On the quantum mechanics of entropic forces (2502.17575v1)

Abstract: It was conjectured thirty years ago that gravity could arise from the entropic re-arrangement of information. In this paper, we offer a set of microscopic quantum models which realize this idea in detail. In particular, we suggest a simple mechanism by which Newton's law of gravity arises from extremization of the free energy of a collection of qubits or oscillators, rather than from the exchange of virtual quanta of a fundamental field. We give both a local and non-local version of the construction, and show how to distinguish a range of these entropic models from ordinary perturbative quantum gravity using existing observations and near-term experiments.

• The paper introduces a quantum model deriving gravitational interactions from free energy extremization as an alternative to graviton-mediated approaches.
• It employs both non-local and local qubit-based systems to recover Newton's law via thermal state evolution and entropic pressure dynamics.
• The study predicts measurable force noise and decoherence in quantum superpositions, providing clear experimental pathways to validate the model.

On the quantum mechanics of entropic forces

In this paper, the authors propose a quantum mechanical model that derives gravitational interactions from entropic principles rather than through traditional quantum field mediators like gravitons. They introduce microscopic models using qubits or oscillators to demonstrate how Newtonian gravity can emerge from the thermodynamic extremization of free energy in both local and non-local scenarios. The paper explores the differentiation of this entropic model, particularly in how it differs from standard perturbative quantum gravity, and provides details on how it might be distinguished experimentally.

Quantum Model of Entropic Forces

The paper presents two main models for realizing gravity as an entropic interaction:

1. Non-local Model: This construction uses a system of discrete qubits with frequencies dependent on the relative positions of massive bodies. The force arises from the entropic pressure mediating between these masses, similar to classical examples like the ideal gas law. Newton's law of gravity is retrieved by carefully structuring the mediator energy levels as functions of distance. The mediator qubits are assumed to be in a thermal state that evolves to extremize its free energy, resulting in an effective attractive force.

Figure 1

Figure 1: Experimental constraints on the free parameters. The shaded region on the left indicates parameter values for cases using $\zeta$ and $\lambda T^2$ excluded by cesium atom observations, indicating a measurable minimum decoherence rate of 1 Hz based on the rate of gravitational wave decoherence.

1. Local Model: Each massive object interacts quasi-locally with a lattice of qubits, with the interaction driven by local changes to qubit frequencies. The localized entropic forces result from the system's attempts at minimizing free energy surrounding each mass. The lattice acts like a bath, setting boundary conditions in space, and the resulting entropic force can be purely entropic, unlike the non-local model. The authors note this differs from traditional holographic models such as AdS/CFT, where the underlying mechanism involves consistent spin-2 graviton mediators.

Figure 2

Figure 2: Behavior of the entanglement witness illustrating the capacity for gravity to generate entanglement between massive bodies, crucial for interrogating entropic force models against quantum gravitation scenarios.

Experimental Consequences

The paper discusses potential experimental tests that could distinguish entropic force models from standard gravity:

• Force Noise: Entropic models inherently exhibit force noise due to their thermodynamic nature. The model predicts measurable fluctuating forces between test masses, offering a way to distinguish entropic gravity from noiseless virtual graviton-based interactions.
• Decoherence of Superpositions: The paper predicts that masses in quantum superpositions will experience decoherence due to the fluctuating entropic forces. This prediction offers a testable signature, especially in precision experiments like interferometry.
• Entanglement Generation: The presence of noise in the gravitational interaction suggests these models might limit the potential for entanglement between masses due to decoherence, contrasting with quantum gravity models that inherently support entanglement.

Conclusion

The paper presents an innovative framework for understanding gravitational interactions through the thermalization processes of microscopic systems, thus offering a potential alternative to gravitonic interactions. Future work is suggested to explore relativistic versions of these entropic models and to continue experimental advancements to challenge the quantum mechanical nature of gravity. The nuances of experimental constraints, noise characteristics, and potential entanglement tests are emphasized as critical pathways for validating or refuting the proposed entropic mechanics model.