Nonlinear Schrödinger equation in foundations: summary of 4 catches

Abstract

Fundamental modifications of the standard Schrödinger equation by additional nonlinear terms have been considered for various purposes over the recent decades. It came as a surprise when, inverting Abner Shimony's observation of "peaceful coexistence" between standard quantum mechanics and relativity, N. Gisin proved in 1990 that any (deterministic) nonlinear Schrödinger equation would allow for superluminal communication. This is by now the most spectacular and best known anomaly. We discuss further anomalies, simple but foundational, less spectacular but not less dramatic.

5pp, 1photo, incorrect 4 lines replaced by a correct one, below (10)

References in corpus (2)

• Stochastic pure state representation for open quantum systems
• Stochastic extensions of the regularized Schrödinger-Newton equation

Cited by in corpus (10)

• The classical-quantum hybrid canonical dynamics and its difficulties with special and general relativity
• A model of quantum collapse induced by gravity
• Spontaneous Wave Function Collapse with Frame Dragging and Induced Gravity
• Schrödinger--Newton equation with spontaneous wave function collapse
• Nonlinear deterministic-chaotic collapse model -- preliminaries, philosophy, locality
• Causality violation of Schrödinger-Newton equation: direct test on the horizon?
• Linear and integrable nonlinear evolution of the qutrit
• Semiclassical world is one of infinite many cloneworlds in common spacetime
• What is the Gravitational Field of a Mass in a Spatially Nonlocal Quantum Superposition?
• Testing classical-quantum gravity with geodesic deviation