observers only by increasing the number of dimensions of the space-time or—which is in a sense equivalent—by releasing the reality condition (i.e., introducing also imaginary quantities). In the past we always adopted the latter procedure. Here we show the (...) connection between that procedure and the former one. In other words, in order to clarify the physical meaning of the imaginary units entering the classical theory of tachyons, we have temporarily to call into play anauxiliary six-dimensional space-time M(3, 3); however, we are eventually able to go back to the four-dimensional Minkowski space-time. We revisit the introduction of the Superluminal Lorentz transformations also under another aspect. In fact, the generalized Lorentz transformations had been previously written down in a form suited only for the simple case of collinear boosts (e.g., they formed a group just for collinear boosts). We express now the Superluminal Lorentz transformations in a more general form, so that they constitute a group together with the ordinary—orthochronousand antichronous—Lorentz transformations, and reduce to the previous form in the case of collinear boosts. Our approach introduces either real or imaginary quantities, with exclusion of (generic) complex quantities. In the present context, a procedure—in two steps—for interpreting the imaginary quantities is put forth and discussed. In the case of a chain of generalized Lorentz transformations, such a procedure (when necessary) is to be applied only at the end of the chain. Finally, we justify why we call “transformations” also the Superluminal ones. (shrink)