Discrete Model of Electron

Abstract

An electron model is developed based on a 4D sphere with a diameter of the Planck length. This model allows us to explain and calculate the intrinsic properties of the electron, such as its mass, charge, spin, etc., from the fundamental constants. Using this Planck sphere in four dimensions, we reach the conclusion that the electron particle has a size that is fixed by the Planck dimensions. The rotation of the Planck sphere generates the electron wave, the size of which depends on its wavelength. Our hypothesis is that the universe is composed of Planck spheres in four spatial dimensions, with two possible states: a rest state and rotational movement.

The Quantization of Mass

“…Each Planck 4D sphere can rotate both in 3D space and in the fourth dimension (u = ct, Figure 2), resulting in the following possible combinations Garrigues-Baixauli, 2016, 2017a, b & 2019: These spheres constitute a solid and incompressible space that transmits the waves. "Since space transmits waves and forces, it is absurd to assume that it is empty, hereas it must be a solid, incompressible medium.…”

The Origin of the Fundamental Constants

“…The Planck sphere rotates one complete revolution in three-dimensional space (ωe) at the same time that it rotates the fourth dimension (ωu), so that the particle is upside down (ωe = 2 ωu), which we see as a half spin. [49] Figure 3. Two-dimensional representation of the electron The 4D Planck spheres are linked by the Planck force, so rotating one of them will drag it to the adjacent spheres.…”

“…The mass will be due to the rotational energy of the 4D Planck sphere. This allows us to relate the mass and electric charge of the electron by applying the Heisenberg uncertainty principle [49][50][51][52] as a certainty principle.…”

“…Said Planck sphere reduces its speed of rotation until it reaches the minimum value of rotation, which gives rise to the electron. The minimum acceleration corresponds to the rotating central sphere and then: On the other hand, the speed of the electron in a free state is c [49] and the acceleration corresponding to that speed will be:…”