Semi-classical Gravity Theories Demonstrate Absence of Entanglement Between Massive Systems, Contrasting Newtonian Predictions

The question of whether gravity can induce entanglement between massive objects represents a fundamental test of the boundary between quantum mechanics and general relativity, and recent proposals suggest an experimental approach to investigate this connection. Ward Struyve from KU Leuven, Belgium, and colleagues demonstrate that certain semi-classical theories of gravity, which treat gravity classically within a quantum framework, predict no entanglement between massive systems, despite the potential for entanglement predicted by standard Newtonian gravity. The team’s analysis encompasses models including the Newton-Schrödinger model, the Bohmian analogue, and a related interpolating model, revealing a key distinction between these approaches and those that allow for gravitational entanglement. This research significantly advances our understanding of how gravity and quantum mechanics might interact, and clarifies the theoretical landscape for interpreting potential experimental results designed to detect gravitationally induced entanglement.

These models were analysed in the context of a proposed experiment and contrasted with the standard Newtonian potential, which does generate entanglement. One of the central open problems in theoretical physics is the reconciliation of quantum theory with gravity, requiring that the classical framework of general relativity be modified or extended to accommodate quantum matter.

Entangling Macroscopic Objects via Quantum Gravity

This research investigates the possibility of experimentally demonstrating quantum effects in gravity, specifically by creating and detecting entanglement between two massive objects. The central idea is that if gravity is fundamentally quantum, even macroscopic objects should exhibit quantum behaviour, like entanglement. The authors explore different theoretical models that predict how this entanglement might manifest and how it could be detected in a laboratory setting. The research focuses on a theoretical analysis of a proposed experiment involving two massive objects, such as mirrors, placed in close proximity.

The goal is to create entanglement between these objects by exploiting the quantum nature of gravity. The proposed method involves placing the mirrors into a superposition of positions, and the interaction between their gravitational fields is expected to create entanglement. Scientists propose using an entanglement witness, a mathematical tool, to detect the presence of entanglement, which is negative if entanglement is present. Detailed calculations predict the behaviour of the entanglement witness for different theoretical models, analysing how it depends on parameters such as the mass of the objects, the distance between them, and the time.

The authors compare the predictions of different models to determine which are most consistent with experimental observations. The authors derive expressions for the entanglement witness for different theoretical models, demonstrating that it can be used to discriminate between them. For example, the witness has a different form for the Schrödinger-Newton equation than for a spontaneous localization model. They acknowledge that decoherence, the loss of quantum coherence due to environmental interactions, is a major challenge for this experiment, estimating that significant decoherence effects occur after about two seconds. The experiment is sensitive to parameters such as the mass of the objects and the distance between them, requiring precise control over these parameters to achieve a successful experiment. Importantly, a purely separable potential will not generate entanglement, meaning that detecting a negative witness would provide evidence for non-classical gravity.

Gravitational Potentials Prevent Massive Entanglement

Scientists investigated whether gravitational interactions can induce entanglement between massive systems. The research team examined several semi-classical models, treating gravity classically through potential terms within the Schrödinger equation, and demonstrated that these models do not generate entanglement. Specifically, the team analysed the Newton-Schrödinger model, the Bohmian analogue, and an interpolating model, finding that none of these produce entanglement. The analysis focused on the form of the gravitational potential, revealing that an additively separable potential prevents the generation of entanglement.

If the potential can be expressed as the sum of individual particle potentials, an initially separable wave function will remain separable over time. The team rigorously demonstrated this using both direct analysis of the Schrödinger equation and by examining the Dyson series solution, confirming that the degree of entanglement remains constant even with an initially entangled state. Experiments revealed that only the standard Newtonian potential generates entanglement, while the Newton-Schrödinger and Bohmian potentials, as well as the interpolating model, are additively separable. Despite the absence of entanglement generation, the team noted that systems still exhibit dependencies, potentially allowing for faster-than-light signalling, challenging assumptions about locality in gravitational interactions.

To test these predictions, the team proposed an experiment involving two massive systems, each in a superposition of two states, separated by a distance with a spatial separation. Calculations show that the dynamics of the system will produce phase shifts. The team’s work establishes a clear link between the form of the gravitational potential and the potential for generating entanglement, offering a pathway for experimental verification of these theoretical predictions.

Semi-Classical Models Fail to Entangle Massive Systems

This research rigorously examines the potential for generating entanglement between massive systems using semi-classical models. Scientists explored several models, including the Newton-Schrödinger model and its Bohmian analogue, analysing their ability to produce entanglement in a proposed experimental setup. The team demonstrated that these semi-classical models, despite their mathematical similarities to quantum descriptions, fundamentally fail to generate entanglement, contrasting with predictions based on standard Newtonian potentials which do exhibit this property. The investigation involved detailed calculations of the wave function evolution and the use of an entanglement witness to determine the presence or absence of entanglement.

Researchers found that previously reported entanglement in one model stemmed from an incorrect application of the dynamics, highlighting the importance of precise mathematical treatment. The study acknowledges that accurate modelling of measurement processes within the Newton-Schrödinger framework requires either a collapse postulate or a spontaneous collapse mechanism, and that deviations from the Born rule may occur in the Bohmian model, though these are likely small. This work provides a clear distinction between classical and quantum behaviours, and establishes limits on the ability of semi-classical models to reproduce quantum entanglement.