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Theodor Kaluza's Theory of Everything: revisited - update April 2023
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Abstract
Using a Kaluza-type model, a combination of differential geometry with electromagnetic theory, including spin, provides a coherent, comprehensive and quantitative description of phenomena related to particles, including the values for electroweak coupling constants, a convergent series of quantized particle energies with limits given by the energy values of the electron and the Higgs vacuum expectation value, and the fractional electric charges as well as the magnetic moments of baryons. Electromagnetic and gravitational terms will be linked by a series expansion, the corresponding relation suggests the existence of a cosmological constant in the correct order of magnitude. The model can be expressed ab initio, necessary input parameters are the electromagnetic constants. 1 Introduction Theodor Kaluza in 1919 developed a unified field theory of gravitation and electromagnetism that produced the formalism for the field equations of the general theory of relativity (GR) and Maxwell's equations thus unifying the major forces known at his time. His 5-dimensional model [1] is mainly known as Kaluza-Klein theory today, including the contributions of Klein [2] who introduced the idea of compactification and attempted to join the model with the emerging principles of quantum mechanics. This version became a progenitor of string theory. The classical Kaluza model was developed further as well [3], Wesson and coworkers elaborated a general non-compactified version to describe phenomena extending from particles to cosmological problems. The equations of 5D space-time may be separated in a 4D Einstein tensor and metric terms representing mass and the cosmological constant, Λ. Particles may be described as photon-like in 5D, traveling on time-like paths in 4D. This version is known as space-time-matter theory [4]. Both successor theories give general relationships rather than providing quantitative results for specific phenomena such as particle energy. The model described in the following does not attempt to give a complete solution for a 5D theory but to demonstrate that Kaluza's ansatz provides very simple, parameter-free and in particular quantitative solutions for a wide range of phenomena. Basic equations from the existing literature may be used, with one significant simplification: Kaluza's approach presupposes electromagnetic units. To reproduce the Einstein field equations (EFE) he chose a gravitational term to keep the electromagnetic potential terms in the metric dimensionless, a rather unfitting combination 1. This assumption will be dropped in this work, the equations will be interpreted in 1 st approximation as related to electromagnetism. Gravitational terms will be recovered via a series expansion of the electromagnetic equations. Curvature of space-time based on an electromagnetic version of the field equations of GR will be strong enough to localize a photon in a self trapping kind of mechanism, yielding energy states in the range of the particle zoo. Circular polarized light is part of conventional electromagnetic theory, in the following this feature will be treated equivalently with the terms angular momentum or spin as intrinsic property of a photon and will be a necessary boundary condition in the equations used. In particular, unless noted otherwise, it is assumed that particles posses half-integer spin or are composed of half-integer spin components (e.g. mesons). The basic proceeding will be as follows: Kaluza's equations for flat 5D-space may be arranged to give [4, chapter 6.6] 1) Einstein-like equations for space-time curved by electromagnetic and scalar fields (equ. (5)), 2) Maxwell equations where the source depends on the scalar field, 3) a wave-like equation connecting the scalar with the electromagnetic tensor (equ. (6)). Solutions for the scalar Φ of 3) in a flat 5D-metric will be used as general ansatz in a 4D-metric. This is considered to be a proof of concept only, a more thorough ansatz has to be expected to incorporate angular momentum/spin into the field equations appropriately. The results obtained seem to justify this to be a
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The ratio of the nucleon F_{2} structure functions, F_{2}^{n}/F_{2}^{p}, is determined by the MARATHON experiment from measurements of deep inelastic scattering of electrons from ^{3}H and ^{3}He nuclei. The experiment was performed in the Hall A Facility of Jefferson Lab using two high-resolution spectrometers for electron detection, and a cryogenic target system which included a low-activity tritium cell. The data analysis used a novel technique exploiting the mirror symmetry of the two nuclei, which essentially eliminates many theoretical uncertainties in the extraction of the ratio. The results, which cover the Bjorken scaling variable range 0.19<x<0.83, represent a significant improvement compared to previous SLAC and Jefferson Lab measurements for the ratio. They are compared to recent theoretical calculations and empirical determinations of the F_{2}^{n}/F_{2}^{p} ratio.
Modern developments in theoretical and applied science depend on knowledge of the properties of mathematical functions, from elementary trigonometric functions to the multitude of special functions. These functions appear whenever natural phenomena are studied, engineering problems are formulated, and numerical simulations are performed. They also crop up in statistics, financial models, and economic analysis. Using them effectively requires practitioners to have ready access to a reliable collection of their properties. This handbook results from a 10-year project conducted by the National Institute of Standards and Technology with an international group of expert authors and validators. Printed in full color, it is destined to replace its predecessor, the classic but long-outdated Handbook of Mathematical Functions, edited by Abramowitz and Stegun. Included with every copy of the book is a CD with a searchable PDF of each chapter.
Using the data on deep inelastic muon scattering on iron and deuterium the ratio of the nucleon structure functions F2N(Fe)/F2N(D) is presented. The observed x-dependence of this ratio is in disagreement with existing theoretical predictions.
This book is a summing up of the prospects for unification between relativity and particle physics based on the extension of Einstein's theory of General Relativity to five dimensions. This subject was first established by Paul Wesson in his previous best-seller, Space-Time-Matter, and discussed from a different perspective in Five-Dimensional Physics, both published by World Scientific in 1999 and 2006 respectively. This third book brings the field up to date and details many new developments and connections to particle theory and wave mechanics in particular. It was in largely finished form at the time of Paul Wesson's untimely death in 2015, and has been completed and expanded by his former student and longtime collaborator, James Overduin.
This paper gives the 2014 self-consistent set of values of the constants and conversion factors of physics and chemistry recommended by the Committee on Data for Science and Technology (CODATA). These values are based on a least-squares adjustment that takes into account all data available up to 31 December 2014. Details of the data selection and methodology of the adjustment are described. The recommended values may also be found at physics.nist.gov/constants.
REVIEW OF PARTICLE PHYSICS
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Ab Initio Determination of Light Hadron Masses
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- T Schindelbeck
Schindelbeck, T., http://doi.org/10.5281/zenodo.832957;