⚛️ quantum physics

Classical theories of gravity produce entanglement

This paper challenges the prevailing view that observing entanglement between two masses via gravitational interaction proves the quantum nature of gravity, by arguing that classical gravitational theories can also generate such entanglement through local processes that transmit quantum information.

Original authors: Joseph Aziz, Richard Howl

Published 2026-07-02

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CC BY 4.0

Original authors: Joseph Aziz, Richard Howl

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The Big Question: Is Gravity Quantum?

For a long time, scientists have been trying to marry two giant theories: Quantum Mechanics (which rules the tiny world of atoms) and General Relativity (which rules the heavy world of gravity). They don't get along well.

To test if gravity is actually quantum, scientists proposed a famous experiment (originally by Richard Feynman). The idea is simple:

Take two heavy objects.
Put each one in a "quantum superposition" (think of them as being in two places at once, like a coin spinning on a table that is both heads and tails).
Let them interact only through gravity.
Check if they become entangled.

Entanglement is a spooky connection where two objects share a single fate; if you measure one, you instantly know the state of the other, no matter how far apart they are.

The Old Rule: Scientists believed that if two objects become entangled only through gravity, then gravity must be quantum. The logic was that a "classical" (non-quantum) force is like a strict postal service: it can only send classical letters (information like "I am here" or "I am there"). It cannot send quantum letters (superpositions). Therefore, a classical postal service cannot create a quantum connection (entanglement) between two people.

The Paper's New Discovery

Aziz and Howl argue that this "Old Rule" has a loophole. They claim that even if gravity is purely classical, it can still create entanglement.

They don't say gravity itself is quantum. Instead, they say the matter (the heavy objects) is quantum, and the way matter interacts with a classical gravity field is more complex than previously thought.

The Analogy: The Ghostly Messenger

Imagine two people, Alice and Bob, standing in two different rooms. They want to communicate, but they can only use a Classical Gravity System.

The Old View: The gravity system is like a rigid, solid wall. If Alice moves, the wall shifts slightly, and Bob feels it. But the wall is just a static object. It can't carry a "quantum message."
The New View (Aziz & Howl): The gravity system is more like a crowded hallway filled with invisible ghosts (virtual particles).
- Alice and Bob are made of quantum matter.
- Even though the "gravity field" (the hallway) is classical and doesn't change its rules, the ghosts inside it are quantum.
- When Alice is in a superposition (being in two spots at once), the ghosts she interacts with also have to be in two different "paths" to reach Bob.
- Because the ghosts are quantum, they can carry a quantum connection between Alice and Bob, even if the hallway itself is classical.

The authors show that these "ghosts" (which they call virtual matter propagators) travel between the objects. Because the objects are in superposition, the ghosts have to travel different distances depending on which "branch" of reality they are in. This difference in travel creates the entanglement.

The "Feynman Diagram" Explanation

In physics, scientists draw pictures called Feynman diagrams to show how particles interact.

Quantum Gravity: Usually, they draw a picture where two objects exchange a "graviton" (a quantum particle of gravity). This creates entanglement.
Classical Gravity (The Paper's Claim): The authors draw a new picture. Here, the objects don't exchange a graviton. Instead, they exchange virtual matter particles (like electrons or atoms) that are "borrowed" from the quantum field of the objects themselves.
- Think of it like this: Two people are talking. In the quantum view, they pass a quantum ball back and forth. In the classical view, the authors say they don't pass a ball; instead, they both reach out and shake hands with a third person (a virtual particle) who is standing in a superposition of locations. That handshake creates the link.

Why Does This Matter?

This changes how we interpret the upcoming experiments.

The "Smoking Gun" is Fuzzy: If an experiment shows that two masses become entangled, we can no longer say, "Aha! This proves gravity is quantum!"
- Why? Because, according to this paper, a classical gravity theory could also produce that same entanglement through these "ghostly" virtual matter processes.
The Scale Matters: The paper calculates that for very small masses (like the ones we can build in labs today), the "classical gravity" effect is tiny. So, for near-future experiments, seeing entanglement might still be a strong hint of quantum gravity.
The Future Challenge: However, if we use very heavy masses (approaching the "Planck mass"), the classical effect becomes huge. In that case, seeing entanglement would not prove gravity is quantum, because the classical theory could explain it just as well.

Summary

The Goal: Prove gravity is quantum by seeing if it can entangle two objects.
The Old Belief: Classical gravity is too "dumb" to create entanglement.
The New Finding: Classical gravity isn't dumb enough. Because matter is quantum, the interaction between matter and a classical gravity field involves "virtual matter" particles that can create entanglement.
The Result: Observing entanglement is no longer a guaranteed proof that gravity is quantum. We need to be much more careful with our experiments and the size of the masses we use to tell the difference between a "quantum gravity" world and a "classical gravity with quantum matter" world.

In short: The paper doesn't say gravity is classical. It says that even if it were classical, it could still trick us into thinking it's quantum by using the quantum nature of the matter it interacts with.

Problem Statement
The unification of gravity and quantum mechanics remains a central open question in physics. While electromagnetism and the nuclear forces have been successfully integrated with quantum theory, standard quantization methods fail for gravity. A proposed route to experimentally test the quantum nature of gravity involves placing massive objects in a spatial quantum superposition and observing if they become entangled through their gravitational interaction. Current theoretical arguments, based on theorems regarding Local Operations and Classical Communication (LOCC), suggest that if two systems become entangled solely via a classical gravitational interaction, this would be impossible. Consequently, the observation of such entanglement is widely regarded as unambiguous evidence that gravity must be a quantum field capable of transmitting quantum information (i.e., mediated by virtual gravitons). The prevailing assumption is that a classical gravitational field acts only as a classical channel, incapable of generating entanglement between quantum systems.

Methodology
The authors challenge the assumption that classical gravity can only transmit classical information by analyzing the interaction within the framework of Quantum Field Theory (QFT). Rather than treating matter as simple point particles or ignoring the quantum nature of the matter fields themselves, the paper treats matter using a massive complex scalar field in QFT.

Theoretical Framework: The authors compare perturbative quantum gravity (where the metric is quantized) with perturbative classical gravity (where the metric remains a classical field, $h_{\mu\nu}$ , but matter is quantized). They utilize Feynman diagrams and Wick contractions to calculate the evolution of the quantum state of two massive objects in superposition.
Interaction Hamiltonians:
- Quantum Gravity: The interaction involves the exchange of virtual gravitons and virtual matter particles.
- Classical Gravity: The interaction Hamiltonian is derived from linearized general relativity with a classical metric, but the matter fields ( $\hat{\phi}$ ) remain quantized. The interaction is local, involving the coupling of the classical gravitational potential to the quantum energy-momentum tensor of the matter.
Calculation of Entanglement: The authors calculate the transition amplitudes for the system to evolve from an initial product state to a final entangled state. They perform calculations up to the fourth order in the Dyson series.
- In the quantum gravity case, entanglement arises at the second order via virtual graviton exchange.
- In the classical gravity case, the authors demonstrate that while second-order processes involving only the classical field do not generate entanglement (producing only local phases), fourth-order processes involving virtual matter propagators do generate entanglement.
Experimental Model: The analysis is applied to a version of Feynman's thought experiment (similar to the Bose-Marletto-Vedral proposal), where two spherical mass distributions are placed in a superposition of two locations. The authors calculate the specific amplitudes for entanglement generation under both quantum and classical gravity assumptions, considering factors such as mass, separation distance, and interaction time.

Key Contributions

Virtual Matter Mechanism: The primary contribution is the identification of a mechanism by which a classical gravitational interaction can generate entanglement. The authors argue that because matter obeys QFT, the interaction between a classical gravitational field and quantum matter involves the propagation of virtual matter particles. These virtual matter particles can travel different distances in different branches of the superposition, effectively acting as a quantum mediator that entangles the two massive objects.
Refutation of LOCC Exclusivity: The paper argues that previous theorems ruling out entanglement via classical gravity relied on a restrictive view of the interaction, considering only the mediation of the gravitational field (gravitons) and ignoring the contribution of virtual matter propagators inherent in QFT. By including these matter propagators, the interaction is no longer strictly a "Local Operations and Classical Communication" (LOCC) process in the sense that prevents entanglement.
Scaling Analysis: The authors provide a detailed scaling analysis comparing the strength of the entanglement generated by the classical gravity process (via virtual matter) versus the standard quantum gravity process (via virtual gravitons).

Results

Entanglement Generation: The calculations show that a classical gravitational interaction, when treated with quantum matter fields, can generate entanglement between two massive objects in superposition. This occurs at the fourth order of the perturbation series, mediated by virtual matter propagators.
Magnitude of Effect: The strength of this classical gravity-induced entanglement depends strongly on the mass ( $M$ $M$ ) and interaction time ( $t$ $t$ ).
- For small masses (e.g., $M \approx 10^{-14}$ kg) and long times, the classical effect is significantly smaller than the quantum gravity effect.
- However, for larger masses (approaching the Planck mass, $M_p \approx 10^{-8}$ kg) or specific experimental configurations, the classical gravity effect can become substantial (e.g., $\vartheta \approx 0.1$ ).
Implication for Experiments: The results imply that the mere observation of entanglement in such experiments is not sufficient to prove the quantum nature of gravity if the masses and times are in a regime where the classical virtual matter effect is significant. Distinguishing between the two requires operating in a parameter regime where the classical effect is negligible compared to the quantum effect.

Significance
The paper claims that the observation of gravitationally induced entanglement is not an absolute "witness" for the quantization of gravity unless the experimental parameters are carefully chosen to suppress the classical virtual matter contribution. The authors argue that:

Theoretical Nuance: The assumption that classical gravity cannot transmit quantum information is incorrect when matter is treated fully within QFT. The "quantumness" of the interaction can arise from the matter sector (virtual matter) even if the gravitational field remains classical.
Experimental Design: Future experiments aiming to test the quantum nature of gravity must account for this classical mechanism. To definitively evidence quantum gravity, experiments must operate in a regime (specifically regarding mass and time) where the classical virtual matter contribution is negligible compared to the quantum graviton contribution.
Local Processes: The paper emphasizes that this entanglement generation occurs through physically local processes (virtual matter propagation), respecting the principles of locality and causality, and does not require non-local "action-at-a-distance" mechanisms often proposed in alternative classical gravity models.

In summary, the paper argues that classical gravity, when coupled to quantum matter fields, possesses the capacity to generate entanglement through virtual matter processes. This challenges the interpretation of current and near-future experiments, suggesting that entanglement alone is not a definitive proof of quantum gravity without a rigorous exclusion of the classical virtual matter contribution.