Entangled Wavefunctions from Classical Oscillator Amplitudes

TL;DR

This paper demonstrates that classical oscillators can be constructed to replicate quantum wavefunction amplitudes, showing that classical systems can reproduce quantum coherence through an exact analogy.

Contribution

It establishes an equivalence between classical oscillator dynamics and quantum wavefunction amplitudes for N-level systems with real couplings.

Findings

Classical oscillators can mimic quantum coherence.

Quantum amplitudes can be represented by classical position and momentum variables.

The analogy provides a new perspective on quantum-classical correspondence.

Abstract

In the first days of quantum mechanics Dirac pointed out an analogy between the time-dependent coefficients of an expansion of the Schr\"odinger equation and the classical position and momentum variables solving Hamilton's equations. Here it is shown that the analogy can be made an equivalence in that, in principle, systems of classical oscillators can be constructed whose position and momenta variables form time-dependent amplitudes which are identical to the complex quantum amplitudes of the coupled wavefunction of an N-level quantum system with real coupling matrix elements. Hence classical motion can reproduce quantum coherence.