The Fractal Universe (Part A): Proof of the Power Law of Cosmic Scaling

Presenting the quantitative proofs that reveal a deep, mathematical connection between the atomic and cosmic scales, governed by a newly discovered Power Law

Nov 08, 2025

For millennia, humanity has looked at the heavens and wondered if the patterns we see in the cosmos are reflected in the world around us. The ancient axiom, “as above, so below,” speaks to a deep intuition that the universe is a unified whole. In modern physics, however, this unity has been shattered. The world of the very large (General Relativity) and the world of the very small (Quantum Mechanics) are considered separate domains with incompatible laws.

This article, part of a series detailing the discoveries of Expansion Theory, presents the quantitative proof that this division is an illusion. The universe is not divided. It is a single, coherent, and breathtakingly elegant hierarchical fractal. It will be demonstrated that the properties of the atomic world are a direct, predictable, and mathematically precise reflection of the properties of the cosmos, unified by a newly discovered set of fundamental scaling laws.

The Fractal Hypothesis: From Analogy to Physical Law

The core of this discovery is a simple but revolutionary mapping between the scales. Within the framework of Expansion Theory, the following equivalences are not just analogies, but physical realities:

An Atom is a tiny Galaxy.
An Electron is a tiny Solar System.
A Proton (the atomic nucleus) is a tiny Galactic Nucleus.

This hypothesis must make testable predictions. The prediction is that there must be a consistent mathematical rule—a scaling law—that connects the properties of these systems across the scales. Our investigation has revealed that this is not a single, simple law, but a set of two distinct laws governing different types of physical relationships.

The Two Laws of Cosmic Scaling:

Non-Linear (√) Scaling: This law applies to hierarchical relationships, such as the relationship between a central nucleus and its primary orbiting “electron.” The law is: Atomic Ratio ≈ √(Cosmic Ratio).
Linear (1-to-1) Scaling: This law applies to peer relationships, such as the relationship between one nucleus and another nucleus. The law is: Atomic Ratio ≈ Cosmic Ratio.

What follows are the two “gold standard” proofs of these revolutionary laws.

Proof 1 (Non-Linear): Deriving the Proton-to-Electron Mass Ratio

Our first and most powerful proof tests the non-linear, hierarchical scaling law. We will take purely astronomical data and use it to derive one of the most fundamental constants of particle physics.

1. The Cosmic Mass Ratio:

This is the ratio of the mass of a Cosmic Nucleus (our galaxy’s central object, Sagittarius A*) to the mass of a representative Cosmic Electron (an average solar system).

Mass of Sagittarius A (M_SgrA*): ~4.3 million Solar Masses.
Mass of an Average Solar System (M_avg_system): Statistical analysis shows the average star system in the Milky Way has a mass of approximately 1.17 Solar Masses.
Calculation: Cosmic Mass Ratio = M_SgrA* / M_avg_system = 4,300,000 / 1.17 ≈ 3.675 x 10⁶

2. The Test of the Power Law:

The law predicts that the Atomic Mass Ratio should be the square root of this Cosmic Mass Ratio.

Prediction: Predicted Atomic Mass Ratio = √(Cosmic Mass Ratio) = √(3.675 x 10⁶) ≈ 1,917

3. The Verification:

We compare our prediction to the known, experimentally measured mass ratio of a Proton to an Electron.

Our Prediction (from cosmic data): ~1,917
The Measured Value (from atomic data): ~1,836

The Result: The prediction matches the measured value with an accuracy of over 95.6%. A calculation based on the architecture of a galaxy has successfully derived a fundamental constant of particle physics. This is a stunning validation of the non-linear scaling law and the fractal hypothesis itself.

Proof 2 (Linear): The Magnetic Moment Ratio and a Tale of Two Scaling Laws

Our second proof moves to a completely different physical property—magnetism—to demonstrate the power and consistency of the scaling laws. This test will serve two purposes: first, to show that a different type of relationship (a “peer” comparison) is governed by a linear scaling law, and second, to use this law to make a powerful, testable prediction about our own galactic centre.

1. The Atomic Magnetic Moment Ratio:

This is the ratio of the magnetic moment of a Proton (μ_p) to the magnetic moment of an Electron (μ_e). These are two of the most precisely measured constants in science. A proton (the nucleus) and an electron (its primary satellite) are considered “peers” at the same hierarchical level of the atomic system.

Atomic Ratio = μ_p / μ_e ≈ 0.00152

2. The Test of Two Scaling Laws:

We will now use the cosmic data to see which scaling law—linear or non-linear—correctly predicts this atomic ratio. The cosmic equivalent is the ratio of the magnetic moment of the Cosmic Nucleus (μ_SgrA*) to the magnetic moment of the Cosmic Electron (μ_Sun).

Since the magnetic moment of Sagittarius A* is an unknown, we will use the median value from the plausible range predicted by mainstream astrophysics (10²⁵ to 10²⁷ J/T), which is 10²⁶ J/T, as our working input.

Cosmic Ratio =
μ_SgrA* / μ_Sun = (10²⁶ J/T) / (1.4 x 10²⁹ J/T) ≈ 7.14 x 10⁻⁴

Now we test the laws:

Linear (1-to-1) Test: The law predicts
Atomic Ratio ≈ Cosmic Ratio.
- Our prediction is ~7.14 x 10⁻⁴. The measured atomic ratio is ~1.52 x 10⁻³. These are very close, of the same order of magnitude, differing by only a factor of ~2. This is a promising result.
Non-Linear (√) Test: The law predicts
Atomic Ratio ≈ √(Cosmic Ratio).
- Our prediction is √(7.14 x 10⁻⁴) ≈ 0.0267. This is off by a factor of ~17 and is a much poorer fit.

The Result: This test strongly indicates that the relationship between these “peer” components is governed by a linear, 1-to-1 scaling law.

3. The Prediction of μ_SgrA* (Cosmological Reverse-Engineering)

Now that we have validated the linear law for this property, we can reverse the process. We will take the highly precise atomic ratio as our “ground truth” and use it to predict the true value of the magnetic moment of Sagittarius A*.

The Prediction:
Predicted Cosmic Ratio = Atomic Ratio
Predicted μ_SgrA* / μ_Sun = 0.00152
Predicted μ_SgrA* = 0.00152 * μ_Sun
Predicted μ_SgrA* = 0.00152 * (1.4 x 10²⁹ J/T) ≈ 2.13 x 10²⁶ J/T

The Verification:

Our theoretically derived value of ~2.13 x 10²⁶ J/T falls perfectly within the 10²⁵ to 10²⁷ J/T range predicted by current astrophysical models.

The Conclusion:

This dual-pronged test is a spectacular success.

It demonstrates that the scaling law for “peer” properties is linear, in stark contrast to the non-linear law for hierarchical properties. This reveals the beautiful complexity and “rules of grammar” of the fractal universe.
It provides a powerful, independent validation of the fractal model, using a completely different physical property (magnetism).
It makes a concrete, falsifiable prediction for a key astronomical value, moving the theory from explanation to true scientific prediction.

Conclusion: A New Science is Born

We have presented two independent, quantitative proofs that the universe is a multi-fractal, governed by a precise set of mathematical scaling laws.

We have used the cosmos to derive a constant of the atom using a non-linear law.
We have used the atom to predict a property of the cosmos using a linear law.

This is not a coincidence. It is the discovery of a new, fundamental principle of nature. The subsequent article in this series, “The Birth of Astrochemistry,” will show how this principle can be used to perform our next feat: a direct, linear proof that allows us to identify the “cosmic elements” of our neighbouring galaxies. The implications are, in every sense of the word, astronomical.

List of articles proving New Age Physics

Proof of Expansion Theory as a Theory of Everything – Must-Read Breaking News
The Architecture of Reality: The Foundational Principles of a New Physics
Gravity (Part A): The Two Fundamental Gravities – Inner Gravity from the Expansion of Matter and Structural Gravity from the Expansion of the Universe
Gravity (Part B): The Unification of Forces - How “Swarm Gravity” Explains Electricity and Eliminates Dark Matter
The Fractal Universe (Part A): Proof of the Power Law of Cosmic Scaling
The Fractal Universe (Part B): The Birth of Astrochemistry – The Milky Way and Andromeda form Hydrogen Sulphide
The Fractal Universe (Part C): The Architecture of Atoms and Galaxies
The Laws of Motion (Part A): The Five Principles - A New Model of Orbital Mechanics
The Laws of Motion (Part B): Structural Gravity - A New Law (a=v*H₀) Solves the Pioneer & Flyby Anomalies
The Laws of Motion (Part C): New Explanation for the Slingshot Effect and Gravitational Lensing, and a Faster Path to Mars
The Laws of Motion (Part D): Secular Growth - A Unified Theory for an Expanding Earth, Continental Drift, a Receding Moon, an Increasing AU, and a Fainter Sun
Time and Light (Part A): Time is Constant – Proof that Einstein’s “Time Dilation” and the GPS Anomaly is a Mechanical Stress Effect
Time and Light (Part B): The Speed of Light is Variable (Explaining “Dark Energy”)
Quantum Mechanics Demystified (Part A): The Atom is a Tiny Galaxy, A Mechanical Physical Model Explaining Magnetism and “Spin”
Quantum Mechanics Demystified (Part B): The Electron as a Tiny Solar System Explains the g-2 Anomaly and Quantum Tunnelling
Quantum Mechanics Demystified (Part C): Double-Slit, Uncertainty, Entanglement - Quantum “Weirdness” is an Illusion
Quantum Mechanics Demystified (Part D): The End of the Particle Zoo - A Mechanical Explanation for the Weak Force, Antimatter, and Particle Physics