4,450 research outputs found
On the anomalies of gravity
The paper is based on the recently proposed 4-dimensional optical space
theory and draws some of its consequences for gravitation. Starting with the
discussion of central movement, the paper proceeds to establish the a metric
compatible with Newtonian mechanics which can be accommodated by the new theory
and finds a correction term which can be neglected in most practical
circumstances. Being effective in the very short range, the correction term
affects substantially the results when continuous mass distributions are
considered. The main consequence is the possibility of explaining the orbital
speeds found around galaxies, without the need to appeal for a lot of dark
matter. The speed of gravity is also discussed and the theory is found
compatible with a gravitational speed equal to the speed of light. On the
subject of black holes, it is suggested that they are just a possibility but
not a geometric inevitability.Comment: 8 pages, submitted to GRG. Some correction
An hypersphere model of the Universe - The dismissal of dark matter
One can make the very simple hypothesis that the Universe is the inside of an
hypersphere in 4 dimensions, where our 3-dimensional world consists of
hypersurfaces at different radii. Based on this assumption it is possible to
show that Universe expansion at a rate corresponding to flat comes as a direct
geometrical consequence without intervening critical density; any mass density
is responsible for opening the Universe and introduces a cosmological constant.
Another consequence is the appearance of inertia swirls of expanding matter,
which can explain observed velocities around galaxies, again without the
intervention of dark matter. When restricted to more everyday situations the
model degenerates in what has been called 4-dimensional optics; in the paper
this is shown to be equivalent to general relativity in all static isotropic
metric situations. In the conclusion some considerations bring the discussion
to the realm of 4D wave optics.Comment: Corrected in Eq. 18 and following. Added comparison to Friedman
equation. 12 page
Can physics laws be derived from monogenic functions?
This is a paper about geometry and how one can derive several fundamental
laws of physics from a simple postulate of geometrical nature. The method uses
monogenic functions analysed in the algebra of 5-dimensional spacetime,
exploring the 4-dimensional waves that they generate. With this method one is
able to arrive at equations of relativistic dynamics, quantum mechanics and
electromagnetism. Fields as disparate as cosmology and particle physics will be
influenced by this approach in a way that the paper only suggests. The paper
provides an introduction to a formalism which shows prospects of one day
leading to a theory of everything and suggests several areas of future
development.Comment: 47 pages. Will appear in a book about ether and the Universe to be
published by The Hadronic Pres
Unification of classic and quantum mechanics
This paper is a serious attempt at reconciling quantum and classical
mechanics through the concept of dynamic space and the acceptance of non-zero
Ricci tensor for vacuum. Starting with scalar particles, the paper shows that
with those two points allow predictions of General Relativity to be made with
an equation which includes Klein-Gordon as a special case; this equation is
designated the \emph{source equation}. The paper then moves on to show that
Dirac equation is compatible with the source equation written in a more general
form. 4-dimensional optics is introduced as an alternative to space-time, which
is shown to allow similar predictions except in extreme situations, but has the
great advantage of ascribing both gravity and electro dynamics to space
curvature.Comment: 8 pages, submitted to Found. Phys. Lett. Several important
corrections in V
Geometric algebra and particle dynamics
In a recent publication the I showed how the geometric algebra ,
the algebra of 5-dimensional space-time, can generate relativistic dynamics
from the simple principle that only null geodesics should be allowed. The same
paper showed also that Dirac equation could be derived from the condition that
a function should be monogenic in that algebra; this construction of the Dirac
equation allows a choice for the imaginary unit and it was suggested that
different imaginary units could be assigned to the various elementary
particles. An earlier paper had already shown the presence of standard model
gauge group symmetry in complexified , an algebra isomorphic to
.
In this presentation I explore the possible choices for the imaginary unit in
the Dirac equation to show that SU(3) and SU(2) symmetries arise naturally from
such choices. The quantum numbers derived from the imaginary units are unusual
but a simple conversion allows the derivation of electric charge and isospin,
quantum numbers for two families of particles. This association to elementary
particles is not final because further understanding of the role played by the
imaginary unit is needed.Comment: 15 pages. Presented at the 7th International Conference on Clifford
Algebra
Elementary Particles as Solutions of a 4-Dimensional Source Equation
The author discusses particular solutions of a second order equation
designated by source equation. This equation is special because the metric of
the space where it is written is influenced by the solution, rendering the
equation recursive. The recursion mechanism is established via a first order
equation which bears some resemblance to Dirac equation. In this paper the
author limits the discussion to solutions with constant norm but makes use of
4-dimensional hypercomplex numbers in matrix representation, a concept that is
formally introduced in a section devoted to that aspect. The particular
solutions that are found exhibit symmetries that can be assigned to spin,
electric and color charges of elementary particles, leaving mass as a free
parameter. Massless particles can also be assigned to special solutions of the
source equation, with the cases of photons, gluons and gravitons clearly
identified, together with another massless particle which does not seem to be
related to anything detected experimentally. Another section deals with
particle dynamics under fields, showing that both gravitational and
electrodynamics can be modelled by geodesics of the spaces whose metric tensors
result from the recursion mechanism. Finally the author suggests two lines of
future work, one deriving fields from densities and currents of masses and
charges and the other one aimed at determining particles' masses.Comment: 13 pages, 1 figure. Minor corrections and format change in V
Standard-model symmetry in complexified spacetime algebra
Complexified spacetime algebra is defined as the geometric (Clifford) algebra
of spacetime with complex coefficients, isomorphic . By
resorting to matrix representation by means of Dirac-Pauli gamma matrices, the
paper demonstrates isomorphism between subgroups of CSTA and SU(3). It is shown
that the symmetry group of those subgroups is indeed and that there are 4 distinct copies of this group within CSTA.Comment: 8 pages, revised and extended compared to V.
Prospects for unification under 4-dimensional optics
4-dimensional optics is here introduced axiomatically as the space that
supports a Universal wave equation which is applied to the postulated Higgs
field. Self-guiding of this field is shown to produce all the modes necessary
to provide explanations for the known elementary particles. Forces are shown to
appear as evanescent fields due to waveguiding of the Higgs field, which
provide coupling between waveguides corresponding to different particles.
Carrier particles are also discussed and shown to correspond to waveguided
modes existing in 3-dimensional space.Comment: 14 page
Choice of the best geometry to explain physics
Choosing the appropriate geometry in which to express the equations of
fundamental physics can have a determinant effect on the simplicity of those
equations and on the way they are perceived. The point of departure in this
paper is the geometry of 5-dimensional spacetime, where monogenic functions are
studied. Monogenic functions verify a very simple first order differential
equation and the paper demonstrates how they generate the line interval of
special relativity, as well as the Dirac equation of quantum mechanics.
Monogenic functions act as a unifying principle between those two areas of
physics, which is in itself very significant for the perception one has of
them. Another consequence is the possibility of studying the same phenomena in
Euclidean 4-dimensional space, providing a different point of view to physics,
from which one has an unusual and enriching perspective.Comment: 4 page
An alternative to Minkowski space-time
The starting point of this work is the principle that all movement of
particles and photons must follow geodesics of a 4-dimensional space where time
intervals are always a measure on geodesic arc lengths. The last 3 coordinates
(alpha = 1,2,3) are immediately associated with the usual physical space
coordinates, while the first coordinate (\alpha=0) is later found to be related
to proper time. Avoiding the virtually hopeless effort to prove the initial
hypothesis, the work goes through several examples of increasing complexity, to
show that it is plausible. Starting with special relativity it is shown that
there is perfect mapping between the geodesics on Minkowski space-time and on
this alternative space. The discussion than follows through light propagation
in a refractive medium, and some cases of gravitation, including
Schwartzschild's outer metric. The last part of the presentation is dedicated
to electromagnetic interaction and Maxwell's equations, showing that there is a
particular solution where one of the space dimensions is eliminated and the
geodesics become equivalent to light rays in geometrical optics. A very brief
discussion is made of the implications for wave-particle duality and
quantization.Comment: 18 pages, 2 figures. Submitted to GRG. Minor revisions in V
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