[Paper Review] Quantum equivalence, the second law and emergent gravity

Dries Sels, Michiel Wouters|arXiv (Cornell University)|Nov 14, 2014

Quantum Mechanics and Applications1 references3 citations

TL;DR

This paper proposes that emergent gravity arises from the intrinsic structure of quantum mechanics, specifically through an area law in entanglement entropy during short-time unitary evolution in a natural configuration space. By showing that typical initial states and local Hamiltonians lead to slow relaxation and area-law scaling—mirroring gravitational correlations—it argues that gravity is not fundamental but emerges from quantum entanglement and the second law of thermodynamics.

ABSTRACT

Since the advent of quantum mechanics we have mainly been concerned with its predictions from the perspective of an external observer. This is in strong contrast to the theory of general relativity, where the physics is governed by the intrinsic properties of space-time. At the same time, the precise relation between space-time and quantum mechanics is still one of the greatest problems of theoretical physics. This immediately raises the question on the completeness of our understanding of quantum mechanics. Here we address the problem by making an intrinsic analysis of observables in generic quantum systems. We show that there is an extreme fine tuning problem for the emergence of physics from the Hilbert space dynamics. However, for any initial condition and Hamiltonian, there exists a special set of observables. We show that these observables are intimately linked to the natural configuration space in which an area law for the entanglement is inevitable. We argue that this implies emergent gravity.

Motivation & Objective

• To address the foundational problem of how classical spacetime and gravity emerge from quantum mechanics without relying on external observers.
• To resolve the fine-tuning problem in quantum thermalization by identifying a natural configuration space where initial states are separable and entanglement grows via an area law.
• To establish a connection between the second law of thermodynamics, entanglement entropy scaling, and the emergence of gravitational-like interactions.
• To propose that gravity is not a fundamental force but an entropic, emergent phenomenon arising from the structure of quantum evolution in Hilbert space.

Proposed method

• Perform an intrinsic analysis of observables in generic quantum systems, focusing on time evolution under unitary dynamics.
• Use the quantum equivalence principle to identify a special set of observables that are invariant under unitary transformations of energy eigenstates.
• Apply results from quantum quench dynamics to show that for any Hamiltonian and initial state, a natural configuration space exists where the initial state is separable.
• Demonstrate that under local Hamiltonian evolution, entanglement entropy scales with the area of the boundary, not the volume, for short times.
• Link the area law scaling to slow relaxation of local observables and the emergence of thermodynamic behavior.
• Argue that the resulting long-range correlations in entanglement mimic gravitational interactions, leading to emergent gravity without additional assumptions.

Experimental results

Research questions

• RQ1 Why do most observables in quantum systems rapidly thermalize, and what conditions are required for deviations from thermal equilibrium?
• RQ2 What determines the natural configuration space in which initial states are separable and entanglement follows an area law?
• RQ3 How does the second law of thermodynamics emerge from unitary quantum evolution without open system assumptions?
• RQ4 Can gravitational-like correlations arise purely from entanglement scaling in quantum systems without assuming gravity a priori?
• RQ5 What is the role of the initial state and Hamiltonian structure in enabling emergent spacetime and gravity?

Key findings

• For any initial state and Hamiltonian, there exists a natural configuration space in which the initial state is separable, enabling a universal description of quantum evolution.
• Under local Hamiltonian evolution, entanglement entropy scales with the area of the boundary for short times, a hallmark of gravitational systems.
• The area law for entanglement is a direct consequence of the initial state's separability and local dynamics, not ground state properties.
• The slow relaxation of local observables—governed by the Boltzmann time scale—results from dephasing of energy eigenstate components with random phases.
• The emergent long-range correlations in entanglement, governed by the area law, are interpreted as a signature of emergent gravity.
• Gravity is not a fundamental interaction but arises from the entropic constraints of quantum evolution, specifically the slow growth of entanglement entropy via area scaling.