Discreteness of space from the generalized uncertainty principle

Various approaches to Quantum Gravity (such as String Theory and Doubly Special Relativity), as well as black hole physics predict a minimum measurable length, or a maximum observable momentum, and related modifications of the Heisenberg Uncertainty Principle to a so-called Generalized Uncertainty Principle (GUP). We propose a GUP consistent with String Theory, Doubly Special Relativity and black hole physics, and show that this modifies all quantum mechanical Hamiltonians. When applied to an elementary particle, it implies that the space which confines it must be quantized. This suggests that space itself is discrete, and that all measurable lengths are quantized in units of a fundamental length (which can be the Planck length). On the one hand, this signals the breakdown of the spacetime continuum picture near that scale, and on the other hand, it can predict an upper bound on the quantum gravity parameter in the GUP, from current observations. Furthermore, such fundamental discreteness of space may have observable consequences at length scales much larger than the Planck scale.     

The possibility of superluminal sources and their Doppler effect

From the Special Relativity Theory, the existence of Superluminal reference-frames and faster-than-light objects can be inferred, when its validity is not arbitrarily confined to subluminal velocities. The ‘Extended Theory of Relativity’ allows in particular extending the Doppler effect formulae to Superluminal sources. This point is here explored, due to its possible astrophysical interest. Some other questions are briefly considered, regarding the possibility of ‘radio contact’ between subluminal and Superluminal objects.     

Special Relativity,the Source of Electron Deep Orbits

In this paper, we explicitly point out the reasons why Special Relativity must be considered as the source of electron deep orbits, and dominates their behavior. We show that the cause is the quadratic form of the relativistic expression of energy, and this clearly appears when we explicitly develop the relativistic Schrödinger equation and compare it with the non-relativistic one.     

Equivalence Principle and the Principle of Local Lorentz Invariance

In this paper we scrutinize the so called Principle of Local Lorentz Invariance (PLLI) that many authors claim to follow from the Equivalence Principle. Using rigourous mathematics, we introduce in the General Theory of Relativity two classes of reference frames (PIRFs and LLRFs) which as natural generalizations of the concept of the inertial reference frames of the Special Relativity Theory. We show that it is the class of the LLRFs that is associated with the PLLI. Next we give a definition of physically equivalent reference frames. Then, we prove that there are models of General Relativity Theory (in particular on a Friedmann universe) where the PLLI is false. However our finding is not in contradiction with the many experimental claims vindicating the PLLI, because theses experiments do not have enough accuracy to detect the effect we found. We prove moreover that PIRFs are not physically equivalent.     

On Metric and Matter in Unconnected, Connected, and Metrically Connected Manifolds

From Einstein's point of view, his General Relativity Theory had strengths as well as failings. For him, its shortcoming mainly was that it did not unify gravitation and electromagnetism and did not provide solutions to field equations which can be interpreted as particle models with discrete mass and charge spectra, As a consequence, General Relativity did (and does) not solve the quantum problem, either. Einstein tried to get rid of the shortcomings without losing the achievements of General Relativity Theory. Stimulated by papers of Weyl (Sitzungsber. Preuss. Akad. Wiss (1918) 465) and Eddington (Proc. R. Soc. Hond. 99 (1921) 194), from 1923 onward, he believed that, to reach this goal, one has to transit to space–times which possess more comprehensive geometrical structures than the Riemann space–time. This was the beginning of a decade's lasting search for a unitary field theory. We describe this exciting part of the history of physics, discuss achievements and failures of this development, and ask how these early attempts of a unified theory strike us today. Taking into account the fact that the Equivalence Principle only speaks for a geometrization of gravitation, we consider an alternative way to give those non-Riemannian structures which were introduced by the unitary field approach a physical meaning, namely the meaning of a generalized gravitational field. This is interesting since there are arguments in favor of such a generalization of General Relativity Theory, e.g., the problems the latter theory meets with if one tries to quantize it and to unify gravitation with other interactions.     

The interpretation of the Theory of Relativity

The presently accepted interpretation of the (Special) Theory of Relativity is considered by the author to be inadequate in certain respects. An alternative interpretation is suggested     

Cosmological constant and Minkowski space

Using the framework of classical gravitational field theory, it is shown that the equations of Einstein’s General Relativity with a cosmological constant, if requested to be compatible with the Minkowski space, change form and become the equations of Relativistic Theory of Gravitation. These equations, in contrast to General Relativity, lead us to fundamentally different physical conclusions about the Universe’s evolution and Collapse.     

Did Günter Nimtz discover tachyons?

It is argued that in the famous G. Nimtz experiment tachyons were produced and annihilated. We base our considerations on the new version of Special Relativity elaborated recently by one of the authors.     

Electromagnetism as a second-order effect

The Electric and Magnetic Fields of a charge moving with uniform velocity are derived from Coulomb's law taking the transformations of the Special Theory of Relativity as axiomatic.     

Teilchen-Modelle und effektive Radien in der Allgemeinen Relativitätstheorie

Particle Models and Effective Radius in the General Theory of Relativity We discuss the role of the classical particle radius defined in the classical field models of particles for the general relativistic particle problem suggested by EINSTEIN. The main point is that in General Relativity the point-like particles without field masses may be self-consistent but not the model particles with an effective radius given by the Schwarzschild radius of the mechanical particle mass.     

Topics in Noncommutative Geometry Inspired Physics

In this review article we discuss some of the applications of noncommutative geometry in physics that are of recent interest, such as noncommutative many-body systems, noncommutative extension of Special Theory of Relativity kinematics, twisted gauge theories and noncommutative gravity.     

The Evidence For and Against Various Theories of Light

The ether-wave theory of light, suitably modified, is fully supported by all known evidence. Further observation and analysis will be required to determine which of its several forms accurately represents reality. On the other hand, the tactile theory, the Newtonian corpuscular theory, the Ritz extinction theory, and the Special Theory of Relativity are not supported by the evidence.     

The Einsteinian Star Model in Treder's Tetrad Theory of Gravitation

By means of a simple star model proposed by EINSTEIN (point-particle cluster) the collapse behaviour in General Relativety and in TREDER 's [14] Tetrad Theory has been compared. Within both theories the heavy mass of a point-particle cluster with a fixed radius cannot exceed a critical value. However, contrary to General Relativity, within the framework of TREDER 's Tetrad Theory, for a fixed particle number N, the radius of the cluster is allowed to be arbitrarily small. In this sense, the Tetrad Theory is a collapse-free relativistic theory of gravitation.     

Antiparticles from special Relativity with ortho-chronous and antichronous Lorentz transformations

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.Work partially supported by FAPESP and CNPq (Brazil).     

Electromagnetism as a second order effect

An historical survey of the theories of the forces between current elements is given and Ampère's formula is compared with the Biot-Savart law. It is shown that the Biot-Savart law, in differential form, is consistent with both Classical Electromagnetism and the Special Theory of Relativity.     

From flavour to SUSY flavour models

If supersymmetry (SUSY) will be discovered, successful models of flavour not only have to provide an explanation of the flavour structure of the Standard Model fermions, but also of the flavour structure of their scalar superpartners. We discuss aspects of such “SUSY flavour” models, towards predicting both flavour structures, in the context of supergravity (SUGRA). We point out the importance of carefully taking into account SUSY-specific effects, such as 1-loop SUSY threshold corrections and canonical normalisation, when fitting the model to the data for fermion masses and mixings. This entangles the flavour model with the SUSY parameters and leads to interesting predictions for the sparticle spectrum. We demonstrate these effects by analyzing an example class of flavour models in the framework of an SU(5) Grand Unified Theory with a family symmetry with real triplet representations. For flavour violation through the SUSY soft breaking terms, the class of models realises a scheme we refer to as “Trilinear Dominance”, where flavour violation effects are dominantly induced by the trilinear terms.     

On the Consistency between the Assumption of a Special System of Reference and Special Relativity

In a previous work, we have shown that the null result of the Michelson–Morley experiment in vacuum is deeply connected with the notion of time. The same is true for the postulate of constancy of the two-way speed of light in vacuum in all frames independently of the state of motion of the emitting body. The argumentation formerly given is very general and has to be true not only within Special Relativity and its “equivalence” of all inertial frames, but as well as in Lorentz-Poincaré scenario of a preferred reference frame. This paper is the second of a trilogy intending to revisit the foundations of Special Relativity, and addresses the question of the constancy of the one-way speed of light and of the differences and similarities between both scenarios. Although they manifestly differ in philosophy, it is debated why and how the assumption of a “special system of reference experimentally inaccessible” is indeed compatible with Einstein’s Special Relativity, as beautifully outlined and discussed by Bell [Speakable and Unspeakable in Quantum Mechanics (Cambridge University Press, Cambridge, 1988)]. This rather trivial statement is still astonishing nowadays to a big majority of scientists. The purpose of this work is to bring such assertion into perspective, widening the somewhat narrow view of Special Relativity often presented in textbooks and scientific papers.     

Newtonian gravitational field theory: Two-body problem

The effects of a dual force which appears in a consistent field theory of Newtonian gravitation are explored by a study of the motion of two bodies which interact with each other through the gravitational field. The equations of motion are solved exactly. Among the results obtained, we find that the present theory formulated in accordance with the Special Theory of Relativity leads to the same analytical result for the precession of the perihelion of the orbit as does Einstein's General Theory of Relativity. Another result is that classical particles are endowed with an intrinsic angular momentum of constant magnitude—a helicity of classical origin. Other results, such as the period of revolution, are similar to Kepler's law, except for relativistic corrections. A slight deviation from the planar orbit of classical theory results, and may be observable. This deviation is related to the magnitude of the precession of the perihelion of the orbit. The significance of these results for charged particles, viewed classically or quantum mechanically, are discussed.     

From Dark Energy &; Dark Matter to Dark Metric

We present a new approach to the mathematical objects of General Relativity in terms of which a generic f(R)-gravity theory gravitation is written in a first-order (à la Palatini) formalism, and introduce the concept of Dark Metric which could bypass the emergence of disturbing concepts as Dark Energy and Dark Matter. These issues are related to the fact that General Relativity could not be the definitive theory of Gravitation due to several shortcomings that come out both from theoretical and experimental viewpoints. At large scales, the attempts to match it with the recent observational data lead to invoke Dark Energy and Dark Matter as the bulk components of the cosmic fluid. Since no final evidence, at fundamental level, exists for such ingredients, it could be useful to reconsider the gravitational sector in order to see if suitable extensions of General Relativity could solve the shortcomings present at infrared scales.     

A fundamental length as a candidate for dark energy: A DSR inspired FRW spacetime

We show that the existence of a fundamental length, introduced in Deformed Special Relativity (DSR) inspired minisuper-(phase-)space, causes the behavior of the scale factor of the universe to change from that of a universe filled with dust to an accelerating universe driven by a cosmological constant.