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Charles Schwartz

Publications and source records attributed to Charles Schwartz.

At least 19 recordsLinked to original sources
arXiv2025

Equation of State for Tachyon Neutrinos in Cosmology

This paper reports improvements and new results for a well developed theory of tachyons (faster-than-light particles) and follows the suggestion that neutrinos - especially the low energy neutrinos in the Cosmic Neutrino Background - may be tachyons. Starting with an application of the Thomas-Fermi method for studying a mass of particles obeying the Pauli exclusion principle, we find the following (and unusual) equations of state: $p \sim n^{1/2} \sim \rho^{1/3}$ , where n is the particle number density, $\rho$ is the energy density, and $p$ is the pressure. We then use these relations in the FLRW model for the evolution of the universe, focusing on the dominant role of the tachyon pressure. The result is a simple formula for the scale factor a(t); and this is found to provide an excellent fit to the famous observational data plotting "Luminosity distance" vs redshift from Type Ia supernovae. There are no free parameters in this theory; and the major uncertainty is an estimate of the tachyon mass at $0.1 eV/c^2$. With successful quantitative explanations for both Dark Energy and Dark Matter, this tachyon-neutrino theory is presented as a strong alternative to the currently popular $\Lambda CDM$ theory.

physics.gen-ph↗
arXiv2023

Tachyon Interactions

A consistent theory of free tachyons has shown how tachyon neutrinos can explain major cosmological phenomena, Dark Energy and Dark Matter. Now we investigate how tachyon neutrinos might interact with other particles: the weak interactions. Using the quantized field operators for electrons and tachyon neutrinos, the simplest interaction shows how the chirality selection rule, put in by force in the Standard Model, comes out naturally. Then I wander into a re-study of what we do with negative frequencies of plane wave solutions of relativistic wave equations. The findings are simple and surprising, leading to a novel understanding of how to construct quantum field theories.

physics.gen-ph↗
arXiv2022

Theoretical Search for Gravitational Bound States of Tachyons

The mission here is to see if we can find bound states for tachyons in some gravitational environment. That could provide an explanation for the phenomena called Dark Matter. Starting with the standard Schwarzschild metric in General Relativity, which is for a static and spherically symmetric source, it appears unlikely that such localized orbits exist. In this work the usual assumption of isotropic pressure is replaced by a model that has different pressures in the radial and angular directions. This should be relevant to the study of neutrinos, especially if they are tachyons, in cosmological models. We do find an arrangement that allows bound orbits for tachyons in a galaxy. This is a qualitative breakthrough. Then we go on to estimate the numbers involved and find that we do have a fair quantitative fit to the experimental data on the Galaxy Rotation Curve. Additionally we are led to look in the neighborhood of a Black Hole and there we find novel orbits for tachyons.

physics.gen-ph↗
arXiv2022

A Consistent Theory of Tachyons with Interesting Physics for Neutrinos

Working strictly within the physics theories of Special and General Relativity, I have produced a series of studies developing a consistent mathematical description of tachyons, using both classical and quantum frameworks for particles and fields. The most important choices throughout this work concern the question of which habits from the study of ordinary particles (those that are restricted to velocities less than that of light) should be kept and which should be changed. The first part of this paper notes an alternative set of theories wherein that question is answered differently from the choices of this author; and the results of that are severe in terms of physical symmetry. Following that is a broad summary of what has been accomplished in this work: this starts with the recognition that low energy tachyons will create large gravitational fields through the space-components of the energy-momentum tensor and leads to studying properties of the cosmic neutrino background. Lastly there is a discourse on the various arguments that have been given against the very possibility for tachyons to exist.

physics.gen-ph↗
arXiv2021

Tachyons with any Spin

In earlier work we showed how to handle the Group Theoretical issue of the Little Group for spin 1/2 tachyons by introducing a special metric in the Hilbert space of one-particle states. Here that technique is extended to tachyons of any spin. Examining the bi-linear algebra of the generating matrices for spin 5/2, we find a complete basis for the Gell-Mann matrices that form the Lie algebra for SU(3). A Dirac-like equation is developed for tachyons of any integer-plus-one-half spin; and it shows multiple distinct mass eigenvalues. The primary model shows a mass spectrum (in the case of j = 5/2) that roughly mimics the known data on masses of the three neutrinos; the model can be tweaked to fit that experimental data precisely.

physics.gen-ph↗
arXiv2019

An Approach for Modelling Tachyons with Gravitation

This work expands previous efforts, within the classical theories of Special and General Relativity, to include tachyons (faster-than-light particles) along with ordinary (slower-than-light) particles at any energy. The objective here is to construct a Hamiltonian that includes both the particles and the gravitational field that they produce. We do this with a linear approximation for the Einstein field equations; and we also assume a time-independent gravitational metric implied by a static picture of the particles' motion. The resulting formula will allow serious modelling to test the idea that cosmic background neutrinos may be tachyons, which can produce the observed gravitational effects now ascribed to some mysterious Dark Matter.

gr-qc↗
arXiv2017

Tachyon Dynamics - for Neutrinos?

Following earlier studies that provided a consistent theory of kinematics for tachyons (faster-than-light particles) we here embark on a study of tachyon dynamics, both in classical physics and in the quantum theory. Examining a general scattering process we come to recognize that the labels given to "in" and "out" states are not Lorentz invariant for tachyons; and this lets us find a sensible interpretation of negative energy states. For statistical mechanics, as well as for scattering problems, we study what should be the proper expression for density of states for tachyons. We review the previous work on quantization of a Dirac field for tachyons and go on to expand earlier considerations of neutrinos as tachyons in the context of cosmology. We stumble into the realization that tachyon neutrinos would contribute to gravitation with the opposite sign compared to tachyon antineutrinos. This leads to the gobsmacking prediction that the Cosmic Neutrino Background, if they are indeed tachyons, might explain both phenomena of Dark Matter and Dark Energy. This theoretical study also makes contact with the anticipated results from the experiments KATRIN and PTOLEMY, which focus on beta decay and neutrino absorption by Tritium.

physics.gen-ph↗
arXiv2017

Revised Theory of Tachyons in General Relativity

A minus sign is inserted, for good reason, into the formula for the Energy-Momentum Tensor for tachyons. This leads to remarkable theoretical consequences and a plausible explanation for the phenomenon called Dark Energy in the cosmos.

physics.gen-ph↗
arXiv2016

Toward a Quantum Theory of Tachyon Fields

We construct momentum space expansions for the wave functions that solve the Klein-Gordon and Dirac equations for tachyons, recognizing that the mass shell for such fields is very different from what we are used to for ordinary (slower than light) particles. We find that we can postulate commutation or anticommutation rules for the operators that lead to physically sensible results: causality, for tachyon fields, means that there is no connection between spacetime points separated by a timelike interval. Calculating the conserved charge and 4-momentum for these fields allows us to interpret the number operators for particles and antiparticles in a consistent manner; and we see that helicity plays a critical role for the spinor field. Some questions about Lorentz invariance are addressed and some remain unresolved; and we show how to handle the group representation for tachyon spinors.

hep-th↗
arXiv2014

Nonorthogonal bases in variational calculations and the loss of numerical accuracy

The most common method for calculating accurate numerical solutions for complicated linear differential equations - for example, finding eigenvalues and eigenfunctions of the Schrodinger equation for many-electron atoms - is the variational method with some convenient basis of functions. This leads to a finite matrix representation of the operators involved; and standard numerical operations - such as Gaussian elimination - may be employed. When the basis functions are not orthogonal, one expects substantial loss of numerical accuracy in those matrix manipulations; and so multiple-precision arithmetic is often required for useful results. In this paper, for the first time, we offer a way to estimate the rate at which numerical cancellations will grow in severity as one increases the basis size. For the familiar case of using simple power series, x^n, n<N as the basis instead of orthogonal polynomials, we predict a loss of about 2N bits or 4N bits of numerical accuracy.

physics.comp-ph↗
arXiv2012

More Special Functions Trapped

We extend the technique of using the Trapezoidal Rule for efficient evaluation of the Special Functions of Mathematical Physics given by integral representations. This technique was recently used for Bessel functions, and here we treat Incomplete Gamma functions and the general Confluent Hypergeometric Function.

math.NA↗
arXiv2012

Numerical Calculation of Bessel Functions

A new computational procedure is offered to provide simple, accurate and flexible methods for using modern computers to give numerical evaluations of the various Bessel functions. The Trapezoidal Rule, applied to suitable integral representations, may become the method of choice for evaluation of the many Special Functions of mathematical physics.

math.NA↗
arXiv2012

A Conjecture about Conserved Symmetric Tensors

We consider T(x), a tensor of arbitrary rank that is symmetric in all of its indices and conserved in the sense that the divergence on any one index vanishes. Our conjecture is that all integral moments of this tensor will vanish if the number of coordinates in that integral moment is less than the rank of the tensor. This result is proved explicitly for a number of particular cases, assuming adequate dimensionality of the Euclidean space of coordinates (x); but a general proof is lacking. Along the way, we find some neat results for certain large matrices generated by permutations.

math-ph↗
arXiv2011

Tachyons in General Relativity

We consider the motion of tachyons (faster-than-light particles) in the framework of General Relativity. An important feature is the large contribution of low energy tachyons to the energy-momentum tensor. We also calculate the gravitational field produced by tachyons in particular geometric arrangements; and it appears that there could be self-cohering bundles of such matter. This leads us to suggest that such theoretical ideas might be relevant to major problems (dark matter and dark energy) in current cosmological models.

math-ph↗
arXiv2010

Numerical Method in Classical Dynamics

A set of algorithms is presented for efficient numerical calculation of the time evolution of classical dynamical systems. Starting with a first approximation for solving the differential equations that has a "reversible" character, we show how to bootstrap easily to higher order accuracy.The method, first shown for a single particle in one dimension, is then neatly extended to many dimensions and many particles.

physics.class-ph↗
arXiv2008

Calculus with a Quaternionic Variable

Most of theoretical physics is based on the mathematics of functions of a real or a complex variable; yet we frequently are drawn to try extending our reach to include quaternions. The non-commutativity of the quaternion algebra poses obstacles for the usual manipulations of calculus; but we show in this paper how many of those obstacles can be overcome. The surprising result is that the first order term in the expansion of F(x+delta) is a compact formula involving both F'(x) and [F(x) - F(x*)]/(x-x*). This advance in the differential calculus for quaternionic variables also leads us to some progress in studying integration.

math.FA↗