Quantum Mechanics of Hyperbolic Metamaterials: Modeling of Quantum Time and Everett's Universal Wavefunction

TL;DR

This paper explores how hyperbolic metamaterials can model quantum mechanics and the Everett wavefunction in a (2+1)D spacetime, creating a laboratory analogy of a toy big bang and quantum superpositions.

Contribution

It introduces a novel use of hyperbolic metamaterials to emulate covariant quantum mechanics and the Everett formalism in an effective spacetime model.

Findings

Hyperbolic metamaterials can model quantum superpositions.

The toy big bang model demonstrates quantum superposition of parallel universes.

Experimental setup emulates covariant quantum mechanics in (2+1)D spacetime.

Abstract

Modern advances in transformation optics and electromagnetic metamaterials made possible experimental demonstrations of highly unusual curvilinear optical spaces, such as various geometries necessary for electromagnetic cloaking. Recently we demonstrated that mapping light intensity in a hyperbolic metamaterial may also model the flow of time in an effective (2+1) dimensional Minkowski spacetime. Curving such an effective spacetime creates experimental model of a toy big bang. Here we demonstrate that at low light levels this model may be used to emulate a fully covariant version of quantum mechanics in a (2+1) dimensional Minkowski spacetime. When quantum mechanical description is applied near the toy big bang, the Everett universal wave function formalism arises naturally, in which the wave function of the model universe appears to be a quantum superposition of mutually orthogonal parallel universe states.