Written by: Stephen Hsu

Primary Source: Information Processing

The paper below will appear in Int.J.Mod.Phys.A. We went through a strange series of referees during the last year, with reactions ranging from

*this result is correct but trivial *

to

*this result is highly nontrivial but possibly correct*

to, finally,

*this is a nice result and should be published. *

I would like to lock the first two referees in a room to exchange ideas! (*What!? Of course, HE is the idiot, not ME!*)

A consequence of the process is the added appendix which proves (rather pedantically)

Ψ[ φ ] ≈ ψ_A [ φ_A ] × ψ_B [ φ_B ] × · · ·

for our coherent state example.

Locality and Nonlinear Quantum Mechanics

(http://arxiv.org/abs/1401.7018)Chiu Man Ho, Stephen D.H. Hsu

Nonlinear modifications of quantum mechanics generically lead to nonlocal effects which violate relativistic causality. We study these effects using the functional Schrodinger equation for quantum fields and identify a type of nonlocality which causes nearly instantaneous entanglement of spacelike separated systems. We describe a simple example involving widely separated wave-packet (coherent) states, showing that nonlinearity in the Schrodinger evolution causes spacelike entanglement, even in free field theory.

Some excerpts:

The linear structure of quantum mechanics has deep and important consequences, such as the behavior of superpositions. One is naturally led to ask whether this linearity is fundamental, or merely an approximation: Are there nonlinear terms in the Schrodinger equation?

Nonlinear quantum mechanics has been explored in [1–6]. It has been observed that the fictitious violation of locality in the Einstein-Podolsky-Rosen (EPR) experiment in conventional linear quantum mechanics might become a true violation due to nonlinear effects [7, 8] (in [8] signaling between Everett branches is also discussed). This might allow superluminal communication and violate relativistic causality. These issues have subsequently been widely discussed [9].

Properties such as locality or causality are difficult to define in non-relativistic quantum mechanics (which often includes, for example, “instantaneous” potentials such as the Coulomb potential). Therefore, it is natural to adopt the framework of quantum field theory: Lorentz invariant quantum field theories are known to describe local physics with relativistic causality (influences propagate only within the light cone), making violations of these properties easier to identify. …

… Our results suggest that nonlinearity in quantum mechanics is associated with violation of relativistic causality. We gave a formulation in terms of factorized (unentangled) wavefunctions describing spacelike separated systems. Nonlinearity seems to create almost instantaneous entanglement of the two systems, no matter how far apart. Perhaps our results are related to what Weinberg [11] meant when he wrote “… I could not find any way to extend the nonlinear version of quantum mechanics to theories based on Einstein’s special theory of relativity … At least for the present I have given up on the problem: I simply do not know how to change quantum mechanics by a small amount without wrecking it altogether.”

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