Hybrid Classical-Quantum Newtonian Gravity with stable vacuum

TL;DR

The GPSL framework presents a hybrid classical–quantum description in which Newtonian gravity arises from discrete, Poissonian collapses of the mass density operator, guaranteeing vacuum stability and applicability to identical particles. Gravity is incorporated entirely through jump operators, producing short-range back-reaction and potentially smaller decoherence than continuous weak-measurement schemes, while avoiding vacuum instabilities that plague relativistic extensions. The authors derive the GPSL master equation, perform a perturbative expansion, and analyze both single-particle and macroscopic rigid-body dynamics, yielding explicit decoherence profiles and clear experimental avenues to bound its parameters. Overall, GPSL offers a robust non-relativistic foundation for future relativistic hybrid gravity theories and a testable alternative to continuous weak-monitoring models in mesoscopic and macroscopic regimes.

Abstract

We investigate the Gravitational Poissonian Spontaneous Localization (GPSL) model, a hybrid classical-quantum model in which classical Newtonian gravity emerges from stochastic collapses of the mass density operator, and consistently couples to quantum matter. Unlike models based on continuous weak measurement schemes, we show that GPSL ensures vacuum stability; this, together with its applicability to identical particles and fields, makes it a promising candidate for a relativistic generalization. We analyze the model's general properties, and compare its predictions with those based on continuous weak measurement schemes. Notably, here the gravitational feedback enters entirely through the non-Hermitian jump operators, without modifying the unitary part of the dynamics. We show that this leads to a short-range gravitational back-reaction and permits decoherence rates below those of any model based on continuous weak measurement schemes. We provide explicit examples, including the dynamics of a single particle and a rigid sphere, to illustrate the distinctive phenomenology of the model. Finally, we discuss the experimental testability of GPSL, highlighting both interferometric and non-interferometric strategies to constrain its parameters and distinguish it from competing models.

Figures (4)

• Figure 1: Pictorial explanation of the localization dynamics with gravitational back-reaction, starting from a balanced superposition of a particle in two different locations. In the GPSL model (above the timeline), the superposition remains balanced and the gravitational field is always zero until the instantaneous collapse (represented by the red circle) occurs. When it does, the body immediately localizes and the instantaneously generated field can only have effect where the body is located, thus explaining the absence of long-range decoherence due to the gravitational back-reaction. In the continuous weak monitoring models (below the timeline), the spatial superposition is gradually suppressed by the continuous weak measurements (represented by the small red circles) and the gravitational back-reaction acts during this process, giving rise to additional long-range decoherence due to the gravitational back-reaction.
• Figure 2: The plot shows a numerical evaluation of $\tilde{F} (\tilde{d})$ using the "Adaptive MonteCarlo" built-in method in Mathematica. We then fitted the resulting curve with $4.49 \times \tilde{d}^2$ on the left and $2.1\times \exp{-(\tilde{d} - 3.5)/1.3}$ on the right.
• Figure 3: The plot shows the functions $K_{G}^{\rm GPSL} \left(x\right)$, $K_{G}^{\rm DP} \left(x\right)$, and $K_{G}^{\rm CSL} \left(x\right)$.
• Figure 4: The plot shows the function $\tilde{F}_G (d_r)$, defined in Eq. \ref{['APPeq:NumericalAverageForces']} and its perturbative forms defined in Eq. \ref{['APPeq:ExtremeRegimesAverageForces']}.