Global Journal of Science Frontier Research, A: Physics and Space Science, Volume 23 Issue 1

The Toroidal Fine-Structure of the Electron Gene Gryziecki Abstract - Developments in physics in the past two decades have expanded the well-known mass-energy equation into a rigorous set of relations that provide the electric and magnetic fine-structure and the volumetric structure of the electron as a closed-flux torus, all in agreement with 2018 Codata values. In light of these developments, the present communication questions the physical meaning of the Bohr radius and its implications – the Bohr-Heisenberg theory of the hydrogen atom and its description of an electron as a point-mass particle that only exists when its probability wave collapses. Keywords: energy, electron, mass-energy, bohr radius, torus, wavelength, wavefunction. I. I ntroduction The Bohr theory of the hydrogen atom, theorized by Niels Bohr (1885-1962), includes a negatively charged point-mass electron that travels in a circular orbit about a positively charged nucleus. In the atom’s lowest energy (or ground) state, the distance between the two particles is called the Bohr radius and is equal to 0.529 x 10 -10 m. Since then, further investigation indicated that sometimes the electron behaves like a wave and sometimes like a particle [1]. Thus, the Bohr-Heisenberg model of the atom arose where the electron exists only as a cloud or fuzzy cavity about the nucleus and measurements are based upon the probability of a point particle being found at a certain location in the cloud. Recently, there has been some rather meticulous scientific research work by Dr. Paulo Correa and his team that has put forth a novel description of the electron as a torus ring, and a heuristic understanding of the Bohr radius and the Bohr-Heisenberg model of the atom. This paper is intended to provide an introduction to, and overview of, an important aspect of this work. II. M ethods and R esults Building upon the work of Wilhelm Reich (1897-1957) and his research on gravitational pendulums, it became possible to decipher his formula for determining the functional equivalence between mass and length [2]. Reich’s work supported the idea that “atomic weights are gravitational functions that can be functionally replaced by pendulum lengths.” He selected pendulum lengths, in centimeters (cm), such that they were numerically equal to the gram-molar masses, and thus to the atomic weights, of various elements, while keeping the actual weight of the pendulum constant at 1 gram. For example, the length of gravitational pendulums for Hydrogen, Helium and Oxygen would be 1, 4 and 16 cm, respectively [3]. His process transforms “inertial mass into the rotary or pendular wavelength of the linear free fall motion” understood as weight [4]. In the case of the electron (the entirety of this paper applies to the electron and all reference values have been taken from a single source, CODATA 2018 [5]), this gravitational wavelength is resonant with the “wavelength of the energy circularized as mass-energy (see below) and on which the inertia of a state of rest is anchored as a reaction of that inert mass or of that mass-energy,” referred to as the mass-equivalent or amplitude [6] wavelength [7]. In fact, for the electron, these two wavelengths, gravitational and mass-equivalent, are numerically equal, and the wavelength of concern in this paper is the electron mass-equivalent wavelength. The equation for the mass to length transformation for the electron can be shown as: Length = λ e = m e N A 10 -2 in meters [2] (1) where λ e is the mass-equivalent wavelength of the inert mass of the electron, m e is the electron mass (in grams), and N A is Avogadro’s number: λ e = (9.109 x 10 -31 kg) (10 3 gm / 1kg) (6.022 x 10 23 / mole) (10 -2 ) (m) = 5.486 x 10 -6 m (2) Using this tremendous insight and the famous equation for calculating rest energy or mass-energy, where energy E equals the product of mass m times the speed of light squared c 2 , E = mc 2 , one can determine a functional equivalent to the mass-energy of an electron using two physical quantities rather than three, incorporating length and time instead of mass, length, and time. Accordingly, E = m e c 2 =∫= λ e c 2 (3) 1 Year 2023 1 © 2023 Global Journals Global Journal of Science Frontier Research Volume XXIII Issue ersion I VI ( A ) Author: e-mail: gwgryziecki@yahoo.com