Constraints
Any candidate for a "Programmer God (1)" simulation universe source code, including this model, must satisfy these conditions;
1. It can generate physical structures (mass, space, time ...) from mathematical forms.
2. The universe in totality is dimensionless (existing as data on a celestial hard disk).
3. It must be able to explain observations of nature (aka physics, chemistry ...).
4. The mathematical logic must be unknown to us (the Programmer is a non-human intelligence).
5. The coding should have an 'elegance' commensurate with the Programmer's level of skill.
Introduction
At the sub Planck level the tau-loop (the engine of the universe) runs a continuous loop generating rotation and expansion until it reaches the boundary conditions (pi and e) defined within the formula \(\Omega = \sqrt{ \left(\pi^e e^{(1-e)}\right)}\). At the boundary the pi and Omega components constructed by the tau-loop convert to the Planck units M=1, T=\(\pi\) and P=\(\Omega\). The tau-loop then resets and the process begins again, the physical universe built in these incremental Planck steps. Particles are tau-loop branches that take longer to reach closure (the boundary condition) and photons are endless loops (without closure).
The electron formula \(\psi = 4\pi^2(2^6 3 \pi^2 a \Omega^5)^3\), although a dimensionless mathematical formula, embeds all the information required to generate the physical electron parameters.
Instead of a wave-particle duality, particles are treated as an oscillation between an electric wave-state (duration particle frequency) and a mass point-state (duration 1 Planck time). We can then replace gravitational and electric forces with wave-wave and point-point orbitals (the gravitation simulation program can also be used to map electron transitions in the H atom). We then find that 'gravity' has a magnitude of the strong force, it is not weak. Electrons do not jump between orbitals but instead follow a semi-continuous spiral path. The stable orbital regions (the n-levels) are dictated along the spiral by pi; at n=1 the phase = 2pi, continuing at n=3 phase = (4/3)pi, at n=4 phase = pi, at n=5 phase = 4/5pi ...
The 3-D universe is the surface of an expanding at the speed of light hypersphere (driven by the tau-loop). Relativity then becomes the mathematics of perspective, translating between 3D and hypersphere coordinate systems.
I used Gemini AI to make podcasts to introduce the sections, it is easier to wade through math if you know what is about. Gemini tends to be a little grandiose and there are mistakes, spin 1/2 becomes spin 12 etc, but these are easy to pick up, otherwise the quality is not bad.
Three oscillation levels
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: Sub Planck scale, the tau function
\(\psi_{\tau}\)
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 the algorithm's internal logic.
Read ArticleLevel 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 ArticleResearch 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.
I used wiki sites originally as their link structure could be used to reduce the text length (most physical terms have well maintained pages of their own). The pages are still up although not regularily maintained.
(1) wiki God_(programmer), theprogrammergod.com/
(2) wiki Planck_units_(geometrical)
(3) wiki Electron_(mathematical)
(4) wiki Gravity_via_Atomic_orbitals