This preprint (arXiv:2603.26075v1) is a purely theoretical study that mathematically classifies all possible models of non-quantized gravity consistent with Galilean invariance in the non-relativistic limit while reproducing Newtonian gravity on average. There is no experimental component, no sample size, and no empirical data; the methodology consists of deriving general constraints from first principles and then applying them to specific proposals. The core result is clear: any such non-quantized model must inject a quantifiable minimum amount of noise (stochasticity or irreversibility) into the system to prevent gravitational interactions from entangling massive objects.

This directly confronts one of the deepest open questions in physics: must gravity be quantized? For decades, thought experiments have suggested that a fully classical gravitational field cannot mediate entanglement. The new work goes further by calculating the exact lower bound on noise required for any consistent classical model. It tests this bound on two concrete frameworks: the classical-quantum gravity models developed by Jonathan Oppenheim and collaborators, and a Newtonian entropic-force model inspired by Erik Verlinde’s 2010 proposal.

Previous discussions of Oppenheim’s hybrid theory have often portrayed it as a clean way to keep gravity classical. What this paper reveals, and what much coverage has missed, is that the theory cannot remain perfectly reversible; it must carry an irreducible noise floor. Similarly, Verlinde’s entropic gravity, usually discussed in thermodynamic terms, here appears as another member of the same family of noisy classical models. Synthesizing these with the Diosi-Penrose collapse models shows a recurring pattern across quantum-gravity research: attempts to avoid quantizing gravity repeatedly require additional stochasticity or decoherence to stay consistent with quantum mechanics.

The preprint’s limitations are significant. It operates only in the non-relativistic, weak-field regime and assumes strict Galilean invariance, leaving open questions about relativistic extensions or strong-gravity regimes near black holes. As an unreviewed preprint, its conclusions await scrutiny from the broader community.

The genuine implication is experimental: table-top efforts to entangle micron-scale masses through gravity now have a precise noise threshold. Falling below that threshold without observing decoherence would effectively demonstrate that Newtonian gravity is entangling, providing indirect but powerful evidence that the gravitational field must be quantized. This reframes the quantization debate from philosophical preference to a testable, quantitative prediction.