The Mathematical Electron

Simulation Universe Hypothesis modelling at the Planck scale

In this site we look at a simulation universe that is programmed at the Planck scale,
3 fundamental Planck units are assigned geometrical objects M=1, T=\(\pi\) and P=\(\Omega\) (table below).
Embedded within these objects are attributes; mass, time, momentum ... we can then combine these objects
to build a geometrical electron \(\psi_e\). This permits a Minimum Description Length coding approach
(low Kolmogorov complexity) that requires only 3 constants; \(\pi\), fine structure constant \(\alpha\) and Euler's e.

Malcolm J. Macleod

email: malcolm@simulationuniverse.org

Programming Planck units from a virtual electron: a simulation hypothesis.
Eur. Phys. J. Plus 133, 278 (2018).

Constraints

Any candidate for a "Programmer God" simulation universe source code 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

As geometrical objects, the Planck units can be combined to form more complex objects, the object apple has mass because embedded within it are the objects for mass M. This however requires a unit number relationship \(\theta\) between units that governs this 'assembly'. Here is a Gemini AI podcast discussing the model.

The table shows how, from \(\pi\), Euler's number e and \(\alpha\) we can derive geometrical formulas for the physical constants; \(G\), \(h\), \(c\), \(q_e\), \((y_e/g_e)\), \(m_e\), and \(k_B\) via \(\theta\) and the Planck units (see article 6. for a statistical analysis). The electron formula \(\psi_e\) is a construct of magnetic monopoles and time, nevertheless it is dimensionless. Scalars v and r are used to convert from geometrical objects to the SI units.


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.

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Level 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.

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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?

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Research Path (Article series transcribed to HTML)

2. Relativity and the Hypersphere

Explores geometric interpretations of relativistic phenomena using hyperspherical models.

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Gemini AI deep-dive podcasts

3. Gravitational Orbitals

Examines whether gravitational systems exhibit orbital structures analogous to atomic systems.

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4. Atomic Orbitals

Develops the Mathematical Electron framework and its connection to atomic structure.

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5. The W-Axis

Introduces an additional geometric degree of freedom used throughout the model.

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6. Physical Constant Anomalies

Investigates numerical relationships among physical constants and possible geometric origins.

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7. Monopole Quarks

Develops the monopole framework and explores quark-like structures emerging from geometric constraints.

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8. Holographic Universe

Examines whether holographic descriptions emerge naturally from the Mathematical Electron framework.

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Source 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.

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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.