A geometric approach to physical constants, atomic structure, gravitation, relativity, and cosmology.
The Mathematical Electron is a simulation universe model centered on a dimensionless geometrical formula for the electron that explores whether physical reality can be described from an emergent computational geometry.
The model uses only 1 physical constant (the fine structure constant alpha) and 2 mathematical constants pi and Euler's number e. Beginning with geometrical guard-rails and 2 primary Planck units; mass M = 1 and time T = pi, the project investigates relationships between Planck-scale structure, relativity, gravitation, atomic orbitals, monopole-like configurations, holographic principles, and cosmological observations.
This then raises the question; could the Minimum Description Length (Kolmogorov complexity) characteristic of this model be considered as evidence of Programming (see Article 6 for statistical analysis).
Investigates possible links between Planck-scale discretization and observed cosmological structure.
Read ArticleExplores geometric interpretations of relativistic phenomena using hyperspherical models.
Read ArticleExamines whether gravitational systems exhibit orbital structures analogous to atomic systems.
Read ArticleDevelops the Mathematical Electron framework and its connection to atomic structure.
Read ArticleIntroduces an additional geometric degree of freedom used throughout the model.
Read ArticleInvestigates numerical relationships among physical constants and possible geometric origins.
Read ArticleDevelops the monopole framework and explores quark-like structures emerging from geometric constraints.
Read ArticleExamines whether holographic descriptions emerge naturally from the Mathematical Electron framework.
Read Article\(\psi_0\) = 1
The innermost oscillation. The continuous \(\tau\)-loop within a single Planck step forces the emergence of Euler's number \(e\), the boundary phase \(\pi\), and the expansion eigenvalue \(\Omega = \sqrt{\pi^e e^{1-e}}\). Action is quantised geometrically.
Read Article\(\Omega = \sqrt{\pi^e e^{1-e}}\)
While alpha is associated with the radiation domain, the other primary constant Omega is associated with dimensioned parameters (momentum, velocity, length).
Read Article\(\psi_1 = 4\pi^2(2^6 3 \pi^2 a \Omega^5)^3\)
The electron emerges as the first joint phase-closure resonance of the base-15 cascade. Its invariant dictates the number of Planck steps between mass point-states, yielding mass, wavelength, and frequency from first principles.
Read Article\(\psi_2 = 1.832 \times 10^{121}\)
The outermost oscillation is the cosmic expansion itself. The universe winding number dictates the CMB temperature, the Hubble constant, and the cosmological constant \(\Lambda \sim 1/\psi_2\).
Read Article (pending)A general mathematical universe has no defined boundaries and can potentially extend to infinity in all directions (there is no smallest possible unit). A simulation universe however is a specific mathematical universe in that it is fundamentally discrete (pixelated). I argue that this model resembles the simulation universe variation in which the OS is programmed at the Planck scale. Alpha does not appear as an 'internal' derived constant and therefore may be a given (encoded within the source code itself). Pi and e can be derived by an expanding universe in series and so are labelled here as mathematical constants.