# Bulletin of the American Physical Society

# APS March Meeting 2024

## Monday–Friday, March 4–8, 2024; Minneapolis & Virtual

### Session FF00: Virtual Poster Session I (4pm-5:30pm CST)

4:00 PM,
Tuesday, March 5, 2024

Chair: Yuhua Duan, Natl Energy Technology Lab; Erbin Qiu, UCSD; Runze Li, ShanghaiTech University

### Abstract: FF00.00065 : Revisiting Einstein's Formula to Shed Light on the Mass and Charge Distributions of Slow Electrons

#### Presenter:

Kenneth E Caviness

(School of Engineering and Physics, Southern Adventist University, Tennessee)

#### Authors:

Vola Masoandro Andrianarijaona

(School of Engineering and Physics, Southern Adventist University, Tennessee)

Colton H Davis

(School of Engineering and Physics, Southern Adventist University, Tennessee)

Kenneth E Caviness

(School of Engineering and Physics, Southern Adventist University, Tennessee)

^{2}/c

^{2}= p

^{2}+ m

_{0}

^{2}c

^{2}, Dirac concluded that electrons possess oscillatory motions so that the instantaneous speed would be always equal to c. Based on his results, several models of the electron trajectory were proposed. One of the goals was to shed light on the mass and electric charge distributions of the electron. However, most of the findings failed to fit together with fundamental quantities such as the magnetic moment. As Einstein’s energy equation mirrors the Pythagorean Theorem, a simple point of view suggests that (pc) and (m

_{o}c

^{2}) could be thought of as the two orthogonal energy-axes of a plane. According to de Broglie's hypothesis, the pc-axis is related to the wave properties, whereas the other axis, containing the mass, is connected to the particle properties such as moment of inertia. By embracing the wave-particle duality, the aforementioned equation is very helpful for considering possible models of the electron in a quantum setting. We suggest that the two axes are quantized because, on one side, wave properties may lead to quantization and, on the other side, the moment of inertia is a quantity connected to the spin. Intuitively, Pythagorean triples, which are three positive integers satisfying the Pythagorean theorem, constitute sets of solutions, also effectively quantized. We determine the possible charge and mass distributions and study the agreement with the oscillatory motion and Dirac's prediction of the magnetic moment.

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