Emergent Quantum Mechanics at the Boundary of a Local Classical Lattice Model

TL;DR

This paper introduces a classical lattice model with an extra dimension that reproduces quantum mechanics at its boundary, providing a new perspective on quantum emergence from classical systems.

Contribution

It presents a novel classical model with an additional dimension that approximates quantum mechanics, including Schrödinger's equation, and explains Bell nonlocality within a classical framework.

Findings

Model reproduces Schrödinger's equation at the boundary

Simulations validate analytical deviation estimates

Achieves Bell nonlocality through bulk information transfer

Abstract

We formulate a conceptually new model in which quantum mechanics emerges from classical mechanics. Given a local Hamiltonian $H$ acting on $n$ qubits, we define a local classical model with an additional spatial dimension whose boundary dynamics is approximately -- but to arbitrary precision -- described by Schr\"{o}dinger's equation and $H$. The bulk consists of a lattice of classical bits that propagate towards the boundary through a circuit of stochastic matrices. The bits reaching the boundary are governed by a probability distribution whose deviation from the uniform distribution can be interpreted as the quantum-mechanical wavefunction. Bell nonlocality is achieved because information can move through the bulk much faster than the boundary speed of light. We analytically estimate how much the model deviates from quantum mechanics, and we validate these estimates using computer simulations.