Outline of a Nonlinear, Relativistic Quantum Mechanics of Extended Particles

Abstract

A quantum theory of intrinsically extended particles similar to de Broglie's Theory of the Double Solution is proposed. A rational notion of the particle's extension is enthroned by realizing its internal structure via soliton‐type solutions of nonlinear, relativistic wave equations. These droplet‐type waves have a quasi‐objective character except for certain boundary conditions which may be subject to stochastic fluctuations. More precisely, this assumption amounts to a probabilistic description of the center of a soliton such that it would follow the conventional quantum‐mechanical formalism in the limit of zero particle radius. At short interaction distances, however, a promising nonlinear and nonlocal theory emerges. This model is not only capable of achieving a conceptually satisfying synthesis of the particle‐wave dualism, but may also lead to a rational resolution of epistemological problems in the quantum‐theoretical measurement process. Within experimental errors the results for, e.g., the hydrogen atom can be reproduced by appropriately specifying the nature of the nonlinear self‐interaction. It is speculated that field theoretical issues raised by such notions as identical particles, field quantization and renormalization are already incorporated or resolved by this nonlocal theory, at least in principle.