On a Generalized Theory of Relativity

Since its final version and publication in 1916, it is widely reported in several specialized textbooks and research articles that General Relativity theory reduces to Newton's theory of gravity in the limit of a weak gravitational field and slowly moving material bodies. In the present paper, the so-called reducibility of Einstein's geodesic and field equations, to Newton's equation of motion and Poisson's gravitational potential equation, respectively, is scrutinized and proven to be mathematically, physically and dimensionally incorrect, and that the geometrization of gravity is unnecessary.

2008

Nature, 1961

Here we present a new point of view for general relativity and/or space-time metrics that is remarkably different from the well-known viewpoint of general relativity. From this unique standpoint, we attempt to derive a new metric as an alternative to the Schwarzschild metric for any planet in the solar system. After determining the metric by means of some simple mathematical and physical manipulations, we used this alternative metric to recalculate the perihelion precession of any planet in the solar system and deflection of light that passes near the sun, as examples of this new viewpoint. While we obtained the result of classical general relativity for the perihelion procession, we found a slightly different result, relative to classical general relativity, for the deflection of light.

The relativists have not understood the geometry of Einstein's gravitational field. They have failed to realise that the geometrical structure of spacetime manifests in the geometrical relations between the components of the metric tensor. Consequently, they have foisted upon spacetime quantities and geometrical relations which do not belong to it, producing thereby, grotesque objects, not due to Nature, but instead, to faulty thinking. The correct geometry and its consequences are described herein.

2006

There are now at least eight experiments extending over more than 100 years that have detected the anisotropy of the speed of light, implying the absolute motion of the detecting apparatus through a dynamical space. This light-speed anisotropy is consistent with relativistic effects and Lorentz symmetry, contrary to prevailing beliefs in physics. The theoretical and experimental evidence implies that physics has failed to realise the existence of a dynamical 3-space, and that motion relative to that space is the cause of various relativistic effects, as proposed by Lorentz in 1899. This has resulted in a necessary generalisation of the Maxwell, Schrodinger and Dirac equations, which then provide an explanation for gravity as an emergent phenomenon within the new physics. From the generalised Dirac equation we show that the spacetime formalism is derivable, but as merely a mathematical construct whose geodesics arise from the trajectories of quantum wavepackets in the 3-space. Howeve...

arXiv (Cornell University), 2010

We propose in this paper a mathematicians' view of the Kaluza-Klein idea of a five dimensional space-time unifying gravitation and electromagnetism, and extension to higher-dimensional space-time. By considering the classification of positive Einstein curvature tensors and the classical Cauchy-Choquet-Bruhat theorems in general relativity, we introduce concepts of types and rigidity. Then, abandoning the usual requirement of a Ricci-flat five dimensional space-time, we show that a unified geometrical frame can be set for gravitation and electromagnetism, giving, by projection on the classical 4-dimensional space-time, the known Einstein-Maxwell-Lorentz equations for charged fluids. Thus, although not introducing, at least at this stage, new physics, we get a very aesthetic presentation of classical physics in the spirit of general relativity. The usual physical concepts, such as mass, energy, charge, trajectory, Maxwell-Lorentz law, are shown to be only various aspects of the geometry, for example curvature, of space-time considered as a Lorentzian manifold; that is no physical objects are introduced in space-time, no laws are given, everything is only geometry. We will then extend this setting to more than 5 dimensions, giving a precise mathematical frame for possible additional physical effects, preserving gravitation and electromagnetism. Version 22 04 2013. 1

Arxiv preprint arXiv:0910.3582, 2009

The gravitation equations of the general relativity, written for Riemannian space-time geometry, are extended to the case of arbitrary (non-Riemannian) space-time geometry. The obtained equations are written in terms of the world function in the coordinateless form. These equations determine directly the world function, (but not only the metric tensor). As a result the space-time geometry appears to be non-Rieamannian. Invariant form of the obtained equations admits one to exclude influence of the coordinate system on solutions of dynamic equations. Anybody, who trusts in the general relativity, is to accept the extended general relativity, because the extended theory does not use any new hypotheses. It corrects only inconsequences and restrictions of the conventional conception of general relativity. The extended general relativity predicts an induced antigravitation, which eliminates existence of black holes.

2009

The Gravitational, Electromagnetic, Weak & the Strong force are here brought together under a single roof via an extension of Reimann geometry to a new geometry (coined Reimann-Hilbert Space); that unlike Reimann geometry, preserves both the length and the angle of a vector under parallel transport. The affine connection of this new geometry-the Reimann-Hilbert Space, is a tensor and this leads us to a geodesic law that truly upholds the Principle of Relativity. The geodesic law emerging from the General Theory of Relativity (GTR) is well known to be in contempt of the Principle of Relativity which is a principle upon which the GTR is founded. The geodesic law for particles in the GTR must be formulated in special (or privileged) coordinate systems i.e. gaussian coordinate systems whereas the Principle of Relativity clearly forbids the existence of special (or privileged) coordinate systems in manner redolent of the way the Special Theory of Relativity forbids the existence of an absolute (or privileged) frame of reference. In the low energy regime and low spacetime curvature the unified field equations derived herein are seen to reduce to the well known Maxwell-Procca equation, the none-abelian nuclear force field equations, the Lorentz equation of motion for charged particles and the Dirac Equation. Further, to the already existing four known forces, the theory predicts the existence of yet another force. We have coined this the super-force and this force obeys S U(4, 4) gauge invariance. Furthermore, unlike in the GTR, gravitation is here represented by a single scaler potential, and electromagnetic field and the nuclear forces are described by the electromagnetic vector potential (A µ) which describes the metric tensor i.e. g µν = A µ A ν. From this (g µν = A µ A ν), it is seen that gravity waves may not exist in the sense envisaged by the GTR.

2015

The four dimensional spacetime continuum, as originally conceived by Minkowski, has become the default framework within which to describe physical laws. Due to its fundamental nature, there have been various attempts to derive this structure from more fundamental physical principles. In this paper, we show how the Minkowski spacetime structure arises directly from the geometrical properties of three dimensional space when modeled by Clifford geometric algebra of three dimensions Cℓ(ℜ 3). We find that a time-like dimension, as well as three spatial dimensions, arise naturally, as well as four additional degrees of freedom that we identify with spin. Within this expanded eightdimensional arena of spacetime, we find a generalisation of the invariant interval and the Lorentz transformations, with standard results returned as special cases. The power of this geometric approach is shown by the derivation of the fixed speed of light, the laws of special relativity and the form of Maxwell's equations, without any recourse to physical arguments. We also produce a unified treatment of energy-momentum and spin, as well as predicting a new class of physical effects and interactions.

arXiv (Cornell University), 2018

Do, or do not. There is no try. -Master Yoda, The Empire Strikes Back Let me finish with the warmest thank to all my family as I owe them everything. To my lovely cousins, aunts, uncles, and my grandparents, who would have been very proud. To Belén, Txiki, Arantxa, Keko, and Ondina. To Carla, no matter how much we fought in the past, I love to have you in my life and visit you around the world. To Berta, for your visits, concern, care, love, and for always being there for me. Finally, to my parents to whom I dedicate this thesis. You have supported me, believed in me, and encouraged me beyond my wildest imagination. You two were, are, and will be an inspiration. I will cherish all the teachings I have learned from you. I probably do not tell you this enough but for sure you know: ¡os quiero mucho y gracias de todo corazón! VI VII VIII 1 -Mathematical background luke: But I need your help. I've come back to complete the training. yoda: No more training, do you require. Already know you that which you need. luke: Then I am a Jedi. yoda: Not yet. -Return of the Jedi Never underestimate the joy people derive from hearing something they already know. This sentence, attributed to Enrico Fermi, is one of the two reasons to include this chapter. The other reason, less Machiavellian, is to gather all the basic but important results that will be used through this work and, in the meantime, fix the notation. Much of what has been included in this first chapter might be well known and can be skipped by the advanced readers. Nonetheless, we warn them that some topics are well worth reading as they are not usually covered at a introductory level. In particular, the mathematical description of the spaces of embeddings, the GNH algorithm, and the Fock construction. Whenever necessary, we will use the abstract index notation 1 introduced by Penrose [81], although in this chapter we will try to stick to the no-index mathematical convention. Some useful technical results, that might not be so well known, are included in appendix A. We also gather in section A.III of the appendix all the formulas appearing in this chapter (and some more) together with the abstract index version of such formulas. The first traces of the use of geometry date from around 3000BC when some civilizations, such as the Harappans and the Babylonians, made several empirical discoveries concerning angles, lengths, areas, and volumes. Their motivation was most certainly for practical purposes in astronomy, construction, or agriculture. There is also evidence that, fifteen hundred years before Pythagoras was born, the Babylonians and the Egyptians developed already the Pythagoras' theorem. But it was not until Thales and the Pythagoreans, around 500BC, that geometry became an abstract and axiomatic science, which allowed it to flourish in an spectacular way. 1 No coordinates were harmed used in the making of this thesis (except at few places that will be mentioned). Definitions 1.37 We say that s ∈ Γ(γ * T M ) is parallel along γ if ∇ γs = 0 for every t ∈ I. 1.38 A geodesic is a curve α : I → M such that α ∈ Γ(α * (T M )) is parallel to itself. Visually, if we follow a geodesic what we are doing is walking always at the same pace in the direction that our nose is pointing without ever turning our head.