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
Thirteen papers developing a unified framework connecting gravitational decoherence, holographic dark energy, information-theoretic bounds, and experimental predictions. Each paper is self-contained; Paper C provides the axiomatic foundation.
Reading order & paper relationships
Foundations
Paper A — Gravitational decoherence (the core experimental prediction)
Paper B — Holographic dark energy (thermodynamic framework)
Paper C — Axiomatic framework (the formal foundation — start here for the full picture)
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.
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.
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.
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},
doi = {10.5281/zenodo.19181583},
note = {Quantum-Geometric Duality Series, Paper D},
url = {https://doi.org/10.5281/zenodo.19181583}
}
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.
Entanglement Decay from Gravitational Decoherence: A Unique Signature of Gravity's Quantum Role
We identify a distinctive experimental signature of gravitational decoherence: when one member of an entangled pair undergoes gravitational decoherence due to spatial superposition, the entanglement with its distant partner decays at a rate determined by the decohering particle's gravitational self-energy. Specifically, if particle A with mass M is placed in superposition with separation d while entangled with distant particle B, the concurrence decays as C(t) = C(0)exp(−GM²t/ℏd).
This prediction distinguishes gravitational decoherence from all other decoherence mechanisms: standard environmental decoherence affects only local coherence, leaving entanglement with distant partners intact. We analyze the experimental requirements for testing this prediction using levitated optomechanics, finding that proof-of-principle experiments are feasible within the next decade.
Gravitational Decoherence as a Fundamental Limit on Massive Quantum Technologies
The Diósi-Penrose hypothesis predicts that gravity causes irreducible decoherence of spatial superpositions at a rate Γ_grav = GM²/(ℏd), where M is the superposed mass and d the separation. We analyze implications for quantum computing platforms. Conventional qubits (superconducting, trapped ion, photonic) have gravitational decoherence times exceeding the age of the universe and are entirely unaffected.
Emerging massive quantum technologies—optomechanical oscillators and electromechanical resonators—approach a regime where gravitational decoherence could become the dominant coherence-limiting mechanism. For a levitated nanosphere of mass 10⁻¹² kg in a 10 μm superposition, the predicted decoherence time is approximately 16 μs. Three experimental signatures uniquely distinguish gravitational from environmental decoherence: M² scaling, material independence at fixed mass and separation, and temperature independence below a critical threshold.
@article{Sperzel2026QuantumTech,
author = {Sperzel, Marc},
title = {Gravitational Decoherence as a Fundamental Limit on Massive Quantum Technologies},
year = {2026},
doi = {10.5281/zenodo.19181597},
note = {Quantum-Geometric Duality Series, Paper J},
url = {https://doi.org/10.5281/zenodo.19181597}
}
Gravitational Decoherence at O(G): The Wheeler-DeWitt Constraint on the Feynman-Vernon Influence Functional
Standard perturbative quantum field theory predicts gravitational decoherence rates scaling as G², yielding decoherence times of order 10²⁶ years for laboratory masses—effectively unobservable. The Diósi-Penrose hypothesis, by contrast, predicts G¹ scaling with τ_dec ~ ℏd/(GM²), giving nanosecond-scale decoherence for microgram masses. We show that this discrepancy traces to the initial state: the standard Feynman-Vernon influence functional assumes a product state |ψ_matter⟩ ⊗ |0_grav⟩, which violates the linearized Wheeler-DeWitt constraint.
Imposing the constraint forces an entangled initial state (|L⟩|Φ_L⟩ + |R⟩|Φ_R⟩)/√2, where |Φ_A⟩ are coherent states of the gravitational field determined by the mass configuration. The constrained influence functional replaces the noise-kernel mechanism (G²) with a coherent-state-overlap mechanism (G¹). The resulting decoherence rate is Γ = C × GM²/(ℏd) + O(G²), with C ∈ [1/2, 2] (best estimate C = 1, matching the Diósi master equation).
@article{Sperzel2026ConstrainedFV,
author = {Sperzel, Marc},
title = {Gravitational Decoherence at O(G): The Wheeler-DeWitt Constraint on the Feynman-Vernon Influence Functional},
year = {2026},
doi = {10.5281/zenodo.19181605},
note = {Quantum-Geometric Duality Series, Paper K},
url = {https://doi.org/10.5281/zenodo.19181605}
}
Paper LMay 27, 2026
Gravitational Decoherence in Quantum Field Theory: From Fock States to Inflationary Perturbations
We extend the Diósi-Penrose gravitational decoherence formalism from point particles to quantum fields. The mass density operator μ̂(x) in the Diósi master equation is replaced by the stress-energy operator T̂⁰⁰(x)/c², yielding decoherence rates for arbitrary field-state superpositions. For Fock state superpositions (|n⟩+|m⟩)/√2 of a single mode, we derive Γ = G(n−m)²ℏω²C_cube/(c⁴L), where C_cube ≈ 1.192 is a geometric factor. This reduces to the standard Diósi-Penrose rate Γ = GM²/(ℏd) in the single-particle limit, providing a non-trivial consistency check.
For coherent and squeezed states, the rates are negligible for electromagnetic fields but can be significant for massive bosons. Applied to inflationary cosmology, we find that the self-gravitational decoherence of scalar perturbations becomes faster than the Hubble expansion at N_dec ≈ (1/4)ln(16/ε_grav) e-folds after horizon crossing, where ε_grav = (ℏH_inf/E_P)². For GUT-scale inflation (H_inf ~ 10¹³ GeV), N_dec ≈ 7.7—well before recombination for all observable modes. Physical arguments suggest this provides a universal mechanism for the quantum-to-classical transition of primordial perturbations, with the same parametric scaling as environmental decoherence but arising from the self-gravitational field alone; the result is a motivated estimate subject to O(1) corrections from the de Sitter kernel and gauge choice.
@article{Sperzel2026QFTDecoherence,
author = {Sperzel, Marc},
title = {Gravitational Decoherence in Quantum Field Theory: From Fock States to Inflationary Perturbations},
year = {2026},
note = {Quantum-Geometric Duality Series, Paper L}
}
Paper MMay 27, 2026
A Mass-Independent Visibility Suppression in the Bose-Marletto-Vedral Experiment from Quantum-Geometric Duality
The Bose-Marletto-Vedral (BMV) and QGEM proposals seek to witness the quantum nature of gravity by detecting entanglement generated between two massive particles each placed in spatial superposition. Standard quantum-gravity treatments predict the entanglement amplitude reaches the witness threshold after a time τ_BMV ~ ℏd³/(Gm²Δ²), where d is the inter-particle separation and Δ the superposition arm. Quantum-Geometric Duality (QGD)—through the constrained Feynman-Vernon influence functional—predicts a competing per-particle decoherence rate Γ = Gm²/(ℏΔ) that suppresses the visibility of the off-diagonal density-matrix element by V(τ_BMV) = exp(−O(1)(d/Δ)³) at the witness criterion.
The suppression depends only on the geometric ratio Δ/d and on the arm-to-axis angle θ: it is mass-independent and parameter-free, in sharp contrast with continuous-spontaneous-localisation models and the Diósi-Penrose collapse rate. The angular dependence is a Legendre P₂(cos θ): the leading dipole contribution vanishes identically at the magic angle cos²θ_m = 1/3, where the quadrupole takes over and the visibility scales as a quintic exp[−(9π/7)(d/Δ)⁵]. An apparatus that can rotate its arms relative to the inter-particle axis sweeps three qualitatively distinct QGD signatures with the same hardware. Observation of mass-independent cubic/quintic visibility suppression would distinguish QGD from all extant collapse models in a single experiment.
@article{Sperzel2026BMV,
author = {Sperzel, Marc},
title = {A Mass-Independent Visibility Suppression in the Bose-Marletto-Vedral Experiment from Quantum-Geometric Duality},
year = {2026},
note = {Quantum-Geometric Duality Series, Paper M}
}
Paper NMay 27, 2026
Cosmic Gravitational Decoherence on a de Sitter Background: Resolving a Causality Paradox in Quantum-Geometric Duality
The gravitational decoherence rate Γ = GΔm²/(ℏd) of Quantum-Geometric Duality (QGD), applied at cosmic scale with Δm the mass of the observable universe and d the Hubble radius R_H, returns Γ ~ 10¹⁰³ Hz—exceeding the causal bound c/R_H ~ H₀ by 121 orders of magnitude. We show that the divergence is an artifact of using the Minkowski graviton propagator at separations d ~ R_H, where it is not valid.
Recomputed on a de Sitter background with Bunch-Davies modes, the coherent-state decoherence functional acquires a physical infrared cutoff at the horizon scale: super-horizon modes freeze and cease to drive decoherence. The rate gains a closed-form form factor, Γ_dS = (GΔm²/ℏd) g(Hd/c) t with g(x) = 1 − (2/π)Si(x), which recovers the Minkowski result for Hd/c ≪ 1 and is finite and causal at d = R_H. The cosmic rate is governed not by the total mass M_U but by the elementary branch granularity of the cosmic wavefunction; arguments from quantum cosmology identify this granularity with the de Sitter thermal mass Δm_dS = ℏH/(2πc²) per horizon mode. Summed over the S_dS holographic horizon modes, the cosmic decoherence rate is Γ_total ≈ H/(10π) ≈ 7×10⁻²⁰ Hz, manifestly sub-causal.
@article{Sperzel2026CosmicDecoherence,
author = {Sperzel, Marc},
title = {Cosmic Gravitational Decoherence on a de Sitter Background: Resolving a Causality Paradox in Quantum-Geometric Duality},
year = {2026},
note = {Quantum-Geometric Duality Series, Paper N}
}
Paper OMay 27, 2026
The Past Hypothesis from Holographic Dark Energy: A Quantum-Geometric Resolution of Penrose's Weyl Curvature Asymmetry
Three apparently independent puzzles in fundamental physics—the Past Hypothesis (why was the early universe in a low-entropy state?), Penrose's Weyl Curvature Asymmetry (why does the Weyl tensor vanish at the Big Bang but diverge at black-hole singularities?), and the cosmological constant problem (why is ρ_DE/ρ_Pl ~ 10⁻¹²²?)—are shown, within the Quantum-Geometric Duality (QGD) framework, to be a single mystery viewed through three lenses. The connecting tissue is a single identity, exact in the de Sitter attractor of any FRW cosmology: ρ_DE^∞ · S_dS^∞ = 3c⁷/(8G²ℏ).
The identity itself is a tautology, but its coupling to the Past Hypothesis and to Penrose's Weyl Curvature Hypothesis is not. The Past Hypothesis is implemented automatically by the holographic bound S(t) ≤ S_dS(t) applied to a shrinking past horizon; Penrose's 10¹²³ is reinterpreted as the capacity of the de Sitter horizon rather than a probability of fine-tuning; and the smallness of ρ_DE in Planck units is the reciprocal of that capacity. The Weyl asymmetry is recovered as a consequence of the direction of cosmic decoherence. The framework introduces no new axioms and no new free parameters; the gain is conceptual: one mystery dressed in three vocabularies.
@article{Sperzel2026PastHypothesis,
author = {Sperzel, Marc},
title = {The Past Hypothesis from Holographic Dark Energy: A Quantum-Geometric Resolution of Penrose's Weyl Curvature Asymmetry},
year = {2026},
note = {Quantum-Geometric Duality Series, Paper O}
}
Paper PMay 30, 2026
The Horizon Clock: A Single de Sitter Frequency Behind the MOND Scale, Cosmic Decoherence, and the Chaos Bound
The MOND acceleration scale a₀ ≈ cH₀/2π and the cosmic gravitational decoherence rate Γ_cos ≈ g(1)H/4π are usually treated as unrelated numerical coincidences with the Hubble rate—one a fact about galactic dynamics, the other about the quantum-to-classical transition at the largest scales. We show they are the same quantity. Both are the Gibbons-Hawking temperature of the cosmological horizon, written as a frequency: the horizon clock ω_L ≡ k_B T_dS/ℏ = H/2π, which is also the rate of Tomita-Takesaki modular flow of the de Sitter vacuum.
The MOND scale is this frequency carried by c (an acceleration), a₀ = c·ω_L = κ_dS/2π with κ_dS = cH the horizon surface gravity; the cosmic decoherence rate is the same frequency carried by a pure number, Γ_cos = (1/2)g(1)·ω_L. Consequently the two are locked at a parameter-free ratio, a₀/(c·Γ_cos) = 2/g(1) = 5.03, in which every cosmological input cancels. The single non-trivial number g(1) = 1 − (2/π)Si(1) = 0.398 is the sub-horizon fraction of the gravitational self-energy at one Hubble radius. We place this in a horizon clock family—one clock κ/(2πc) per causal horizon—with intensive (per-mode) readings the acceleration scale (de Sitter: MOND) and the chaos/Lyapunov rate (de Sitter: λ = H; black hole: the Maldacena-Shenker-Stanford bound), and extensive readings (summed over the S_dS horizon modes) the cosmic decoherence rate and the dark-energy density.
@article{Sperzel2026HorizonClock,
author = {Sperzel, Marc},
title = {The Horizon Clock: A Single de Sitter Frequency Behind the MOND Scale, Cosmic Decoherence, and the Chaos Bound},
year = {2026},
note = {Quantum-Geometric Duality Series, Paper P}
}