Nonlinear Quantum Theory, Development of the Superposition Principle and Possible Tests

TL;DR

This paper proposes extending quantum superposition and linear operators into a nonlinear framework, exploring implications for fundamental interactions, and discussing potential experimental tests of nonlinear quantum effects.

Contribution

It introduces a nonlinear extension of quantum theory, including nonlinear equations and interactions, and discusses their implications and possible experimental tests.

Findings

Nonlinear quantum equations like Klein-Gordon and Dirac are proposed.

Nonlinear effects may influence four fundamental interactions.

Potential tests include observing entropy decrease in isolated systems.

Abstract

First, we point out that the present applied superposition principle is linear, it must be developed into a generality. Next, the linear operators and equations should be developed nonlinearly. They will include nonlinear Klein-Gordon equation and Dirac equations, and corresponding Heisenberg equation. The quantum commutation and anticommutation should be developed. This theory may include the renormalization, which is the correction of Feynman rules of curved closed loops. We think the interaction equations are nonlinear. Many theories, models and phenomena are all nonlinear, for instance, soliton, nonabelian gauge field, and the bag model, etc. The superluminal entangled state, which relates the nonlocal quantum teleportation and nonlinearity, should be a new fifth interaction. Moreover, the NL effects exist possibly for four interactions, for single particle, for high energy, and for small space-time, etc. The relations among NL theory and electroweak unified theory, and QCD, and CP nonconservation, etc., are expounded. Finally, some known and possible tests are discussed. The NL theory relates the possible decrease of entropy in isolated system.