The mathematical electron model comprises a series of articles on different aspects of physics that describe how these aspects may be coded by a simulation universe that operates at the Planck scale. The model is built using \(\pi\) (rotation) and Euler's e (expansion) and the fine structure constant \(\alpha\). For the list of articles, see homepage.
By treating the universe as a continuous internal evaluation function (the \(\tau\)-loop) driven by pi and Euler's identity, we show how the Planck units organically emerge from mathematical forms.
Postulates an expanding 4-axis hypersphere in discrete Planck steps, with relativity as the mathematics of perspective, translating between 2 co-ordinate systems; 3D space and the hypersphere.
Gives an analytical derivation of the fine structure constant using only the CODATA values for the dimensioned physical constants. Proposes a set of natural Planck units (independent of any system of units) and a unit relationship linking the units.
Replaces 'gravity' with a complex of n-body rotating particle-to-particle orbital pairs at the Planck scale. Macro observed orbits emerge over time from the sum of these underlying rotating orbitals.
By replacing wave-particle duality with a wave-state to point-state oscillation, and treating atomic orbitals as a single orbital pair, the gravitational orbital simulation program (#3) can model atomic orbital transitions within the H atom as a semi-continuous spiral and precisely reproduce the Bohr results.
Introduces a geometrical formula for the electron, develops the monopole framework and explores quark-like structures built from the Planck units.
Examines whether holographic descriptions emerge naturally from the Mathematical Electron framework.