26 research outputs found

### Discrete-to-continuum transitions and mathematical generalizations in the classical harmonic oscillator

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.Comment: 14 pages. Typo. correction

### Dynamics and causality constraints

The physical meaning and the geometrical interpretation of causality
implementation in classical field theories are discussed. Local causality are
kinematical constraints dynamically implemented via solutions of the field
equations, but in a limit of zero-distance from the field sources part of these
constraints carries a dynamical content that explains old problems of classical
electrodynamics away with deep implications to the nature of physical
interactions.Comment: 14 pages, 4 eps figure

### Discrete fields, general relativity, other possible implications and experimental evidences

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.Comment: 30 pages, 3 figure

### Gravity and Antigravity with Discrete Interactions: Alternatives I and II

Questioning the experimental basis of continuous descriptions of fundamental
interactions we discuss classical gravity as an effective continuous
first-order approximation of a discrete interaction. The sub-dominant
contributions produce a residual interaction that may be repulsive and whose
physical meaning is of a correction of the excess contained in the continuous
approximation. These residual interactions become important (or even dominate)
at asymptotical conditions of very large distances from where there are data
(rotation curves of galaxies, inflation, accelerated expansion, etc) and
cosmological theoretical motivations that suggest new physics (new forms of
interactions) or new forms (dark) of matter and energy. We show that a discrete
picture of the world (of matter and of its interactions) produce, as an
approximation, the standard continuous picture and more. The flat rotation
curve of galaxies, for example, may have a simple and natural explanation.Comment: 18 page

### Electrodynamics Classical Inconsistencies

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).Comment: 15 pages, Revtex, 1 ps figur

### Discrete Classical Electromagnetic Fields

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.Comment: 13 pages in Revtex,5 ps figure

### Discrete fields on the lightcone

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.Comment: 26 pages, Revtex, 11 ps figure

### Gauge fields in a discrete approach

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.Comment: 8 pages, no figur

### Discrete fields and the Pioneer anomalous acceleration

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.Comment: 8 page

### The Lorents-Dirac equation and the structure of spacetime

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.Comment: Figures correctly adde