Study Confirms Classical Gravity Does Not Entangle Quantized Matter Fields, Refuting Claims from Nature 646, 813(2025)

The question of how gravity interacts with the quantum world remains one of the most profound challenges in modern physics, and recent claims suggested that even classical gravity could induce entanglement in quantum matter fields. Lajos Diósi, from the Wigner Research Center for Physics and Eötvös Loránd University, challenges this idea, demonstrating that classical gravity does not, in fact, entangle quantized matter fields. This work directly addresses a claim made by Aziz and Howl, and through careful recalculation of their example, establishes that no such entangling effect exists. This finding is significant because it clarifies the relationship between gravity and quantum mechanics, and reinforces the need for a fully consistent theory of quantum gravity.

Specifically, the study addresses the assertion that classical theories of gravity cause an exchange of virtual particles between spatially separated components of a second-quantized matter field, leading to entanglement between those components. The team demonstrates that a perturbative calculation presented in another work contradicts their own exact, non-perturbative results, which definitively rule out the proposed entangling effect. The analysis begins by considering an initial state of a boson field with mass, mathematically defined to represent unentangled particles.

Fock State Preparation and Initial Wavefunction Definition

Scientists define spatially separated quantum states over vacuum states, using mathematical operators to describe the creation of particles. Researchers examined the claim that coupling to classical gravity transforms a product state into an entangled state, a claim based on complex calculations and seemingly contradicting the established understanding of semiclassical gravity. The team determined the exact form of the initial unentangled state, providing a precise starting point for their analysis. Consequently, the initial state is defined using mathematical expressions representing unentangled particles.

The time-dependent solution of the system is then expressed mathematically, describing how the particles evolve over time. The wave functions governing the particles evolve according to the Klein-Gordon equation within the classical spacetime determined by the semiclassical Einstein equation. Assuming non-relativistic initial conditions, the semiclassical Einstein equation simplifies to the Poisson equation, describing the gravitational potential. The Klein-Gordon equation then reduces to a non-linear Schrödinger equation, describing the evolution of the particles. As long as the wave functions remain largely separate, the exact solution maintains its factorized form, indicating a lack of entanglement. Researchers conclude that the initial unentangled state remains unentangled, consistent with the understanding of semiclassical gravity, where classical gravity does not induce entanglement in quantized matter. This finding contrasts with previous claims and suggests that earlier results may have exceeded the limits of their validity.

Boson Fields Remain Unentangled by Gravity

Recent work has challenged the notion that classical gravity can induce entanglement in quantized matter, prompting a detailed re-examination of the underlying physics. Researchers rigorously investigated the claim that interactions with classical gravity could create entanglement between spatially separated boson fields, and their analysis demonstrates that this effect does not occur. The team focused on a specific initial state consisting of four boson fields, examining how their evolution might lead to entanglement. The study involved a precise recalculation of the relevant quantum field theory, revealing a discrepancy with previous findings.

Scientists derived an exact solution for the time-dependent evolution of the boson fields, demonstrating that the initial unentangled state remains unentangled even under the influence of classical gravity. This outcome directly contradicts the assertion that classical gravity generates entanglement, aligning with established principles of semiclassical gravity. The team’s calculations show that the time-dependent boson states evolve predictably, maintaining their separation and preventing the formation of entangled pairs. Specifically, the researchers demonstrated that the exact solution can be expressed as a product of individual boson states, each evolving independently in time.

This factorization confirms that the initial unentangled state remains unentangled throughout the evolution, regardless of the gravitational interaction. The analysis employed the Klein-Gordon equation to describe the evolution of the boson wave functions, coupled with the semiclassical Einstein equation to account for the gravitational field. The results indicate that the gravitational field, as described by the Poisson equation, does not introduce any correlations between the spatially separated boson fields.

Classical Gravity Does Not Entangle Quantum Matter

This research rigorously examines the claim that classical gravity can induce entanglement between quantum matter, a proposition recently put forward by other scientists. Through detailed field-theoretic calculations, the authors demonstrate that, contrary to this claim, classical gravity does not generate entanglement. Their analysis reveals that the evolution of quantum states within a classical gravitational field maintains a product state, meaning the particles remain unentangled. This finding aligns with established understanding of semiclassical gravity, where gravitational effects are determined by expectation values rather than individual quantum states.

The team’s approach involved solving the Klein-Gordon equation and the Poisson equation to model the interaction between quantum matter and a classical gravitational field. Importantly, they found that the standard approximations used in these calculations remain valid, suggesting the discrepancy with previous work likely stems from the application of these approximations beyond their limits. While acknowledging the complexity of demonstrating the absence of entanglement, the authors present a concise and clear derivation supporting their conclusion. This work contributes to the ongoing investigation into the interplay between quantum mechanics and gravity, clarifying the conditions under which entanglement may or may not arise from gravitational interactions.