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arXiv:2601.17384 · Physical Review A

The Universe as a Detector: A Quantum Filtering Formulation of the Diósi-Penrose Model

John Gough, Dylon Rees

quant-phgr-qcSubmitted Jan 24, 2026• Announced Jan 27, 2026• 0 citations
arXivHTMLPDF

Abstract

We consider the Diósi-Penrose problem but rather than postulating background gravitational fluctuations, we instead consider the quantum filter that arises from space-time homodyning the continuum of output quadrature described in the open quantum stochastic model presented here. This is described by a quantum Kushner-Stratonovich equation, typical of the form appearing in continuous-time collapse of the wave-function models in Quantum Decoherence Theory

Journal reference
Phys. Rev. A 113, 042225, 28 April, 2026
DOI
10.1103/945v-yvvk

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We consider the Diósi-Penrose problem but rather than postulating background gravitational fluctuations, we instead consider the quantum filter that arises from space-time homodyning the continuum of output quadrature described in the open quantum stochastic model presented here. This is described by a quantum Kushner-Stratonovich equation, typical of the form appearing in continuous-time collapse of the wave-function models in Quantum Decoherence Theory
Abstract The possibility that gravity plays a role in the collapse of the quantum wave function has been considered in the literature, and it is of relevance not only because it would provide a solution to the measurement problem in quantum theory, but also because it would give a new and unexpected twist to the search for a unified theory of quantum and gravitational phenomena, possibly overcoming the current impasse. The Diósi–Penrose model is the most popular incarnation of this idea. It predicts a progressive breakdown of quantum superpositions when the mass of the system increases; as such, it is susceptible to experimental verification. Current experiments set a lower bound R 0 ≳ 4 Å for the free parameter of the model, excluding some versions of it. In this work we search for an upper bound, coming from the request that the collapse is effective enough to guarantee classicality at the macroscopic scale: we find out that not all macroscopic systems collapse effectively. If one relaxes this request, a reasonable (although to some degree arbitrary) bound is found to be: R 0 ≲ 10 6 Å. This will serve to better direct future experiments to further test the model.
Space offers exciting opportunities to test the foundations of quantum physics using macroscopic quantum superpositions. It has been proposed to perform such tests in a dedicated space mission (MAQRO) using matter-wave interferometry with massive test particles or monitoring how the wave function of a test particle expands over time. Such experiments could test quantum physics with sufficiently high precision to resolve potential deviations from its unitary evolution due to gravitational decoherence. For example, such deviations have been predicted by the Diósi–Penrose (DP) model and the Károlyházy (K) model. The former predicts the collapse of massive or large superpositions due to a nonlinear modification of quantum evolution. The latter predicts decoherence because of an underlying uncertainty of space time. Potential advantages of a space environment are (1) long free-fall times, (2) low noise, and (3) taking a high number of data points over several years in a dedicated space mission. In contrast to interferometric tests, monitoring wave function expansion is less complex, but it does face some practical limitations. Here, we will discuss limitations of such non-interferometric experiments due to the limited number of data points achievable during a mission lifetime. Our results show that it will require an interferometric approach to conclusively test for gravitational decoherence as predicted by the DP or K models. In honor of the Nobel prize of Sir Roger Penrose, we will focus our discussion on the Diósi–Penrose model.
The article reviews our recent experimental results on the Continuous Spontaneous Localization (CSL) model and on the gravity related collapse model developed by Diósi and Penrose (DP). These models of dynamical reduction of the wave function consist in non-linear and stochastic modifications of the Schröedinger equation, which lead to a progressive breakdown of the superposition principle, as the size of the system increases. We performed a high sensitivity survey of the spontaneous radiation phenomenon, predicted by the collapse models, in a dedicated experiment operated in the extremely low background of the Gran Sasso underground National Laboratory of INFN in Italy. Our studies set the strongest bounds on the CSL parameters, in a broad region of the parameters space, and rule out the DP in its present formulation.
Time Cosmology (TC) reads the dark sectors as tenses and identifies the present with an irreversible selection performed by the fundamental forces. At the background and recent-universe level TC is observationally degenerate with quintessence. This paper exhibits the program's first non-cosmological discriminant. Carried to the laboratory, the irreversible recording of an outcome into the gravitational ledger is governed by the Penrose energy-time criterion tau ~ hbar/E_G, a parameter-free collapse time for spatial superpositions; TC supplies the ontological reason Penrose left open (collapse = writing to the past) and attaches a Landauer cost. Because TC selection is a quantum non-demolition (QND) measurement by the existing forces, not a stochastic noise field, it carries no continuous momentum diffusion and hence no spontaneous radiation; it therefore survives the 2021 Gran Sasso experiment that excluded the parameter-free Diosi-Penrose model. The prediction is falsifiable: a spatial superposition of ~1e-17 to 1e-15 kg held beyond tau must collapse; the gap to capability is ~6 orders of magnitude for second-scale experiments, shrinking to ~1-2 orders for long-hold MAQRO-class proposals. Scope is stated explicitly: the collapse time reproduces Penrose's (the novelty is the grounding and the non-radiative survival); the non-radiativity rests on strict non-stochasticity, with a residual-diffusion bound left as the central open calculation; the test is not within current reach. All numerical claims are reproduced by the archived code included in this record. Companion records: Indispensable Present (10.5281/zenodo.20707004), N3 (10.5281/zenodo.20564003), N5 calorimeter (10.5281/zenodo.20617808).