The geometry of the Sagnac effect in a stationary region of a spacetime is reviewed with the aim of emphasizing the role of asymmetry of a Finsler metric defined on a spacelike hypersurface associated to a stationary splitting and related to future-pointing null geodesics of the spacetime. We show also that an analogous asymmetry comes into play in the Sagnac effect for timelike geodesics.

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)

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)

What is the sense of saying “now”? We are used to the established temporal relations by their points of reference (like “yesterday”), distinguished one from the other by measurement and the counting of time (which uses yardsticks, like “day”). So, is the now only another one of these points? Husserl tells us that is not only looking at the constituted time and already shared in common by the world that we will comprehend what is the sense of the now. In (...) this article, I try to follow Husserl’s theory of time with the intent to defend how the phenomenological perspective can clarify the relevant distinctions between “point” and “now”, especially when we comprehend “now” as an origin that closes in itself problems categorically distinct from those referred to the measurement in objective time. (shrink)

Ao contrário do que as diversas aproximações entre Husserl e Descartes podem sugerir, Husserl foi um severo crítico do dualismo mente-corpo. Esse texto tem por objetivo explicar o conceito husserliano de corporeidade para assim expor como o autor defende uma concepção não dualista da corporeidade. Para Husserl não se trata de propor ‘eu tenho um corpo’ – o que pressupõe um componente anímico possuidor –, mas sim ‘eu sou um corpo’.

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)

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)

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)

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)

La muerte tiene una gran importancia en la vida y en el pensamiento de Erasmo de Rotterdam. En la literatura renacentista el Ars Moriendi es un tema de enorme actualidad que se manifiesta en el anillo y la medalla de Erasmo, con el dios Terminvs y el Cedo nulli, que fueron objeto de diversas interpretaciones.

O humanista fez parte de um debate, em que, preferia a moderação, pois pretendia não colocar mais “óleo na fogueira”. No entanto, o que aconteceu foi justamente o contrário: ele acirrava ainda mais os ânimos e se colocava entre dois partidos opostos, a saber, a ortodoxia de um lado e, do outro, Lutero e os luteranos. Curiosa situação! Erasmo era a favor e contra a ortodoxia e os dissidentes.

En este ensayo se muestra hasta qué punto en las ideas de Martín Lutero y de Erasmo de Rotterdam pueden encontrarse algunos gérmenes o desarrollos incipientes de un aspecto central del pensamiento en la modernidad: el subjetivismo. Esto es, la vuelta del sujeto sobre sí que está a la base de los modernos conceptos de “yo”, “individuo”, “interioridad”, tal y como se expresa en el giro copernicano kantiano. De esta forma se llega a plantear que en la configuración de (...) una concepción del mundo intervienen elementos diversos que, en principio, parecerían oponerse a ella.---This essay shows to which extent some of Martin Luther’s and Erasmus of Rotterdam’s ideas contain some germs or incipient developments of a main aspect of modern thought: subjectivism; namely, the return to the subject at the basis of the modern concepts of the self, the individual and immanence, such as they are manifest in the Copernican-Kantian turn. Thus the A. contends that several elements initially deemed to be contrary to a new world vision, actually take part in its constitution. (shrink)

Erasmo fue un gran re- novador de la teología a partir del estu- dio de la Sagrada Escritura y de los Pa- dres de la Iglesia mediante su redditio ad fontes. Esta tarea tiene una fecha de partida —la de preparación fue al me- nos de quince años— el annus mirabilis 1516 en el que publica su primera edi- ción del Nuevo Testamento o Novum Instrumentum y su hercúlea edición en nueve tomos de las obras completas u Opera omnia (...) de san Jerónimo. Dos hi- tos en su proyecto bíblico y patrístico que continuará a lo largo de sus últimos veinte años con la edición de más de una docena de Padres tanto griegos como latinos. No menos impor- tante es su labor de traductor —al latín obviamente— de Padres griegos como Crisóstomo, Basilio y Orígenes —aquí estudiados bles bien por ser las primeras en el pa- norama humanístico del siglo xvi bien por la calidad de su latín, que han me- recido figurar —el caso de Juan Crisós- tomo— aún bajo su nombre en la Pa- trología griega de Migne. En este ar- tículo asistimos a la búsqueda apasio- nada por parte de Erasmo de manuscri- tos para editar o traducir, al intercam- bio epistolar con humanistas e impreso- res, y al trabajo bien hecho hasta los úl- timos días de sus vida en su querida ciudad de Basilea, la de los impresores Froben, con la edición de Orígenes que preparaba para la Feria del Libro de Fráncfort —en otoño de 1536— a la que él no llegó —falleció el 12 de ju- lio— pero sí sus dos gruesos volúme- nes, hermoso legado póstumo. (shrink)