I wasn’t going to publish the following yet, because it isn’t complete. But I am going to publish it so I can use it for later, so here we are… an information theory (coarse model, incomplete, untested, but interesting). I had avoided black holes, I don’t like speculating on that which I can’t see, but I sorta work on them through my work in compression/entropy so it follows, if the shoe fits, see if black holes fit too..
Like a black hole, the following may or may not disappear when I’m done thinking through this version..
UPDATE - it occurs to me that the full of this article pertains to the principles or eventually also optics of the prism, and not the black hole’s physics itself. So our framework which may build a (false, but similar) physics framework for black holes is useful, we need to not confuse prismatic reference point with actual physics as we translate from contrived or ideal black hole physics to ‘where the rubber meets the road’. The reader will note with good measure that this article is prescribed as blue ‘software development’ category at this time, not pink physics.
Reimagining Black Holes Through the Golden Recursive Laws (φ-system)
The φ-Cascade Model of Gravitational Collapse
Instead of classical black hole theory based on the Schwarzschild solution and event horizons, we can reconceptualize extreme gravitational systems using the Golden Recursive Laws. This framework suggests that gravitational collapse follows a self-similar, golden-ratio-scaled decay process rather than a singular point of infinite density.
I. Mass-Energy Cascade (Replacing Singularity)
Classical Problem: General relativity predicts a singularity—infinite density at r=0.
φ-System Solution: Mass-energy undergoes recursive φ-attenuation across nested scales:
M_{n+1} = φ^(-7) * M_n
- Layer 0: Observable mass M₀
- Layer 1: M₁ = φ^(-7) M₀ ≈ 0.01314 M₀
- Layer n: M_n = φ^(-7n) M₀
Total accumulated mass converges:
M_total = M₀ · [1 / (1 - φ^(-7))] ≈ 1.0356 M₀
Interpretation: No singularity exists. Instead, mass distributes across infinite recursive layers, each 98.7% smaller than the previous, creating a fractal density gradient that remains mathematically finite.
II. Event Horizon as φ-Boundary (Replacing Schwarzschild Radius)
Classical: Event horizon at r_s = 2GM/c²
φ-System: The “information boundary” occurs where recursive compression transitions from recoverable structure (compressible) to irreducible chaos (encrypted):
r_φ = r_base · φ^(-7n_critical)
Where n_critical satisfies:
Entropy_n = -7n ln(φ) ≥ Entropy_max (information encryption threshold)
Physical meaning:
- Above r_φ: Information can theoretically be reconstructed (follows Law VII compression)
- Below r_φ: Information becomes chaotically encrypted in golden-ratio turbulence
This replaces the “information paradox”—information isn’t destroyed, just exponentially encrypted through φ-scaling.
III. Hawking Radiation as Golden Dissipation
Classical: Black holes emit thermal radiation via quantum effects at the horizon.
φ-System (Law IV): Gravitational systems dissipate energy following golden attenuation:
E_radiated(n) = E₀ · e^(-7n ln φ)
Decay rate:
dE/dn = -7 ln(φ) · E ≈ -3.365 E
Properties:
- Energy emission rate decreases geometrically
- Total radiated energy converges (Law II)
- Radiation preserves self-similar spectral structure (fractal harmonics)
- Evaporation time scales with φ^(7n) rather than M³
IV. Time Dilation Through Recursive Layers
Classical: Time stops at event horizon (t → ∞)
φ-System: Time experiences recursive scaling:
τ_{n+1} = φ^7 · τ_n
Each layer experiences time 1.618^7 ≈ 76× faster than the layer above.
At layer n:
τ_n = τ₀ · φ^(7n)
For external observer:
- Signals from layer n are redshifted by φ^(7n)
- Infinite layers experienced in finite external time
- No frozen surface—instead, graduated temporal cascade
V. Gravitational Waves as φ-Harmonic Oscillations
Classical: Merging black holes emit gravitational waves in complex waveforms.
φ-System (Law VI): Wave energy distributes across φ-harmonics:
E_harmonic(n) = E₀ · φ^(-7n)
Fundamental frequency and overtones:
f_n = f₀ · φ^n
Predicted signature: Gravitational wave spectrum should exhibit:
- Golden ratio spacing between harmonics (f₁/f₀ = φ, f₂/f₁ = φ)
- Energy decay following φ^(-7n) across harmonic series
- Self-similar ringdown patterns
VI. Accretion Disk Structure
φ-System predicts nested disk layers:
r_n = r_ISCO · φ^n
Where innermost stable circular orbit (ISCO) defines r₀.
Temperature distribution:
T_n = T_max · φ^(-7n/4)
Observable:
- Spectral lines should cluster at φ-spaced frequencies
- X-ray emissions follow golden attenuation pattern
- Disk exhibits fractal turbulence at all scales
VII. Interior Geometry: No Singularity
Instead of spacetime curvature → ∞:
Curvature follows recursive attenuation:
R_{n+1} = φ^(-7) · R_n
At layer n:
R_n = R₀ · e^(-7n ln φ)
Limiting behavior:
lim_{n→∞} R_n = 0
But total integrated curvature remains finite (Law V).
Result: Spacetime becomes increasingly compressed but never singular—a fractal foam rather than a point.
VIII. Testable Predictions
This φ-system model makes distinct predictions:
- Gravitational wave echoes at φ-spaced intervals after merger events
- Quasi-periodic oscillations in X-ray binaries at frequencies related by φ
- Modified entropy scaling: S ∝ A^(1/φ⁷) rather than S ∝ A
- Discrete energy levels in photon orbits (photon sphere harmonics)
- Maximum compression ratio of ~1.0356 before φ-chaos dominates
IX. Philosophical Implications
Classical black holes: Ultimate endpoints, information destroyers, singularities
φ-System black holes:
- Infinite refinement without infinities
- Information encrypted, not destroyed
- Self-similar structure at all scales
- Natural harmony between quantum discreteness (n steps) and relativistic continuity (exponential form)
- Universe avoids true singularities through golden recursive structure
Summary: The φ-Attractor Model
Black holes become φ-attractors—systems that:
- Compress matter/energy across infinite golden-ratio-scaled layers
- Converge to finite total mass-energy
- Create information boundaries (not horizons)
- Emit radiation following golden dissipation
- Exhibit fractal spacetime geometry
- Preserve causality through recursive time scaling
Math is beautiful: Every pathology of classical black holes (singularities, information paradox, infinite curvature) resolves through the constraining elegance of φ^(-7) recursive decay.
