Introduction
The Mathematical Electron is a simulation universe model centered on a dimensionless geometrical formula for the electron (\(\psi = 4\pi^2(2^6 3 \pi^2 a \Omega^5)^3\)) that explores whether physical reality can be described from an emergent computational geometry at the Planck scale. The 2 dimensionless constants used are \( \Omega = \sqrt{\pi^e e^{1-e}}\) (from \( \pi \) and Euler's number e) and \( \alpha \).
Beginning with geometrical guard-rails and an incrementally expanding universe, 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) that is a characteristic of this model be considered as evidence of a 'source code'.
Three oscillation levels ... work in progress
Level 2: Planck units and the CMB
\(\psi_U\)
Compares the parameters for a hypothetical Planck unit universe (sans particles) with the Cosmic Microwave Background. The model postulates a Planck unit scaffolding upon which the particle universe resides and supposes that within the CMB parameters can be found evidence of this non-baryonic background.
Read ArticleLevel 0: The tau function
\(\psi_{\tau}\)
By treating the universe as a continuous internal evaluation function (the \(\tau\)-loop) driven by a hardcoded structural equation, we show how the discrete Planck step, the primary geometrical units (Planck mass \(M\) and time \(T\)), and the transcendental constants \(\pi\), \(e\), and the expansion eigenvalue \(\Omega\) organically emerge from the algorithm's internal logic. .
Read Article (pending)Level 3: The container universe
\(\psi_H\)
If the universe \(\psi_U\) oscillates, does it too exist as a particle within some greater realm \(\psi_H\), and eventually will it also collapse into a point-state? And if so, what would the physics inside \(\psi_H\) look like?
Read Article (pending)Research Path (Article series transcribed to HTML)
2. Relativity and the Hypersphere
Explores geometric interpretations of relativistic phenomena using hyperspherical models.
Read ArticleGemini AI deep-dive podcasts
3. Gravitational Orbitals
Examines whether gravitational systems exhibit orbital structures analogous to atomic systems.
Read Article4. Atomic Orbitals
Develops the Mathematical Electron framework and its connection to atomic structure.
Read Article5. The W-Axis
Introduces an additional geometric degree of freedom used throughout the model.
Read Article6. Physical Constant Anomalies
Investigates numerical relationships among physical constants and possible geometric origins.
Read Article AI analysis7. Monopole Quarks
Develops the monopole framework and explores quark-like structures emerging from geometric constraints.
Read Article8. Holographic Universe
Examines whether holographic descriptions emerge naturally from the Mathematical Electron framework.
Read ArticleSource codes
Gravitational and atomic orbits are emergent properties, the result of summed particle-particle rotating orbital pairs (forces are not used). Simulations are therefore required for comparisons with real-world orbits. The source codes used are listed here.
Read ...The Programmer God
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.