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Gravitational Decoherence via Entanglement-Geometry: Testing the Diósi-Penrose Hypothesis

Marc Sperzel

Published Jan 22, 2026• 0 citations
Publisher

Abstract

Why do macroscopic objects appear classical? The Diósi-Penrose conjecture proposes that the classical gravitational self-energy directly determines the decoherence rate for spatial superpositions. We present an exposition and experimental analysis of this hypothesis, interpreting the mechanism in terms of environmental decoherence compatible with unitarity. We identify four distinctive experimental signatures that no other decoherence mechanism exhibits simultaneously. Part of the Quantum-Geometric Duality series (Paper A).

DOI
10.5281/zenodo.19181566

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Why do macroscopic objects appear classical? The Diósi-Penrose conjecture proposes that the classical gravitational self-energy directly determines the decoherence rate for spatial superpositions. We present an exposition and experimental analysis of this hypothesis, interpreting the mechanism in terms of environmental decoherence compatible with unitarity. We identify four distinctive experimental signatures that no other decoherence mechanism exhibits simultaneously. Part of the Quantum-Geometric Duality series (Paper A).
We evaluate the macroscopic entanglement-loss implications of gravitational time dilation, first identified by Pikovski et al. (2015). By moving beyond the idealized zero-temperature single-mode approximation to a continuous Debye model in the canonical ensemble, we derive the explicit phononic heat-capacity limits for spontaneous gravitational decoherence. We find that the decoherence rate driven by internal time-dilation variance strongly scales with σ∝T5/2\sigma \propto T^{5/2}σ∝T5/2 at ultra-low experimental temperatures (T≪ΘDT \ll \Theta_DT≪ΘD​), vanishing strictly at absolute zero. Furthermore, we demonstrate mathematically that translational invariance renders proper-time differences between spatially distinct branches of an identical matter distribution identically zero. Thus, contrary to the Diósi-Penrose approach, an isolated mass in a pure superposition cannot undergo solely self-gravitational state-collapse. Decoherence requires either an external gravitational potential gradient or internal structural asymmetry. Lastly, we prove that the topological spectral dimension dsd_sds​ of the macroscopic test mass determines the decoherence rate scaling, creating a new class of ultra-sensitive 'fracton-gravity sensors'.
We propose a geometric decoherence mechanism within the rotational-order unification framework built upon the Zhang Effective Metric. Stochastic zero-point fluctuations of the internal S³ orientation field generate fluctuations of the effective spacetime metric, imprinting random relative phases on quantum superpositions. The derived decoherence rate scales as M² at leading order, naturally suppressing macroscopic superpositions while preserving coherence for microscopic particles. This mechanism is qualitatively distinct from Diósi–Penrose / Károlyházy gravitational decoherence: the metric fluctuations originate from the internal fibre geometry rather than the mass distribution of the quantum system itself. The fluctuations couple only to massive matter-wave phases at leading order and do not produce photon dispersion. This work predicts a universal, shielding-insensitive noise floor for macroscopic quantum experiments.
We present a unified and minimal theoretical framework addressing the quantum-classical transition, the measurement problem, and the emergence of the arrow of time, grounded in gravitational physics. Building on the insight that quantum superpositions of mass distributions necessarily imply superpositions of gravitational potentials, we show that such states are unavoidably associated with superpositions of proper times due to gravitational time dilation. By extending the system Hilbert space to include a temporal degree of freedom, we demonstrate that matter-time entanglement leads naturally to effective decoherence when the time degree of freedom is traced out. The resulting reduced dynamics takes the form of a Lindblad master equation derived from an underlying unitary evolution. This framework reproduces the correct microscopic and macroscopic limits, clarifies the relation to Diósi-Penrose-type models, and provides a coherent account of classicality and temporal irreversibility without postulating observers, environmental decoherence as fundamental, or objective wavefunction collapse.