Narrow Results

The metric-affine Lagrangian of Ponomarev and Obukhov for the unified gravitational and electromagnetic fields is linear in the Ricci scalar and quadratic in the tensor of homothetic curvature. We apply to this Lagrangian the variational principle with the tetrad and spin connection as dynamical variables and show that, in this approach, the field equations are the Einstein–Maxwell equations if we relate the electromagnetic potential to the trace of the spin connection. We also show that, as in the Ponomarev–Obukhov formulation, the generally covariant Dirac Lagrangian gives rise to the standard spinor source for the Einstein–Maxwell equations, while the spinor field obeys the nonlinear Heisenberg–Ivanenko equation with the electromagnetic coupling. We generalize that formulation to spinors with arbitrary electric charges.

In this paper I introduce tensor multinomials, an algebra that is dense in the space of nonlinear smooth differential operators, and use a subalgebra to create an extension of Einstein’s theory of general relativity. In a mathematical sense this extension falls between Einstein’s original theory of general relativity in four dimensions and the Kaluza–Klein theory in five dimensions. The theory has elements in common with both the original Kaluza–Klein and Brans–Dicke, but emphasizes a new and different underlying mathematical structure. Despite there being only four physical dimensions, the use of tensor multinomials naturally leads to expanded operators that can incorporate other fields. The equivalent Ricci tensor of this geometry is robust and yields vacuum general relativity and electromagnetism, as well as a Klein–Gordon-like quantum scalar field. The formalism permits a time-dependent cosmological function, which is the source for the scalar field. I develop and discuss several candidate Lagrangians. Trial solutions of the most natural field equations include a singularity-free dark energy dust cosmology.

Eisenhart's classical unified field theory is based on a non-Riemannian affine connection related to the covariant derivative of the electromagnetic field tensor. The sourceless field equations of this theory arise from vanishing of the torsion trace and the symmetrized Ricci tensor. We formulate Eisenhart's theory from the metric-affine variational principle. In this formulation, a Lagrange multiplier constraining the torsion becomes the source for the Maxwell equations.

The concept of unified field theory is discussed. Two nonlinear field models with world volume type action are considered, namely extremal space-time film model and Born–Infeld nonlinear electrodynamics. The natural appearance of two long-range fundamental interactions, electromagnetism and gravitation, in these field models is discussed. The quantum behavior of the interacting solitons-particles is considered. The concept of quasi-bounding quantization in nonlinear field models is introduced.

In this paper, we develop an extended space-time geometry that includes an internal space built with division octonions with realization via Pauli matrices and Zorn (vectorial) matrices. Here, we extend a former field theory that used split octonion algebra to a division octonion algebra on a non-Riemannian manifold. The octonionic algebra is the last possible algebra allowed by the Hurwitz theorem. The interpretation of the “octonionic field” in this division octonionic algebra is not straightforward, however it behaves in a similar way to the quaternionic Yang–Mills fields. Former work suggests that this Yang–Mills-like octonionic field is associated with the field governing quarks within nucleons. In this work, we discover that the inclusion of octonionic fields in the geometry of an internal space necessarily excludes the quaternionic (Yang–Mills) fields in an extended non-Riemannian geometry. This is not what is expected from the standpoint of a “unified” field theory, which leads us to propose a different approach to Einstein’s unified field theory.

This paper introduces a fluid aether formed by discrete, 3D-extended energy-like sagions obeying three conservation principles of classical mechanics: total energy, linear momentum, and angular momentum. In contrast to Newtonian mechanics, neither mass, nor force are primitive notions (hence, the Cartesian”), but the theory is atomistic (hence the “neo”). Firstly, the notions of field, continuity, discreteness, extension, and philosophical and empirical reasons leading to reinstating aether are clarified. The collective fluid behaviour is described by the classical wave equation, also known as the homogeneous Klein-Gordon equation (HKGE). Connections of electromagnetism (EM), gravity and quantum mechanics (QM) to the theory of fluids are noted. The goal is to attain a unified field theory that contain as special cases the other “forces”. In particular, QM must be relativistic ab initio for consistency with Einstein’s general theory of relativity (GTR), while GTR must be extended to allow for permanent violation of the principle of equivalence, in the sense that gravity interactions depend upon composition of matter, as effectively observed in the original Eötvös experiment, and in the outstanding, but neglected, experiments of Quirino Majorana. Of particular interest are three families of nonharmonic solutions to the HKGE discovered by this author in the 1990s. The minimum angular momentum in sagion-sagion interactions is identified as Planck constant, thus introducing quantum features in classical mechanics. Coalescence of sagions leads to a kinematic theory of photons and fundamental particles, whose simplest object is a rotating dumbbell, which forms a torus in 3D-space. Acceleration produced by successive pushes of a small projectile (say, a sagion) generates an acceleration curve resembling Einstein’s mass increase, thus giving a different interpretation to some claims of special theory of relativity (STR); in particular, Bertozzi experiment is explained as an inefficient transfer of linear momentum, and the fitting of Bertozzi data by neo-Cartesian predictions is superior to STR’s predictions.

A nagging problem has existed in the way we regard the local physical world around us and the non-local universe at large since the very beginning development of our philosophical and scientific attitudes toward the external world. That problem deals with the dualistic way in which we parse the physical world itself through geometry. Geometry can be based upon two different elements: the extension- or metric-element of Riemann and the point-element. Riemannian geometry can be fixed by expanding it to include the point-element, but even that is not enough. A further physical advance can be made by adopting the idea of the 0-D point Void, first developed intuitively by Sperry Andrews, but understanding the physical role of the 0-D point Void can only be realized by expanding that notion by adopting the physical concept of a discrete geometrical point/twist. It is only when a discrete 0-D point/twist Void replaces the simple point-element missing in the Riemannian system of differential geometry of surfaces that post-modern physics fulfills its promise. Understanding the concept of a point-element, of course, is necessary to understand how the Riemannian geometry has been used in general relativity as well as how it can be expanded to unify all of modern physics, including quantum theory, under a single geometrical paradigm. Whether a scientist is considering the discrete point-particles of the Standard Model or the existence of point singularities in relativity theory, the concerns are exactly the same, which forces the concept of an individual 0-D discrete point void to the center of the unification process. In either case, the human Mind and Consciousness are perceiving and interpreting the physical/material world that science is attempting to theoretically describe so the ultimate question of Consciousness and how it interacts with the Mind/brain as well as our commonly experienced physical reality also needs to be answered within the context of the 0-D point/twist. In other words, this is the point (no pun intended) where scientific logic and non-scientific intuition come together to give a complete theoretical structure of our commonly shared physical reality. Toward that end, the only logical scientific precedent to understand anything like the 0-D point/twist in all of the history of science is only found in the notion of a tesseract, which dates from the late nineteenth century attempts to ‘realize’ the concept of a hyperspace in the absence of being able to detect them through astronomical observations so that a hyperspace geometry could be used to explain nature. The end product of understanding these concepts is a greater insight into how the single field theory explains a much wider range of physical phenomena than any single previous paradigm of physics.

Boscovich provided a unified theory of point-particles, and this served as basis for Modern quantum mechanics. Applications of Boscovich’s theory to quantum problems, such as to Modern chemistry will be considered based on the work of Dragoslav Stoiljkovich. The works of Stoiljkovich having not been published very much in English, and thus has not been more widely known among English-speaking scientists. This author is now engaged in translating these works in corroboration with Stoiljkovich; works that highlight the modern work that is still being pursued based on Boscovich’s unified field theory. Also, briefly the work of Augustus Prince will be dealt with.

Using an analysis from a physical and phenomenological viewpoint employing the renowned and recognized continuity of the Boscovich force curve, a new paradigm is formulated to explicate various physical phenomena in both the micro-world and the macro-world. Within this paradigm, an algorithm is established which produced a functional representation of the various atomic line spectra of hydrogen and the temperature dependent black-body energy distribution of radiation which compared very favorably with the experimental data. The Boscovichian points which are assumed to be endowed with certain characteristics move under the action of a force (acceleration) field that varies inversely proportional to the cube of the radius from the center of force which leads to an orbit described by an equiangular (logarithmic) spiral. This spiral consists of intercepts that correspond to stable and unstable points on the Boscovich curve. These intercepts are the roots of the equations employed and are described in the Pavia paper. Further representations also produced very favorable results for the photoelectric effect, (to be published). In addition, utilizing the shape of Boscovich’s “extended” curve of force, the prospect of the interpretation of the mysterious attractive and repulsive forces beyond the visible Newtonian region of space, often described in terms of “black holes”, “dark energy”, etc. is proposed. The recent LIGO experiments provides a means of using this extended Boscovich’s to analyze these results and is presented herein.

In 1918, Hermann Weyl proposed a generalisation of Riemannian geometry, in order to unify general relativity and electrodynamics. This paper investigates the physical, mathematical and philosophical reasons for his subsequent abandonment of any such attempt towards a unified field theory.

Too many physicists believe the ‘phallacy’ that the quantum is more fundamental than relativity without any valid supporting evidence, so the earliest attempts to unify physics based on the continuity of relativity have been all but abandoned. This belief is probably due to the wealth of pro-quantum propaganda and general ‘phallacies in fysics’ that were spread during the second quarter of the twentieth century, although serious ‘phallacies’ exist throughout physics on both sides of the debate. Yet both approaches are basically flawed because both relativity and the quantum theory are incomplete and grossly misunderstood as they now stand. Had either side of the quantum versus relativity controversy sought common ground between the two worldviews, total unification would have been accomplished long ago. The point is, literally, that the discrete quantum, continuous relativity, basic physical geometry, theoretical mathematics and classical physics all share one common characteristic that has never been fully explored or explained – a paradoxical duality between a dimensionless point (discrete) and an extended length (continuity) in any dimension – and if the problem of unification is approached from an understanding of how this paradox relates to each paradigm, all of physics and indeed all of science could be unified under a single new theoretical paradigm.

I use spherical-numbers to model and study interacting wave functions, and recover known physical laws. A wavefunction interacts with and changes space; the natural forces and quantum properties emerge. The study describes an absolute reality that withstands the tests of relativity. A Bohr-like model of the hydrogen atom dilates the transition frequencies. This alternate approach could provide an ansatz for a unified field theory, however it has a price; most present-day accepted truths need revision.