scholarly journals An Investigation Into The Mathematical and Physical Origins of The Fine-Structure Constant

2021 ◽  
Author(s):  
Lamont Williams
Keyword(s):  
Fine Structure ◽  
Magnetic Moment ◽  
Anomalous Magnetic Moment ◽  
Quantum Physics ◽  
Ad Hoc ◽  
Structure Constant ◽  
Fine Structure Constant ◽  
Quantum Mechanical ◽  
The Standard Model ◽  
Corrective Term

Abstract The fine-structure constant, α, unites fundamental aspects of electromagnetism, quantum physics, and relativity. As such, it is one of the most important constants in nature. However, why it has the value of approximately 1/137 has been a mystery since it was first identified more than 100 years ago. To date, it is an ad hoc feature of the Standard Model, as it does not appear to be derivable within that body of work — being determined solely by experimentation. This report presents a mathematical formula for α that results in an exact match with the currently accepted value of the constant. The formula requires that a simple corrective term be applied to the value of one of the factors in the suggested equation. Notably, this corrective term, at approximately 0.023, is similar in value to the electron anomalous magnetic moment value, at approximately 0.0023, which is the corrective term that needs to be applied to the g-factor in the equation for the electron spin magnetic moment. In addition, it is shown that the corrective term for the proposed equation for α can be derived from the anomalous magnetic moment values of the electron, muon, and tau particle — values that have been well established through theory and/or experimentation. This supports the notion that the corrective term for the α formula is also a real and natural quantity. The quantum mechanical origins of the lepton anomalous magnetic moment values suggest that there might be a quantum mechanical origin to the corrective term for α as well. This possibility, as well as a broader physical interpretation of the value of α, is explored.

scholarly journals Enhanced Derivation of the Electron Magnetic Moment Anomaly from the Electron Charge using Geometric Principles

2018 ◽  
Vol 10 (6) ◽  
pp. 24 ◽  
Author(s):  
Andrew Worsley ◽  
J.F. Peters
Keyword(s):  
Fine Structure ◽  
Standard Model ◽  
Magnetic Moment ◽  
Geometric Model ◽  
Structure Constant ◽  
Fine Structure Constant ◽  
Electron Charge ◽  
Mathematical Equation ◽  
The Standard Model ◽  
Electron Magnetic Moment

The electron magnetic moment anomaly is conventionally derived from the fine structure constant using a complex formula requiring over 13,000 evaluations. However, the charge of the electron is an important parameter of the Standard Model and could provide an enhanced basis for the derivation of the electron magnetic moment anomaly. This paper uses a geometric model to reformulate the equation for the electron’s charge, this is then used to determine a more accurate value for the electron magnetic moment anomaly from first geometric principles. This enhanced derivation uses a single evaluation, using a concise mathematical equation based on the natural log e^pi. This geometric model will lead to further work to theoretically improve the understanding of the electron.

scholarly journals Theory of the Anomalous Magnetic Moment of the Electron

Atoms ◽  
2019 ◽  
Vol 7 (1) ◽  
pp. 28 ◽  
Author(s):  
Tatsumi Aoyama ◽  
Toichiro Kinoshita ◽  
Makiko Nio
Keyword(s):  
Fine Structure ◽  
Magnetic Moment ◽  
Anomalous Magnetic Moment ◽  
Quantum Electrodynamics ◽  
Penning Trap ◽  
Weak Interactions ◽  
Perturbation Expansion ◽  
Structure Constant ◽  
Fine Structure Constant ◽  
Best Value

The anomalous magnetic moment of the electron a e measured in a Penning trap occupies a unique position among high precision measurements of physical constants in the sense that it can be compared directly with the theoretical calculation based on the renormalized quantum electrodynamics (QED) to high orders of perturbation expansion in the fine structure constant α , with an effective parameter α / π . Both numerical and analytic evaluations of a e up to ( α / π ) 4 are firmly established. The coefficient of ( α / π ) 5 has been obtained recently by an extensive numerical integration. The contributions of hadronic and weak interactions have also been estimated. The sum of all these terms leads to a e ( theory ) = 1 159 652 181.606 ( 11 ) ( 12 ) ( 229 ) × 10 − 12 , where the first two uncertainties are from the tenth-order QED term and the hadronic term, respectively. The third and largest uncertainty comes from the current best value of the fine-structure constant derived from the cesium recoil measurement: α − 1 ( Cs ) = 137.035 999 046 ( 27 ) . The discrepancy between a e ( theory ) and a e ( ( experiment ) ) is 2.4 σ . Assuming that the standard model is valid so that a e (theory) = a e (experiment) holds, we obtain α − 1 ( a e ) = 137.035 999 1496 ( 13 ) ( 14 ) ( 330 ) , which is nearly as accurate as α − 1 ( Cs ) . The uncertainties are from the tenth-order QED term, hadronic term, and the best measurement of a e , in this order.

scholarly journals The Anomalous Magnetic Moment of the Electron and Proton Cores According to the Planck Vacuum Theory

2019 ◽  
Vol 4 (6) ◽  
pp. 117-119
Author(s):  
William C. Daywitt
Keyword(s):  
Fine Structure ◽  
Dirac Equation ◽  
Quantum Electrodynamic ◽  
Magnetic Moment ◽  
Anomalous Magnetic Moment ◽  
Structure Constant ◽  
Fine Structure Constant ◽  
The Relationship ◽  
Vacuum Theory ◽  
The Invisible

Despite the resounding success of the quantum electrodynamic (QED) calculations, there remains some confusion concerning the Dirac equation’s part in the calculation of the anomalous magnetic moment of the electron and proton. The confusion resides in the nature of the Dirac equation, the fine structure constant, and the relationship between the two. This paper argues that the Dirac equation describes the coupling of the electron or proton cores to the invisible Planck vacuum (PV) state (involving e2 ); and that the fine structure constant ( = e2/e2 ) connects that equation to the electron or proton particles measured in the laboratory (involving e2).

scholarly journals Fine Structure Constant derived from Principle Theory.

2021 ◽  
Author(s):  
Manfred Geilhaupt
Keyword(s):  
General Relativity ◽  
Fine Structure ◽  
General Theory ◽  
Rest Mass ◽  
Structure Constant ◽  
Fine Structure Constant ◽  
Theory Of Relativity ◽  
General Theory Of Relativity ◽  
The Standard Model ◽  
Principle Theory

Abstract Derivation of mass (m), charge (e) and fine structure constant (FSC) from theory are unsolved problems in physics up to now. Neither the Standard Model (SM) nor the General theory of Relativity (GR) has provided a complete explanation for mass, charge and FSC. The question “of what is rest mass” is therefore still essentially unanswered. We will show that the combination of two Principle Theories, General Relativity and Thermodynamics (TD), is able to derive the restmass of an electron (m) which surprisingly depends on the (Sommerfeld) FSC (same for the charge (e)).

Introductory remarks

1982 ◽  
Vol 304 (1482) ◽  
pp. 3-4
Keyword(s):  
World War Ii ◽  
Magnetic Moment ◽  
Anomalous Magnetic Moment ◽  
Quantum Electrodynamics ◽  
Power Series Expansion ◽  
Structure Constant ◽  
Fine Structure Constant ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Abelian Gauge

The title of this meeting, which refers to gauge theories, could equivalently have specified renormalizable quantum field theories. The first quantum field theory arose from the quantization by Dirac, Heisenberg and Pauli of Maxwell’s classical theory of electromagnetism. This immediately revealed the basic problem that although the smallness of the fine-structure constant appeared to give an excellent basis for a power-series expansion, corrections to lowest order calculations gave meaningless infinite results. Quantum electrodynamics (QED ) is, of course, an Abelian gauge theory, and the first major triumph o f fundamental physics after World War II was the removal of the infinities from the theory by the technique of renormalization developed by Schwinger, Feynman and Dyson, stimulated by the measurement of the Lamb shift and the anomalous magnetic moment of the electron. In the intervening years, especially through the beautiful experiments at Cern on the anomalous magnetic moment of the muon, the agreement between this theory and experiment has been pushed to the extreme technical limits of both measurement and calculation.

scholarly journals Highly Accurate Derivation of the Electron Magnetic Moment Anomaly From Spherical Geometry Using a Single Evaluation

2022 ◽  
Vol 13 (3) ◽  
pp. 30
Author(s):  
Andrew Worsley ◽  
James F. Peters
Keyword(s):  
Fine Structure ◽  
Magnetic Moment ◽  
Geometric Model ◽  
Structure Constant ◽  
Spherical Geometry ◽  
Zero Order ◽  
Fine Structure Constant ◽  
Spherical Bessel Function ◽  
A Value ◽  
Electron Magnetic Moment

The electron magnetic moment anomaly (ae), is normally derived from the fine structure constant using an intricate method requiring over 13,500 evaluations, which is accurate to 11dp. This paper advances the derivation using the fine structure constant and a spherical geometric model for the charge of the electron to reformulate the equation for ae. This highly accurate derivation is also based on the natural log eπ, and the zero-order spherical Bessel function. This determines a value for the electron magnetic moment anomaly accurate to 13 decimal places, which gives a result which is 2 orders of magnitude greater in accuracy than the conventional derivation. Thus, this derivation supersedes the accuracy of the conventional derivation using only a single evaluation.

Sign in / Sign up

Export Citation Format

Share Document