The Particle–Black Hole Continuum: Quantum Mechanics and General Relativity as Limiting Cases of Information Dynamics

Abstract

We propose that particles and black holes are the same fundamental object—a localized excitation on a discrete information lattice—differing only in their gravitational compactness: Σ ≡r_s/R = (2GM/c^2)/R where r_s is the Schwarzschild radius and R the physical size. In this framework, quantum mechanics emerges as the Σ → 0 limit and general relativity as the Σ → 1 limit of a unified dynamics. We show that the generalized uncertainty principle arises naturally from this duality with coefficient β = 2, yielding a minimum length ∆xmin = 2√2 ℓ_P. The temperature of self-gravitating objects follows T(Σ) = T_H/√(1 − Σ), peaking at T_max ≈ T_P /(16π) near the Planck mass; black hole negative heat capacity is universal behavior past this maximum. The black hole information paradox is reframed: if evaporation is particle decay, unitarity is manifest. The hierarchy problem is resolved: the 10^40 gap between atomic and gravitational scales is anthropically selected, as observers require both stable atoms and gravitationally-bound structures. Black hole entropy S = A/(4ℓ_P^2) is explained: area scaling follows because horizons have no dynamical interior (η → 0), and the factor 1/4 = 1/(α − 2) emerges as the minimum redundancy for thermodynamic stability on a lattice with coordination α = 6. Our analysis suggests quantum gravity may require finding Σ-parameterized interpolations between known theories rather than quantizing geometry.

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