Papers on quantum-geometric duality—the hypothesis that quantum mechanics and general relativity are complementary descriptions of a single underlying reality.
Quantum-Geometric Duality Series
Five papers developing a unified framework connecting gravitational decoherence, holographic dark energy, and information-theoretic bounds. Each paper is self-contained; Paper C provides the axiomatic foundation.
Paper AJanuary 22, 2026
Gravitational Decoherence via Entanglement-Geometry: Testing the Diósi-Penrose Hypothesis
Why do macroscopic objects appear classical? The Diósi-Penrose conjecture proposes that the classical gravitational self-energy E_G = GM²/d directly determines the decoherence rate for spatial superpositions, predicting τ_dec ∝ ℏd/(GM²). For a 1 μg particle separated by 1 mm, this predicts τ_dec ~ 10⁻⁹ s—fast enough to explain why macroscopic superpositions are never observed, yet potentially accessible to next-generation experiments.
We present an exposition and experimental analysis of this hypothesis, interpreting the mechanism in terms of environmental decoherence compatible with unitarity. The G¹ scaling is a testable hypothesis, not a derived result: standard quantum field theory predicts G² scaling via graviton exchange, yielding decoherence times 10³⁵ longer. We identify four distinctive experimental signatures: M⁻² mass scaling, temperature independence, vacuum independence, and linear separation scaling. No other decoherence mechanism exhibits all four simultaneously.
@article{Sperzel2026Decoherence,
author = {Sperzel, Marc},
title = {Gravitational Decoherence via Entanglement-Geometry: Testing the Diósi-Penrose Hypothesis},
year = {2026},
note = {Quantum-Geometric Duality Series, Paper A},
url = {https://blog.marcsperzel.com/research#paper-a}
}
Paper BJanuary 22, 2026
Holographic Dark Energy: A Thermodynamic Consistency Framework
The cosmological constant problem—why the observed vacuum energy is 10¹²⁰ times smaller than quantum field theory predicts—remains one of the deepest puzzles in theoretical physics. We develop a thermodynamic consistency framework for holographic dark energy with an event horizon cutoff. The holographic ansatz yields a dark energy density ρ_DE = αc²H²/G from dimensional analysis, with coefficient α = 0.082 ± 0.001 fitted to observations.
We show that de Sitter space is thermodynamically consistent with this formulation: the generalized second law saturation condition HR_h = 1 coincides with the de Sitter geometric identity, yielding equation of state w = −1 as a consistency requirement. However, we emphasize that the cosmological constant problem is not solved—the magnitude α ~ 0.08 encodes the same mystery as Λ, merely reparameterized. The framework offers thermodynamic language for organizing holographic dark energy, not a solution to its fundamental mysteries.
@article{Sperzel2026DarkEnergy,
author = {Sperzel, Marc},
title = {Holographic Dark Energy: A Thermodynamic Consistency Framework},
year = {2026},
note = {Quantum-Geometric Duality Series, Paper B},
url = {https://blog.marcsperzel.com/research#paper-b}
}
Paper CJanuary 22, 2026
Quantum-Geometric Duality: An Axiomatic Framework
We present a complete axiomatic framework for Quantum-Geometric Duality, the hypothesis that quantum mechanics and general relativity are complementary descriptions of a single underlying reality. The framework rests on four primitive axioms: Information Conservation, Entanglement-Geometry Correspondence, the Entropic Action Principle, and Scale-Dependent Unification. Two additional statements complete the structure: an observer-dependent horizon principle adopted as a postulate, and a holographic information bound derivable from the primitives together with the generalized second law.
From the axioms we derive testable predictions including modified Einstein equations with entropy corrections, the generalized uncertainty principle, a minimum measurable length of order the Planck scale, modified dispersion relations with characteristic E² scaling, and vacuum birefringence with E³ scaling observable through gamma-ray burst polarimetry.
@article{Sperzel2026Framework,
author = {Sperzel, Marc},
title = {Quantum-Geometric Duality: An Axiomatic Framework},
year = {2026},
note = {Quantum-Geometric Duality Series, Paper C},
url = {https://blog.marcsperzel.com/research#paper-c}
}
Paper DJanuary 24, 2026
Emergent Gravity from Entanglement Equilibrium: MOND Phenomenology and Covariant Extension
We show that Modified Newtonian Dynamics (MOND) phenomenology emerges naturally from the thermodynamics of de Sitter space within the framework of quantum-geometric duality. The de Sitter cosmological horizon establishes a thermal bath at the Gibbons-Hawking temperature, which generates extensive (volume-law) entropy in addition to the standard area-law contribution. When local entanglement equilibrium fails at low accelerations, the volume entropy becomes dynamically relevant, producing MOND-like corrections to Newtonian gravity.
We demonstrate that the characteristic acceleration scale emerges as a₀ = cH₀/(2π) ≈ 1.1 × 10⁻¹⁰ m/s², matching observed MOND values within 10% with no adjustable parameters. We establish clear criteria for regime separation: GR remains exact when g_N/a₀ ≫ 1 (solar system, pulsars), while MOND corrections become significant when g_N/a₀ ≲ 1 (galaxy outskirts).
We present Entanglement-Elastic Gravity (EEG), a covariant field theory that extends this framework to relativistic regimes. The theory is ghost-free, preserves gravitational wave speed c, and reduces to the modified Poisson equation in the Newtonian limit. Predictions: Flat rotation curves, Tully-Fisher relation v⁴ = GMa₀, weak lensing slip |Φ - Ψ|/|Φ| ≈ 15% beyond 50 kpc, and growth rate suppression Δfσ₈ ≈ -0.03 testable with Euclid and DESI.
@article{Sperzel2026EmergentGravity,
author = {Sperzel, Marc},
title = {Emergent Gravity from Entanglement Equilibrium: MOND Phenomenology and Covariant Extension},
year = {2026},
note = {Quantum-Geometric Duality Series, Paper D},
url = {https://blog.marcsperzel.com/research#paper-d}
}
Paper HJanuary 22, 2026
Information-Theoretic Bounds on Gravitational Decoherence
Gravitational decoherence presents a sharp theoretical puzzle: the Diósi-Penrose mechanism predicts decoherence rates scaling as G¹, while perturbative quantum field theory predicts G², a difference of ~10³⁵ in predicted rates for laboratory-scale masses. We apply the Margolus-Levitin quantum speed limit to establish a fundamental rate scale for gravitational decoherence.
For a mass M in spatial superposition of separation d, the Margolus-Levitin theorem establishes a characteristic rate Γ_ML = 2GM²/(πℏd), where the gravitational self-energy E_G = GM²/d sets the fundamental energy scale. The Diósi-Penrose rate is of the same order, with Γ_DP/Γ_ML = π/2 ≈ 1.57, while the perturbative QFT rate lies a factor of ~10⁻³⁵ below it. This implies that if gravitational decoherence occurs at the Diósi-Penrose rate, gravity extracts information from quantum superpositions at rates characteristic of the fundamental quantum limit.