Abstract

We propose Black Hole Digitization Theory (BHDT): black holes are finite-capacity quantum information registers whose microstate dimension satisfies \( \log \dim \mathcal{H}_{\mathrm{BH}} = A/(4G\hbar) \). Infalling matter is converted to horizon degrees of freedom, rapidly scrambled, and gradually emitted in Hawking radiation that follows a unitary Page curve explained by quantum extremal surfaces (“islands”) and replica wormholes. We extend this with two observationally minded ideas: (i) near-horizon quantum microstructure can induce minute phase/Polarization irregularities (“spotting”) in photons that graze the horizon; (ii) unstable photon orbits act as amplifiers, so higher-order photon rings could magnify Planck-scale effects enough to become measurable in next-generation VLBI. We outline gedanken and analogue experiments (entangled “quantum pings” at horizons; BEC/optical analogues), relate BHDT to fast scrambling, soft hair, MERA fractality, and discuss cosmological implications wherein late-time Hawking radiation forms an informational “archive” that could seed a subsequent aeon in cyclic scenarios. We close with a checklist of ring-level signatures that could provide the first direct evidence of quantum gravity at horizons.

1. Introduction

Black holes sit at the confluence of thermodynamics, quantum information, and geometry. Entropy proportional to area, a temperature set by surface gravity, and the possibility of information loss forced theory to evolve: holography and modern Page-curve computations now suggest evaporation is unitary. We take a pragmatic, operational stance: a black hole is a quantum device with finite capacity, fast scrambling dynamics, and a physical read-out channel—Hawking quanta. We call this the Black Hole Digitization Theory (BHDT).

Building on this core, our extended discussion adds two layers aimed squarely at observation: (a) at quantum scales, wavepackets that skim the horizon can experience partial absorption, leaving the escaping part with tiny but principled distortions (phase or polarization) that manifest as spotting at the extreme edge; and (b) the photon sphere’s unstable orbits and repeated near-horizon passes provide a natural amplification mechanism for such microstructure, making photon rings the best current arena for horizon-scale quantum signatures.

2. Black holes as quantum registers

2.1 Area law as capacity

The Bekenstein–Hawking entropy, \(S_{\mathrm{BH}}=A/(4G\hbar)\), elevates area into an information-theoretic quantity. BHDT reads this literally: the horizon hosts a register with roughly one qubit per Planck area, up to subleading corrections. That makes the horizon a digital surface, where energy and information trade places through the first law \( dM = ( \kappa / 8\pi G )\, dA + \Omega\, dJ + \Phi\, dQ \).

2.2 Scrambling and mirroring

Black holes are conjectured fast scramblers, mixing infalling data across their dofs in time \( t_* \sim (\beta/2\pi)\ln S \). Post-Page, the Hayden–Preskill “mirror” picture implies that freshly injected information reappears rapidly within the outgoing quanta, albeit hidden behind daunting decoding complexity.

2.3 Holography and error correction

AdS/CFT and the Ryu–Takayanagi prescription tie bulk geometry to entanglement entropies. The interior is an encoded object reconstructed from boundary subregions—i.e., a quantum error-correcting code. Islands extend this control to evaporating black holes coupled to baths, recovering the unitary Page curve.

3. Massive quantum objects and the distortion of spacetime

A key conversational insight was that black holes are simultaneously maximally gravitational and genuinely quantum. They supply the cleanest example that quantum systems gravitate: a black hole’s state—finite, discrete, unitary— curves spacetime profoundly. The open question is not whether quantum objects distort spacetime (they do) but whether spacetime itself must be quantized to be consistent with superpositions of geometry. BHDT is compatible with a fully quantum gravity, while remaining practical in semi-classical regimes.

4. Partial absorption and “spotting” at the edge

Photons aren’t bullets; they are wavepackets. Near a horizon, mode-splitting means support can straddle the boundary. The escaping portion may carry minuscule, structured distortions (phase, polarization) arising from interactions with horizon microstates. Aggregated across many geodesics, this could appear as spotting—a speckle-like irregularity—precisely where the photon ring forms.

5. Amplification by unstable photon orbits

5.1 Multiple passes as gain

The photon sphere at \(r=3GM/c^2\) (Schwarzschild) hosts unstable null geodesics. Trajectories with impact parameter near critical can execute multiple orbits before escaping. Each loop re-samples the near-horizon region, compounding tiny phase shifts—an effective gain.

5.2 Chaotic sensitivity

Nearby geodesics diverge exponentially. Chaotic sensitivity can magnify microscopic horizon jitter into macroscopic differences in exit angle/phase, potentially imprinting measurable irregularities in higher-order rings.

5.3 What it would look like

• Brightness speckle along the ring circumference, beyond turbulent-disk variability.
• Polarization “noise” with correlations tied to orbit order (N-ring index).
• Spacing anomalies relative to GR-predicted geometric ratios for successive rings.

6. Photon rings as quantum probes

The Event Horizon Telescope (EHT) has imaged the primary ring (N≈1). Theory predicts a ladder of exponentially fainter, sharper rings for N≥2. If horizon microstructure exists, the rings are where it should surface first. Next-gen EHT (ngEHT) and space-VLBI at higher frequencies aim exactly at resolving these fine substructures. A concordance of ring anomalies and gravitational-wave ringdown deviations would be compelling evidence of horizon-scale quantum structure.

7. Gedanken & analogue experiments

7.1 Quantum “ping” concept

We posited entangling outbound photons with a local quantum register, sending them toward a black hole, and monitoring the register for correlation shifts. Astrophysically impractical (millennia light-time, aiming precision, decoherence), the idea becomes actionable in analogue horizons: Bose–Einstein condensates and optical fibers where Hawking-like partner modes and entanglement have already been observed.

7.2 Collider micro-holes

Low-scale gravity scenarios at colliders have not yielded micro black holes; even if produced, lifetimes would be too short for entanglement interrogation. The value here is conceptual: design programmable fast-scrambling channels in quantum simulators (SYK-like, random circuits) to test decoding/complexity ideas.

7.3 Lab spotting

In analogue platforms, engineer wavepackets that skim the effective horizon multiple times; look for interference speckle/polarization jitter beyond classical expectations. These systems compress “photon-ring amplification” into microseconds on a benchtop.

8. Fractal / multi-scale encoding

Critical collapse exhibits discrete self-similarity (Choptuik scaling), hinting that formation already carries multi-scale structure. MERA tensor networks provide a concrete, hierarchical encoding whose geometry mirrors holographic bulk reconstruction. BHDT adopts this: the horizon register resembles a multi-resolution code (think wavelets), ideal for robust storage and fast scrambling.

9. Cosmological extension

Over eons, black holes evaporate, leaving a bath of Hawking radiation containing a scrambled record of infallen information. In cyclic or conformal cosmologies, this radiation could act as the seed for the next aeon’s low-entropy initial state. BHDT is agnostic on specific bounce dynamics, focusing on the information-preserving character that makes such continuity plausible in principle.

10. Open questions

• UV realization: Which microscopic theory instantiates the horizon code (string fuzzballs, LQG punctures, other)?
• Decode barrier: Are ring-level signatures masked by GRMHD turbulence, or can we isolate quantum residuals?
• Amplification math: Rigorous bounds on how chaotic orbits magnify Planck-scale phase noise.
• Synergy tests: Cross-correlate photon-ring anomalies with gravitational-wave echoes/ringdown shifts.
• Cosmic memory: Can late-time radiation statistics constrain (or falsify) cyclic seed hypotheses?

11. Conclusion

BHDT reframes a black hole as a finite, error-corrected quantum register whose contents are scrambled in, stored on/near the horizon, and read out as Hawking radiation with a unitary Page curve. Our new emphasis is observational: photon rings—especially N≥2—are natural amplifiers of horizon-scale microstructure. Even tiny, Planck-suppressed effects could leak into measurable speckle, polarization, or spacing anomalies once angular resolution and sensitivity cross key thresholds. Detecting such deviations would mark the first direct glimpse of quantum gravity at work on the surface of spacetime.

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