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

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 -- evenchaos" -- 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 ofchaos" -- 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" orthe existence of the quantum," but from sensitive dependence on initial conditions, as is common in the other sciences.