Discussion Overview
The discussion revolves around the existence of nonlinear Schrödinger equations, specifically the Gross-Pitaevskii equation, in the context of quantum mechanics (Q.M.), which is traditionally viewed as a linear theory. Participants explore the implications of this nonlinearity and its relationship to quantum field theory.
Discussion Character
- Debate/contested, Conceptual clarification, Technical explanation
Main Points Raised
- Some participants note that while Q.M. is fundamentally a linear theory, nonlinear Schrödinger equations can arise as approximations from quantum field theory.
- One participant expresses concern that if linearity is violated, it could lead to non-reversible processes, potential cloning of quantum states, and faster-than-light signaling.
- Another participant asserts that the Schrödinger equation remains exact within quantum field theory, suggesting that any nonlinearity is an approximation for practical calculations.
Areas of Agreement / Disagreement
Participants do not reach a consensus on the implications of nonlinearity in quantum mechanics, with some expressing concerns about its consequences while others maintain that linearity holds in exact calculations.
Contextual Notes
The discussion highlights the dependence on definitions of linearity and the context in which nonlinear equations are applied, as well as the unresolved implications of nonlinearity in quantum mechanics.