Document Type
Presentation - Poster - Presentation
Revisiting Einstein's Formula to Shed Light on the Mass and Charge Distributions of Slow Electrons
Department
Physics & Engineering
Date of Activity
Winter 3-5-2024
Abstract
Considering Einstein’s equation as a quantum mechanics wave equation, W2/c2 = p2 + m02c2, 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 (moc2) 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.
Recommended Citation
Andrianarijaona, Vola; Davis, Colton H.; and Caviness, Kenneth E., "Revisiting Einstein's Formula to Shed Light on the Mass and Charge Distributions of Slow Electrons" (2024). Achieve. 2259.
https://knowledge.e.southern.edu/achieve/2259