arXiv subjects
Publications and source records attributed to Manoelito M. de Souza.
Discrete interaction models for the classical harmonic oscillator are used for introducing new mathematical generalizations in the usual continuous formalism. The inverted harmonic potential and generalized discrete hyperbolic and trigonometric functions are defined.
Motivated by improving the understanding of the quantum-to-classical transition we use a simple model of classical discrete interactions for studying the discrete-to-continuous transition in the classical harmonic oscillator. A parallel is traced with gravity for stressing the relevance of such discrete interaction models.
What is the nature - continuous or discrete - of matter and of its fundamental interactions? The physical meaning, the properties and the consequences of a discrete scalar field are discussed; limits for the validity of a mathematical description of fundamental physics in terms of continuum fields are a natural outcome of discrete fields with discrete interactions. Two demarcating points (a near and a far) define a domain where no difference between the discrete and the standard continuum field formalisms can be experimentally detected. Discrepancies, however, can be observed as a continuous-interaction is always stronger below the near point and weaker above the far point than a discrete one. The connections between the discrete scalar field and gravity from general relativity are discussed. Whereas vacuum solutions of general relativity can be retrieved from discrete scalar field solutions, this cannot be extended to solutions in presence of massive sources as they require a true tensor metric field. Contact is made, on passing, with the problem of dark matter and the rotation curve of galaxies, with inflation and the accelerated expansion, the apparent anomaly in the Pioneer spacecraft acceleration, the quantum Hall effect, high-$T_{c}$ superconductivity, quark confinement, and with Tsallis generalized one-parameter statistics as some possible manifestation of discrete interaction and of an essentially discrete world.
The dominant contributions from a discrete gravitational interaction produce the standard potential as an effective continuous field. The sub-dominant contributions are, in a first approximation, linear on n, the accumulated number of (discrete) interaction events along the test-body trajectory. For a nearly radial trajectory n is proportional to the traversed distance and its effects may have been observed as the Pioneer anomalous constant radial acceleration, which cannot be observed on the nearly circular planetary orbits.
The dominant contributions from a discrete gravitational interaction produce the standard potential as an effective continuous field. The sub-dominant contributions are, in a first approximation, linear on $n$, the accumulated number of (discrete) interaction events along the test-body trajectory. For a nearly radial trajectory $n$ is proportional to the transversed distance and its effects may have been observed as the Pioneer anomalous constant radial acceleration, which cannot be observed on the nearly circular planetary orbits. Here we give calculation details of the alternative II, discussed in gr-qc/0106046.
The physical meaning, the properties and the consequences of a discrete scalar field are discussed; limits for the validity of a mathematical description of fundamental physics in terms of continuous fields are a natural outcome of discrete fields with discrete interactions. The discrete scalar field is ultimately the gravitational field of general relativity, necessarily, and there is no place for any other fundamental scalar field, in this context. Part of the paper comprehends a more generic discussion about the nature, if continuous or discrete, of fundamental interactions. There is a critical point defined by the equivalence between the two descriptions. Discrepancies between them can be observed far away from this point as a continuous-interaction is always stronger below it and weaker above it than a discrete one. It is possible that some discrete-field manifestations have already been observed in the flat rotation curves of galaxies and in the apparent anomalous acceleration of the Pioneer spacecrafts. The existence of a critical point is equivalent to the introduction of an effective-acceleration scale which may put Milgrom's MOND on a more solid physical basis. Contact is also made, on passing, with inflation in cosmological theories and with Tsallis generalized one-parameter statistics which is regarded as proper for discrete-interaction systems. The validity of Botzmann statistics is then reduced to idealized asymptotic states which, rigorously, are reachable only after an infinite number of internal interactions . Tsallis parameter is then a measure of how close a system is from its idealized asymptotic state.
A discrete field formalism exposes the physical meaning and origins of gauge fields, their symmetries and singularities. They represent a lack of a stricter field-source coherence.
In a previous work General Relativity has been presented as a microscopic theory of finite and discrete point-like fields that we associate to a classical description of gravitons. The standard macroscopic continuous field is retrieved as an average-valued field through an integration over these gravitons. Here we discuss extreme alternative (the Gauss's and the Coulomb's) ways of obtaining and interpreting the averaged fields, how they depend on the kind of measurements involved, and how do they fit with the experimental data. The field measurements in the classical tests of general relativity correspond to the Coulomb's mode whereas the determination of the overall spacetime curvature in a cosmological scale is clearly a Gauss's mode. As a natural consequence there is no missing mass and, therefore, no such a need of dark mass as the value predicted by General Relativity, in the context of the Gauss's mode, agrees with the observed one.
We develop the General Theory of Relativity in a formalism with extended causality that describes physical interaction through discrete, transversal and localized pointlike fields. The homogeneous field equations are then solved for a finite, singularity-free, point-like field that we associate to a ``classical graviton". The standard Einstein's continuous formalism is retrieved by means of an averaging process, and its continuous solutions are determined by the chosen imposed symetry. The Schwarzschild metric is obtained by the imposition of spherical symmetry on the averaged field.
A discrete field formalism exposes the physical meaning and the origins of gauge fields and of their symmetries and singularities.
The classical electromagnetic field of a spinless point electron is described in a formalism with extended causality by discrete finite transverse point-vector fields with discrete and localized point interactions. These fields are taken as a classical representation of photons, ``classical photons". They are all transversal photons; there are no scalar nor longitudinal photons as these are definitely eliminated by the gauge condition. The angular distribution of emitted photons coincides with the directions of maximum emission in the standard formalism. The Maxwell formalism and its standard field are retrieved by the replacement of these discrete fields by their space-time averages, and in this process scalar and longitudinal photons are necessarily created and added. Divergences and singularities are by-products of this averaging process. This formalism enlighten the meaning and the origin of the non-physical photons, the ones that violate the Lorentz condition in manifestly covariant quantization methods.
We discuss the physical meaning and the geometric interpretation of causality implementation in classical field theories. Causality is normally implemented through kinematical constraints on fields but we show that in a zero-distance limit they also carry a dynamical information, which calls for a revision of our standard concepts of interacting fields. The origin of infinities and other inconsistencies in field theories is traced to fields defined with support on the lightcone; a finite and consistent field theory requires a lightcone generator as the field support.
We introduce a classical field theory based on a concept of extended causality that mimics the causality of a point-particle Classical Mechanics by imposing constraints that are equivalent to a particle initial position and velocity. It results on a description of discrete (pointwise) interactions in terms of localized particle-like fields. We find the propagators of these particle-like fields and discuss their physical meaning, properties and consequences. They are conformally invariant, singularity-free, and describing a manifestly covariant $(1+1)$-dimensional dynamics in a $(3+1)$ spacetime. Remarkably this conformal symmetry remains even for the propagation of a massive field in four spacetime dimensions. The standard formalism with its distributed fields is retrieved in terms of spacetime average of the discrete fields. Singularities are the by-products of the averaging proccess. This new formalism enlightens the meaning and the problems of field theory, and may allow a softer transition to a quantum theory.
We do a critical review of the Faraday-Maxwell concept of classical field and of its quantization process. With the hindsight knowledge of the essentially quantum character of the interactions, we use a naive classical model of field, based on exchange of classical massless particles, for a comparative and qualitative analysis of the physical content of the Coulomb's and Gauss's laws. It enlightens the physical meaning of a field singularity and of a static field. One can understand the problems on quantizing a classical field but not the hope of quantizing the gravitational field right from General Relativity.
A review of old inconsistencies of Classical Electrodynamics (CED) and of some new ideas that solve them is presented. Problems with causality violating solutions of the wave equation and of the electron equation of motion, and problems with the non-integrable singularity of its self-field energy tensor are well known. The correct interpretation of the two (advanced and retarded) Lienard-Wiechert solutions are in terms of creation and annihilation of particles in classical physics. They are both retarded solutions. Previous work on the short distance limit of CED of a spinless point electron are based on a faulty assumption which causes the well known inconsistencies of the theory: a diverging self-energy (the non-integrable singularity of its self-field energy tensor) and a causality-violating third order equation of motion (the Lorentz-Dirac equation). The correct assumption fixes these problems without any change in the Maxwell's equations and let exposed, in the zero-distance limit, the discrete nature of light: the flux of energy from a point charge is discrete in time. CED cannot have a true equation of motion but only an effective one, as a consequence of the intrinsic meaning of the Faraday-Maxwell concept of field that does not correspond to the classical description of photon exchange, but only to the smearing of its effects in the space around the charge. This, in varied degrees, is transferred to QED and to other field theories that are based on the same concept of fields as space-smeared interactions.
We present a pedagogical review of old inconsistencies of Classical Electrodynamics and of some new ideas that solve them. Problems with the electron equation of motion and with the non-integrable singularity of its self-field energy tensor are well known. They are consequences, we show, of neglecting terms that are null off the charge world-line but that give a non null contribution on its world-line. The electron self-field energy tensor is integrable without the use of any kind of renormalization; there is no causality violation and no conflict with energy conservation in the electron equation of motion, when its meaning is properly considered.
A new interpretation of the causality implementation in the Lienard-Wiechert solution raises new doubts against the validity of the Lorentz-Dirac equation and the limits of validity of the Minkowski structure of spacetime.
The problems of Classical Electrodynamics with the electron equation of motion and with non-integrable singularity of its self-field stress tensor are well known. They are consequences, we show, of neglecting terms that are null off the charge world line but that gives a non null contribution on its world line. The self-field stress tensor of a point classical electron is integrable, there is no causality violation and no conflict with energy conservation in its equation of motion, and there is no need of any kind of renormalization nor of any change in the Maxwell's theory for this. (This is part of the paper hep-th/9510160, stripped , for simplicity, of its non-Minkowskian geometrization of causality and of its discussion about the physical meaning of the Maxwell-Faraday concept of field).