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.

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.

The Present Key Importance of the Fine Structure Constant,α, to a Better Knowledge of All the Fundamental Physical Constants

1966 ◽  
Vol 21 (1-2) ◽  
pp. 70-79 ◽  
Author(s):  
Jesse W. M. DuMond
Keyword(s):  
Fine Structure ◽  
Correction Term ◽  
Fundamental Constant ◽  
Structure Constant ◽  
Internal Field ◽  
Fine Structure Constant ◽  
Sources Of Information ◽  
Hydrogen Maser ◽  
A Value ◽  
Structure Splitting

The dilemma is described which exists at the present time between the two present best sources of information as to the numerical value of the Sommerfeld fine structure constant, α. These two sources are the fine structure splitting in deuterium, determined in 1953 by Triebwasser, Dayhoff and Lamb, and the hyperfine structure splitting in hydrogen, measured more recently using the Ramsey hydrogen maser. The theoretical connection between the fine structure measurements and α is subject to little question but the experimental difficulties to obtain a precision of a few ppm are considerable. The relative precision obtained with the hydrogen maser on the other hand, is phenomenal (of order 10-11) but the theoretical connection between the hyperfine splitting and α is subject to a controversial correction for the internal field structure of the proton. Assuming this correction term to be correct at its present value, the hf splitting in Η implies a value of α 26 ppm higher than the fs splitting in D. Present existing sources of evidence, some favourable to the lower and some to the higher value of α, are presented and discussed and the key importance of a better knowledge of this fundamental constant is stressed.

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