Chaos in a Nonlinear Wavefunction Model: An Alternative to Born's Probability Hypothesis

TL;DR

This paper investigates chaos in nonlinear wavefunction models, showing intrinsic randomness through positive Lyapunov exponents, offering an alternative explanation to Born's probability hypothesis based on sensitive dependence on initial conditions.

Contribution

The study analytically and numerically demonstrates chaos in nonlinear wavefunction models, proposing intrinsic randomness as an alternative to Born's probability hypothesis.

Findings

Positive Lyapunov exponent in small models indicating chaos

Extension of instability criterion to continuum models

Chaos may underlie quantum randomness, challenging traditional interpretations

Abstract

In a prior paper, the author described an instability in a nonlinear wavefunction model. Proposed in connection with the Measurement Problem, the model contained an external potential creating a ``classical'' instability. However, it is interesting to ask whether such models possess an intrinsic randomness -- even ``chaos" -- independent of external potentials. In this work, I investigate the criterion analytically and simulate from a small (``3 qubit") model, demonstrating that the Lyapunov exponent -- a standard measure of ``chaos" -- is positive. I also extend the instability criterion to models in the continuum. These results suggest that the boundary between classical and wavefunction physics may also constitute the threshold of chaos, and present an alternative to Max Born's ad hoc probability hypothesis: random outcomes in experiments result not from ``wave-particle duality" or ``the existence of the quantum," but from sensitive dependence on initial conditions, as is common in the other sciences.