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

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

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

Standard-model symmetry in complexified spacetime algebra

Complexified spacetime algebra is defined as the geometric (Clifford) algebra of spacetime with complex coefficients, isomorphic $\mathcal{G}_{1,4}$. 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 $U(1) \otimes SU(2) \otimes SU(3)$ and that there are 4 distinct copies of this group within CSTA.Comment: 8 pages, revised and extended compared to V.

Geometric algebra and particle dynamics

In a recent publication the I showed how the geometric algebra ${G}_{4,1}$, 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 ${G}_{1,3}$, an algebra isomorphic to ${G}_{4,1}$. 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

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

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

Euclidean formulation of general relativity

A variational principle is applied to 4D Euclidean space provided with a tensor refractive index, defining what can be seen as 4-dimensional optics (4DO). The geometry of such space is analysed, making no physical assumptions of any kind. However, by assigning geometric entities to physical quantities the paper allows physical predictions to be made. A mechanism is proposed for translation between 4DO and GR, which involves the null subspace of 5D space with signature $(-++++)$. A tensor equation relating the refractive index to sources is established geometrically and the sources tensor is shown to have close relationship to the stress tensor of GR. This equation is solved for the special case of zero sources but the solution that is found is only applicable to Newton mechanics and is inadequate for such predictions as light bending and perihelium advance. It is then argued that testing gravity in the physical world involves the use of a test charge which is itself a source. Solving the new equation, with consideration of the test particle's inertial mass, produces an exponential refractive index where the Newtonian potential appears in exponent and provides accurate predictions. Resorting to hyperspherical coordinates it becomes possible to show that the Universe's expansion has a purely geometric explanation without appeal to dark matter.Comment: Talk to be delivered at the "Number Time and Relativity Conference", Moscow, August 200

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