With clarity and grace, he also reveals the limited truth of some of the "common sense" assumptions which make it difficult for us to appreciate its full ...

An apparent inadequacy of the velocity addition theorem in handling a Fizeau (like) experiment beyond the resonance frequence is shown not to be a true failing. The proof consists in showing that the invariance of the signal velocity is unrelated to its maximality. Next, Lorentz transformations which connect frames moving with supersignal velocity to those of subsignal velocity are derived, taking a cue from the acoustic case. Methods are also suggested for laboratory verification of the theory.

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.

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)

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)

We comment on the previous paper by L. Basano. In particular, we show that its Section 2 is kinematically incorrect (the dynamics of a two-body interaction through tachyon exchange, incidentally, has already been thoroughly expounded in one paper of ours). Its Section 1 is simply a rather subjective introduction. As to its Section 3, containing indeed interesting problems, we again briefly refer to our earlier work. Our conclusions are still in favor of “au revoir to tachyons!,” even if it is (...) known that inside our cosmos tachyons are more likely to have a role in physics (e.g., in elementary particle and black-hole physics) as “exchanged objects” rather than as “asymptotically free” objects. (shrink)

A new four-component spin-1/2 wave equation for ordinary mass is discussed. It is shown that this equation has a conserved current not easily identified with a transition probability, only pure imaginary energy states, and is covariant. A tachyon-like Klein-Gordon equation is satisfied by this equation, but rest states are explicitly constructed.