The site is a compilation of articles on a Simulation Hypothesis model based on a dimensionless formula
for the electron. This formula embeds the information required to build a 'physical electron' by replacing
the Planck units with the geometrical objects M=1 and T=pi. The simulation requires only 2 inputs;
the fine structure constant alpha, and a cosmological constant \(m_P^2 \times t_p\).
Malcolm J. Macleod
email: malcolm@theprogrammergod.com
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 the fine structure constant (\(a = 1/\alpha \)).
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 Programming (see Article 6 for a statistical analysis, video below by Gemini AI).
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 Article AI analysisDevelops 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 ArticleGravitational 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 ...\(\psi_0\) = 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 \(\Lambda\).
Read Article\(\psi_2 = 1.86 \times 10^{177}\)
The super-structure in which an oscillating universe may be embedded (a holding container).
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.