arXiv subjects

G. B. Mainland

Publications and source records attributed to G. B. Mainland.

8 recordsLinked to original sources

arXiv2026

Theoretical calculation of the fine-structure constant and the permittivity of the vacuum

Light traveling through the vacuum interacts with vacuum fluctuations similarly to the way that light traveling through a dielectric interacts with ordinary matter. And just as the permittivity of a dielectric can be calculated, the permittivity $ε_0$ of the vacuum can be calculated, yielding an equation for the fine-structure constant $α$. The most important contributions to the value of $α$ arise from the interaction of photons with charged lepton-antilepton vacuum fluctuations that appear in the vacuum as on-shell, bound states. Considering these contributions only to first order in alpha, the fully screened $α\cong 1/(8^2\sqrt{3π/2}) \cong 1/139$.

physics.gen-ph↗

arXiv2021

Properties of the quantum vacuum calculated from its structure

Physicists have speculated about the properties of the quantum vacuum for at least 85 years; however, only recently have they understood the quantum vacuum sufficiently well to begin making testable predictions. Specifically, using Maxwell's equations to describe the interaction of the electromagnetic field with charged lepton - antilepton vacuum fluctuations, it has been possible to calculate the permittivity of the vacuum, the speed of light in the vacuum, and the fine structure constant. Physicists are now also beginning to successfully address problems in cosmology based on properties of the quantum vacuum. The terms ``vacuum catastrophe'' and ``old cosmological problem'' refer, respectively, to the predictions that the vacuum energy density and the cosmological constant are both approximately 120 orders of magnitude larger than the observed values. Using properties of the quantum vacuum and well-established physics, it is possible to demonstrate that the huge vacuum energy cannot transfer energy to normal matter; accordingly, vacuum energy contributes neither to the observed energy density of the universe nor to the cosmological constant, which plays a central role in the accelerating expansion of the universe.

physics.gen-ph↗

arXiv2020

The contribution of the quantum vacuum to the cosmological constant is zero: proof that vacuum energy does not gravitate

The consensus among many theoretical physicists is that the calculated contribution of the quantum vacuum to the total energy density of the universe is approximately $10^{121}$ times the observed energy density. This is thought to be one of the worst theoretical predictions of all time. However, as shown here, this immense vacuum energy cannot in and of itself exert forces on normal matter. As a result the huge vacuum energy density predicted by quantum field theory does not contribute to the ordinary energy density of the universe, is not a source for gravitational fields, and, as a result, does not contribute to the value of the cosmological constant.

physics.gen-ph↗

arXiv2020

Polarization of vacuum fluctuations: source of the vacuum permittivity and speed of light

There are two types of fluctuations in the quantum vacuum: type 1 vacuum fluctuations are on shell and can interact with matter in specific, limited ways that have observable consequences; type 2 vacuum fluctuations are off shell and cannot interact with matter. A photon will polarize a type 1, bound, charged lepton-antilepton vacuum fluctuation in much the same manner that it would polarize a dielectric, suggesting the method used here for calculating the permittivity $ε_0$ of the vacuum. In a model that retains only leading terms, $ε_0 \cong (6μ_0/π)(8e^2/\hbar)^2= 9.10\times 10^{-12}$ C/(Vm). The calculated value for $ε_0$ is 2.7\% more than the accepted value. The permittivity of the vacuum, in turn, determines the speed $c$ of light in the vacuum. Since the vacuum is at rest with respect to every inertial frame of reference, $c$ is the same in every inertial reference frame.

quant-ph↗

arXiv2019

How vacuum fluctuations determine the properties of the vacuum

Particle-antiparticle pairs are predicted by quantum field theory to appear as vacuum fluctuations. The model of the vacuum used here is postulated to have the following properties: To minimize the violation of conservation energy allowed by the Heisenberg uncertainty principle and to avoid violating conservation of angular momentum, vacuum fluctuations of charged particle-antiparticle pairs appear as bound states in the lowest energy level that has zero angular momentum. These transient atoms are polarized by electric fields somewhat similarly to the way that ordinary matter is polarized. As a consequence, the permittivity $ε_0$ of the vacuum can be calculated. Once the permittivity of the vacuum has been calculated, formulas for the speed of light $c$ in the vacuum and the fine-structure constant $α$ immediately follow. The values for $ε_0$, $c$, and $α$ calculated here agree with the accepted values to within a few percent. Only the leading terms in the formulas have been retained in the calculations. The absence of dispersion in the vacuum is discussed and explained.

quant-ph↗

arXiv2017

Photon time delay resulting from vacuum fluctuations: the vacuum as a dielectric

It is not possible to detect a vacuum fluctuation without a test particle interacting with the vacuum fluctuation in a measurable manner. In the quantum electrodynamics calculation presented here, a photon traveling through the vacuum is used as the test particle to determine properties of the vacuum resulting from vacuum fluctuations. In particular, this article (1) discusses the mathematical procedure for describing a lepton-antilepton bound state that is a vacuum fluctuation, (2) describes the photon interacting with and being incorporated into the bound state to form a quasi-stationary bound state, and (3) calculates the electromagnetic decay rate of the quasi-stationary bound state.

physics.gen-ph↗

arXiv2009

Could Leptons, Quarks or both be Highly Relativistic Bound States of Minimally Interacting Fermion and Scalar?

The possibility that leptons, quarks or both might be highly relativistic bound states of a spin-0 and spin-1/2 constituent bound by minimal electrodynamics is discussed. Typically, strongly bound solutions of the Bethe-Salpeter equation exist only when the coupling constant is on the order of or greater than unity. For the bound-state system discussed here, there exist two classes of boundary conditions that could yield strongly bound solutions with coupling constants on the order of the electromagnetic fine structure constant. In both classes the bound state must have spin one half, thus providing a possible explanation for the absence of higher-spin leptons and quarks.

hep-ph↗

arXiv2003

The Role of Boundary Conditions in Solving Finite-Energy, Two-Body, Bound-State Bethe-Salpeter Equations

The difficulties that typically prevent numerical solutions from being obtained to finite-energy, two-body, bound-state Bethe-Salpeter equations can often be overcome by expanding solutions in terms of basis functions that obey the boundary conditions. The method discussed here for solving the Bethe-Salpeter equation requires only that the equation can be Wick rotated and that the two angular variables associated with rotations in three-dimensional space can be separated, properties that are possessed by many Bethe-Salpeter equations including all two-body, bound-state Bethe-Salpeter equations in the ladder approximation. The efficacy of the method is demonstrated by calculating finite-energy solutions to the partially-separated Bethe-Salpeter equation describing the Wick-Cutkosky model when the constituents do not have equal masses.

math-ph↗