Chapter 04 · A Theory of Everything/Beneath the Standard Model

Oppenheim's Post-Quantum Classical Gravity

2023 · Jonathan Oppenheim

Speculative

Gravity never becomes quantum. Spacetime stays classical and smooth, while quantum mechanics is modified to make the coupling work, at the cost of fundamental decoherence in both.

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In one sentence

Gravity stays classical forever, while quantum matter is modified to accommodate it. The cost is fundamental randomness in both.

The claim

Most approaches to quantum gravity try to quantize gravity itself, with gravitons and a quantized spacetime. Oppenheim takes the opposite direction. He keeps Einstein's theory of gravity classical, with smooth spacetime, and slightly modifies quantum mechanics so that quantum matter can consistently interact with a classical gravitational field. The price is a small built-in loss of predictability, an intrinsic randomness that shows up as decoherence.

This matters because it offers a testable alternative to quantizing gravity. Instead of waiting for Planck-scale physics, Oppenheim and collaborators argue that tabletop experiments using ultra-precise interferometers with small masses could detect gravity-induced decoherence or random jitter in test masses. If these effects appear with the predicted pattern, gravity is fundamentally classical. If they do not, the framework is ruled out.

The family stance

Familiar physics is not fundamental but emerges from a deeper substrate. Different proposals identify that substrate differently, but they share the claim that quantum mechanics and gravity are not the bottom layer of reality.

Predictions

Spatial superpositions of massive objects should lose quantum coherence at a rate set by their gravitational interaction, even without ordinary environmental noise.
Classical spacetime curvature should undergo tiny random fluctuations that show up as diffusion in the motion of test masses, putting a lower bound on the noise floor of ultra-sensitive position measurements.
Any consistent classical-gravity + quantum-matter theory must obey a quantitative trade-off: if gravitationally induced decoherence is small, spacetime diffusion must be large, and vice versa. Sufficiently precise experiments can exclude regions of parameter space.

Evidence

The framework provides a mathematically consistent, completely positive and trace-preserving dynamics for classical gravity coupled to quantum fields, avoiding known pathologies of naive semiclassical gravity (negative probabilities, superluminal signaling).
A companion line of work proves a general decoherence-diffusion trade-off for any classical-quantum hybrid dynamics, applied to gravity to produce distinctive experimental signatures.
The theory preserves Einstein's classical equations and remains compatible with all current large-scale gravitational tests, including solar system measurements, binary pulsars, and gravitational waves.
Existing interferometry data already constrain parts of the allowed parameter space, and several upcoming experiments are designed with this kind of effect in mind.

Counterpoints

Many quantum gravity researchers argue that gravity must be quantized to preserve linearity and superposition when gravitational fields are sourced by quantum matter, making any classical-gravity theory fundamentally suspect.
The modifications introduce fundamental stochasticity and extra decoherence; critics worry this risks conflict with high-precision quantum experiments unless carefully tuned.
The framework is flexible. Depending on decoherence and diffusion parameters, it can closely mimic standard quantum theory, making a clear experimental smoking gun harder to find.
It is unclear whether the model truly avoids all no-go arguments against classical-quantum couplings, or whether subtle issues reappear in more complex settings like cosmology and black holes.
The approach is new and not yet stress-tested by the broader community compared with established programs like loop quantum gravity, string theory, or asymptotic safety.

Variants in this family

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▸Go deeperTechnical detail with proper terminology

Oppenheim formulates a general classical-quantum dynamics where the joint state is a density operator over quantum degrees of freedom and a probability distribution over classical phase-space variables. Evolution follows a master equation that is linear in the density matrix, completely positive, and trace-preserving. General relativity's Hamiltonian and diffeomorphism constraints are imposed as symmetries.

Coupling quantum matter to a classical metric necessarily generates stochastic evolution of both the metric and the matter density matrix. This produces gravitationally induced decoherence at a rate tied to the classical-quantum coupling strength. It replaces the standard semiclassical prescription, where the classical Einstein tensor equals the expectation value of the quantum stress-energy tensor, which is known to be inconsistent in general.

The companion paper on gravitationally induced decoherence versus spacetime diffusion proves an inequality linking the decoherence rate for superpositions of mass distributions to the diffusion of the classical gravitational degrees of freedom. This gives a concrete parameter space probable by optomechanical interferometry and precision mass measurements.

Proposed experiments include micromechanical superposition tests where a mesoscopic mass is placed in a spatial superposition and coupled gravitationally to another mass. Deviations from standard quantum predictions, as excess decoherence or anomalous Brownian noise, would signal the framework and help distinguish it from fully quantum gravity or other collapse models.

References

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