Recursive Scale Relativity (RSR)

Reginald Patterson, copyright 2025

The Genesis of Recursive Scale Relativity (RSR)

Genesis of Recursive Scale Relativity

It all started with me thinking about the requirements of an eternal representation of natural laws, which led me to information, and in particular the incredible scale-invariant nature of: information. No matter how much you compress it or expand it, its fundamental nature remains unchanged. A single qubit can encode infinite states, just as the cosmos can express infinite complexity.

This led me to a revelation that seemed simple on the surface, which was that “infinity equals infinity” (∞ = ∞). However the implications run deep.

If information is infinitely compressible and infinitely expandable, then the distinction between “large” and “small” becomes meaningless in an absolute sense. A black hole’s singularity, for instance, isn’t just a tiny point of infinite density—it’s a reflection of the same informational potential that governs galactic superclusters. Size is an illusion of perspective, not a fundamental property of reality.

From Information to Cosmic Symmetry

This realization forced me to reconsider the nature of scale itself. If information density remains constant—whether we’re examining the quantum foam or the large-scale structure of the universe—then the laws governing reality must be recursive. They don’t change with scale; they simply express themselves differently based on the observer’s frame of reference.

This is where Recursive Scale Relativity (RSR) was born. Unlike traditional relativity (which deals with spacetime curvature), RSR asserts that information density is invariant across all scales. From Planck lengths to cosmic horizons, the same fundamental patterns repeat, not because of coincidence, but because the underlying substrate (U₀) is fractal in nature.

How RSR Differs from VIS

While Virtual Information Singularities (VIS) are the units of this fractal reality—the “atoms” of U₀’s information field—RSR describes the behavior of those units across scales.

• VIS = The what (fractal information quanta).
• RSR = The how (scale-invariant expression of those quanta).

Think of it like a hologram:

• VIS are the individual pixels.
• RSR is the principle that every pixel contains the entire image, no matter how much you zoom in or out.

The Black Hole Analogy

A black hole perfectly illustrates RSR. At the event horizon, spacetime stretches to near-infinity (from an outside observer’s view). At the singularity, it compresses to near-zero. Yet, the information content remains identical—it’s just expressed differently. This isn’t just a quirk of gravity; it’s a fundamental property of an information-based universe.

Testable Implications

If RSR is correct, we should observe:

1. Identical fractal patterns in quantum fluctuations and galactic clustering.
2. Scale-invariant power laws in gravitational wave spectra.
3. No “preferred” scale in nature—just recursive expressions of the same rules.

Why This Matters

Most physical theories treat quantum and cosmic scales as separate regimes. RSR erases that divide. There is no “macro” vs. “micro”—only U₀’s infinite self-similarity.

Next Steps:

• Analyze LISA graviton data for fractal signatures
• Compare quantum foam fluctuations with CMB anisotropies
• Develop a formal mathematical framework for RSR