Gravity’s Limits: Why Classical Physics Can’t Entangle

Author: Denis Avetisyan

New research shows that classical gravity, as described by Newton-Cartan theory, fundamentally cannot mediate entanglement between particles.

The study demonstrates that any observed entanglement in gravitational interaction experiments must originate from non-classical mechanisms if gravity itself is classical.

Recent proposals to probe the quantum nature of gravity through gravitationally induced entanglement (GIE) remain contentious, often hinging on interpretations of Hamiltonian formalisms. This paper, ‘A demonstration that classical gravity does not produce entanglement’, utilizes a Newton-Cartan analysis to rigorously demonstrate that classical gravity cannot mediate entanglement between spatially separated massive particles. Consequently, any observed entanglement in GIE experiments, if gravity is indeed classical, must originate from a mechanism beyond purely gravitational interactions. This finding prompts a critical re-evaluation of experimental setups and theoretical frameworks used to investigate the interplay between gravity and quantum information – could alternative, non-gravitational forces be responsible for observed correlations?

The Limits of Classical Understanding

General Relativity, Einstein’s masterful theory describing gravity as the curvature of spacetime, has consistently proven accurate in predicting large-scale phenomena – from the bending of light around massive objects to the orbital precession of Mercury. However, this same framework encounters profound difficulties when attempting to integrate with the principles of quantum mechanics, the theory governing the behavior of matter at the atomic and subatomic levels. The core of the conflict lies in their fundamentally different descriptions of reality: General Relativity treats spacetime as smooth and continuous, while quantum mechanics posits a discrete, probabilistic universe. Attempts to reconcile these viewpoints – to create a theory of quantum gravity – consistently yield mathematical inconsistencies, such as infinite values in calculations, suggesting a breakdown of the theory at extremely small distances – the Planck scale, approximately $10^{-35}$ meters. This impasse isn’t merely a mathematical puzzle; it represents a foundational crisis in physics, hindering the development of a complete understanding of the universe, particularly concerning phenomena like black holes and the very early universe where both gravity and quantum effects are dominant.

Even with the refinements of Newtonian dynamics and Einstein’s General Relativity, classical gravity falters when confronted with the universe’s most extreme environments. Observations of black holes, neutron stars, and the very early universe reveal phenomena that these theories simply cannot adequately describe. For instance, singularities – points of infinite density predicted at the heart of black holes – represent a breakdown in the mathematical framework, suggesting the theory is incomplete. Furthermore, attempts to model the universe’s rapid expansion immediately after the Big Bang necessitate introducing concepts beyond the scope of classical gravity. These limitations aren’t merely mathematical curiosities; they signal a fundamental need for a more comprehensive theory-one that potentially merges gravity with the principles of quantum mechanics-to accurately portray reality at these extraordinary scales, where the very fabric of spacetime is pushed to its limits.

Current gravitational models, built upon classical foundations, operate under the assumption of locality – that is, an object is only directly influenced by its immediate surroundings. However, recent observations hint at a more nuanced relationship, suggesting that gravitational interactions may, in fact, be mediated by quantum entanglement-a phenomenon where particles become linked and instantaneously share states, regardless of distance. Calculations demonstrate that within the confines of classical gravity, entanglement plays no discernible role in mediating gravitational forces; the predicted interactions simply do not align with experimental results when entanglement is factored in. This discrepancy implies that a complete understanding of gravity requires moving beyond classical descriptions and embracing the principles of quantum mechanics, potentially revealing a deeper connection between gravity and the fundamental quantum properties of spacetime and matter. The absence of entanglement within these established models poses a significant challenge, necessitating a re-evaluation of the core assumptions underpinning our understanding of how gravity functions at the quantum level.

Beyond Simple Mass: The Newton-Cartan Extension

The Newton-Cartan formulation represents an extension of classical gravity beyond the standard Newtonian model by introducing the concept of spacetime torsion and non-metricity. While Newtonian gravity describes gravitational interactions as resulting from mass, the Newton-Cartan theory allows for a more generalized description incorporating intrinsic properties of spacetime itself. This is achieved through the use of a spacetime manifold equipped with an affine connection – the $ \Gamma^{\lambda}_{\mu\nu}$ – which need not be symmetric, unlike the Levi-Civita connection used in General Relativity. This asymmetry introduces torsion, and the allowance for a non-metric connection introduces non-metricity, both of which can contribute to the gravitational force. Consequently, the Newton-Cartan framework provides a classical description that recovers Newtonian gravity in certain limits but also more closely resembles the geometric structure found in General Relativity, providing a bridge between the two theories.

The Newton-Cartan formulation facilitates the conceptualization of gravitational interactions through the exchange of discrete quanta, termed Newton-Cartan Gravitons. Unlike the strictly geometric interpretation of gravity in General Relativity, this framework allows for a particle-based understanding where the gravitational force arises from the emission and absorption of these massless spin-2 bosons. The theory predicts these gravitons mediate the force between massive objects, analogous to the role of photons in electromagnetic interactions. While the graviton remains a hypothetical particle, the Newton-Cartan structure provides a mathematically consistent space to model its behavior and potential detection, allowing for the calculation of gravitational scattering amplitudes and providing a basis for investigating quantum gravitational phenomena within a classically-rooted framework. The associated field theory, though complex, allows for a perturbative expansion of gravitational interactions based on the exchange of these $N$-Cartan gravitons.

The Newton-Cartan formulation extends classical gravity beyond the limitations of point-particle interactions, allowing for the investigation of quantum phenomena within a non-relativistic, classically-based structure. This approach considers gravitational interactions mediated by what are termed Newton-Cartan Gravitons, providing a framework to explore potential quantum effects without immediately invoking the full complexity of General Relativity. However, recent analyses demonstrate that this framework, when considered in isolation – meaning without additional quantum postulates or modifications – is insufficient to generate quantum entanglement; while it permits the study of quantum-like behaviors, it does not inherently produce the correlations characteristic of entangled systems. This suggests that entanglement, if present in gravitational interactions, requires mechanisms beyond those solely provided by the Newton-Cartan formulation itself.

Quantizing Gravity: The Quantum Newton-Cartan Approach

The Quantum Newton-Cartan (QNC) formulation represents an extension of the classical Newton-Cartan theory of gravity into the quantum domain. This approach treats gravity not as spacetime curvature, but as a manifestation of the torsion and nonmetricity of spacetime, which are then quantized. Specifically, QNC utilizes a Hamiltonian formulation to describe the dynamics of these spacetime properties and their associated gravitational fields. This allows for the investigation of quantum gravitational interactions by applying standard quantum mechanical methods to the gravitational field itself, effectively providing a framework to analyze gravitational phenomena at the quantum level and explore potential deviations from classical General Relativity. The resulting framework allows for the calculation of quantum corrections to classical gravitational effects and provides a basis for investigating the interplay between gravity and quantum entanglement.

The Hamiltonian formalism provides a framework for modeling gravitational interactions by defining the total energy of the system, expressed as the sum of kinetic and potential energies. Within this approach, gravitational phenomena can be analyzed by treating particles as quantum mechanical entities and deriving equations of motion from the Hamiltonian. Specifically, the interaction terms within the Hamiltonian describe the gravitational force between particles, allowing for the investigation of how entanglement-a quantum correlation between particles-affects these interactions. By examining the Hamiltonian’s evolution under various entangled states, we can determine if entanglement can serve as a mediating force in gravity, or if gravitational interactions remain fundamentally local despite quantum correlations between interacting bodies. This allows for the quantitative exploration of entanglement’s role, or lack thereof, in the dynamics of gravitational systems and tests the limits of the Local Observer Correspondence Condition (LOCC).

Analysis within the Quantum Newton-Cartan framework indicates that entanglement cannot function as a mechanism to induce gravitational force. This finding directly challenges the Local Operations and Classical Communication (LOCC) Assumption, which posits that entanglement alone is sufficient to mediate interactions, including gravity. Specifically, calculations demonstrate that attempting to leverage entanglement to create or modify gravitational fields within this model yields no observable effect. Consequently, the results suggest that alternative theoretical approaches beyond entanglement-mediated forces are necessary to fully describe quantum gravity and reconcile it with observed gravitational phenomena.

Probing the Quantum Realm: The GIE Experiment Protocol

The Gravitational Information Entanglement (GIE) experiment proposes a direct test of quantum gravity through the observation of entanglement between two massive quantum systems physically separated in space. This innovative approach bypasses the traditional challenges of detecting quantum gravitational effects, which are typically masked by classical gravity at macroscopic scales. The protocol centers on meticulously controlling and measuring the quantum states of these massive objects – potentially utilizing superconducting circuits or levitated nanoparticles – and searching for correlations that would violate classical predictions. By establishing entanglement, the experiment aims to demonstrate that gravity, at a fundamental level, is not merely a geometric force but is intrinsically linked to the principles of quantum information, opening a pathway to reconcile Einstein’s theory of general relativity with quantum mechanics.

The Gravitational Information Entanglement (GIE) experiment draws heavily on the established framework of Quantum Information Theory to probe the subtle interplay between gravity and quantum mechanics. Traditionally, gravitational interactions have been understood through classical physics, predicting specific relationships between mass, distance, and force. However, if gravity, like other fundamental forces, possesses a quantum nature, deviations from these classical predictions should emerge when examining entangled particles. This experiment seeks to detect such deviations by meticulously measuring the correlations between spatially separated massive objects, treating gravity not simply as a curvature of spacetime, but as a potential carrier of quantum information. By applying concepts like quantum entanglement and coherence to gravitational systems, the GIE experiment offers a novel approach to testing the limits of classical gravity and potentially revealing the quantum underpinnings of this fundamental force.

Detailed calculations within the Gravitational Information Enhancement (GIE) experiment reveal a fundamental limitation regarding the induction of quantum entanglement. The total energy imparted to a particle throughout the experiment’s duration, mathematically represented as $m(ϕ′-ϕ)*T$, is demonstrably insufficient to generate the degree of entanglement necessary for observing measurable quantum gravitational effects. Here, $m$ signifies the particle’s mass, $(ϕ′-ϕ)$ represents the change in gravitational potential experienced by the particle, and $T$ denotes the experiment’s total runtime. This finding indicates that, within the currently defined parameters of the GIE protocol, the energy scale is too low to overcome classical gravitational interactions and reveal the subtle quantum correlations predicted by some theories of quantum gravity. Further refinement of the protocol, or exploration of alternative methodologies, will be necessary to reach the energy thresholds required for successful detection.

Towards a Complete Understanding of the Universe

A complete understanding of the universe hinges on reconciling the seemingly disparate realms of gravity and quantum mechanics. Current physical models excel at describing either the very large – governed by Einstein’s theory of General Relativity – or the very small – described by the laws of quantum mechanics – but break down when attempting to unify them. Theoretical frameworks like Quantum Newton-Cartan offer innovative approaches, attempting to quantize gravity while retaining aspects of classical spacetime. Complementing these theoretical efforts are experimental protocols, such as the Gravitational Interaction of Entangled Particles (GIE) protocol, designed to probe the connection between entanglement and gravity. These investigations aim to determine if gravity can mediate or influence quantum entanglement, potentially revealing crucial insights into the fundamental nature of spacetime and the elusive theory of quantum gravity, which promises a more complete and consistent picture of the cosmos.

Reconciling the well-established framework of classical spacetimes – those described by Einstein’s theory of general relativity – with the probabilistic and often counterintuitive principles of quantum gravity presents a formidable challenge in modern physics. Current investigations aren’t simply about refining existing models, but necessitate genuinely innovative theoretical approaches that move beyond traditional perturbative methods. Researchers are actively exploring modified theories of gravity, such as those incorporating extra dimensions or non-commutative geometries, alongside approaches like loop quantum gravity and string theory, each striving to provide a consistent description of spacetime at the Planck scale. These efforts often involve examining the very nature of spacetime, questioning whether it emerges from more fundamental, discrete structures rather than being a smooth, continuous entity, and require developing novel mathematical tools to handle the complexities arising from quantum effects in strong gravitational fields. The pursuit aims to construct a theory capable of explaining phenomena like black holes and the universe’s earliest moments, where both quantum mechanics and gravity are undeniably significant.

Recent investigations into the fundamental relationship between gravity and quantum entanglement have yielded a surprising result: within the defined experimental parameters, gravitational fields do not appear capable of inducing entanglement between particles. This finding challenges certain theoretical frameworks positing gravity as a direct mediator of quantum correlations and necessitates a reevaluation of existing models attempting to unify quantum mechanics with general relativity. While the explored parameters represent a specific scope of investigation, the absence of induced entanglement suggests alternative mechanisms may be responsible for linking gravity and the quantum realm, potentially involving subtle interactions beyond the scope of current theoretical predictions. Further research focusing on modified gravity theories, exploring the role of spacetime curvature beyond Newtonian approximations, and investigating potential connections to other fundamental forces are now crucial to progress toward a complete theory of quantum gravity.

The pursuit of gravitational entanglement, as detailed in this work, often feels like building an elaborate clockwork mechanism to tell the time with a sundial. The researchers meticulously demonstrate, within the Newton-Cartan framework, that classical gravity simply lacks the necessary gears to induce entanglement. It’s a surprisingly clean result, stripping away layers of potential complexity to reveal a fundamental limitation. As Max Planck observed, “A new scientific truth does not triumph by convincing its opponents and proving them wrong. Eventually the opponents die, and a new generation grows up that is familiar with it.” This study doesn’t necessarily disprove gravitational entanglement, but it clarifies the boundaries – the point where further embellishment becomes unproductive, and a different approach is required. The elegance lies in recognizing what gravity, in its classical form, cannot do.

The Simplest Explanation

The null result detailed herein – that classical gravity, specifically as described by Newton-Cartan theory, fails to induce entanglement – is not a defeat, but a clarification. The pursuit of gravitational entanglement mediation was, perhaps, a misdirection. The question was not whether gravity can entangle, but whether it needs to. The absence of evidence, while not evidence of absence, does necessitate a shift in focus. Future Gravitational Induced Entanglement (GIE) experiments should prioritize isolating and characterizing alternative mechanisms – those not predicated on classical gravitational mediation – to account for any observed entanglement.

The enduring challenge remains the reconciliation of quantum mechanics and general relativity. However, this work suggests that a solution may not lie in modifying gravity itself, but in understanding the subtle quantum processes that appear to be mediated by it. To claim gravity as the agent, when it merely provides a backdrop, is a violation of parsimony. The simplest explanation remains the most probable.

Further investigation should concentrate on refining experimental techniques to distinguish between genuine gravitational effects and spurious correlations. The pursuit of complexity is a distraction; the goal is not to find entanglement in gravity, but to understand entanglement, irrespective of gravitational influence. A focus on fundamental quantum limits, rather than elaborate theoretical constructs, will likely prove more fruitful.

Original article: https://arxiv.org/pdf/2511.19242.pdf

Contact the author: https://www.linkedin.com/in/avetisyan/