[Paper Review] Violation of Bell's inequality in fluid mechanics

Robert M. Brady, Ross Anderson|arXiv (Cornell University)|May 28, 2013

Quantum Mechanics and Applications15 references3 citations

TL;DR

This paper demonstrates that a classical fluid mechanical system—specifically, quasiparticle solutions to Euler’s equation for a compressible inviscid fluid—can violate Bell’s inequality due to long-range correlations in delocalized energy and angular momentum. The violation arises not from non-locality in interactions but from collective, non-local correlations in fluid motion, showing that quantum-like non-locality can emerge from purely local fluid dynamics.

ABSTRACT

We show that a classical fluid mechanical system can violate Bell's inequality because the fluid motion is correlated over large distances.

Motivation & Objective

• To investigate whether classical fluid dynamics can reproduce quantum-like non-local correlations without requiring non-local interactions.
• To demonstrate that Bell’s inequality can be violated in a system governed by local partial differential equations (Euler’s equation).
• To show that collective, delocalized fluid properties—such as energy and angular momentum—can generate correlations analogous to those in entangled quantum systems.
• To challenge the interpretation that Bell’s inequality violation necessitates non-local hidden variables or fundamental non-locality in physical theories.
• To explore the implications for quantum foundations by constructing a classical model that reproduces the spin correlation function of quantum mechanics.

Proposed method

• Modeling fluid dynamics using complex density fields ξ(x,t) to represent compressible, inviscid flow, with ρ = ρ₀(1 + Re(ξ)).
• Analyzing quasiparticle solutions ξₘₙ(x,t) derived from spherical Bessel functions and phase factors, which describe rotating, ring-like compressions and rarefactions in 3D fluid flow.
• Identifying bound pairs of quasiparticles with opposite chirality and angular momentum, ensuring finite total angular momentum despite long-range field contributions.
• Using quadratic terms in the fluid velocity (e.g., Bernoulli pressure ∝ u²) to model coupling between quasiparticles, enabling parametric excitation and energy transfer.
• Applying linearized perturbation theory to calculate transition rates between states, with coupling strength proportional to cos²(½θ) for rotation angle θ.
• Computing the correlation function of deflections in a Stern-Gerlach-like setup, deriving a correlation of −cosθ matching the quantum mechanical prediction.

Experimental results

Research questions

• RQ1 Can a classical fluid system with only local interactions violate Bell’s inequality due to non-local correlations in collective variables?
• RQ2 Do quasiparticle solutions in compressible, inviscid fluid flow exhibit correlations analogous to those in entangled quantum particles?
• RQ3 Is the violation of Bell’s inequality in this system due to non-local interactions or to delocalized conserved quantities like energy and angular momentum?
• RQ4 Can the quantum-like correlation function −cosθ be reproduced in a purely classical hydrodynamic model?
• RQ5 Does this model challenge the conclusion that Bell’s inequality rules out local hidden variable theories?

Key findings

• Quasiparticle solutions to Euler’s equation for compressible, inviscid fluids exhibit long-range correlations due to delocalized energy and angular momentum, violating Bell’s inequality.
• The correlation function of deflections in a fluid-based Stern-Gerlach-like setup is −cosθ, matching the quantum mechanical prediction for spin-½ particles.
• The violation arises not from non-local interactions but from collective, non-local properties of the fluid field, such as conserved angular momentum and energy distributed over large distances.
• The system maintains finite total angular momentum through the formation of bound pairs of quasiparticles with opposite chirality and rotation sense.
• Parametric coupling via quadratic terms (e.g., Bernoulli pressure) enables resonant transitions between states, with transition rates proportional to cos²(½θ), consistent with quantum measurement statistics.
• The model shows that Bell’s inequality violation does not logically entail non-locality in the fundamental dynamics, challenging the idea that quantum mechanics cannot be explained by local classical theories.