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I heard that there have been some propositions about describing the collapse of the wave-function by adding non-linear terms, but I couldn't anything in any any textbooks or even articles (probably those propositions never reached a good level of consistency). However, I'd like to read about it. Could someone send me a reference?

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4 Answers 4

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The Ghirardi-Rimini-Weber Model is such a theory. See for instance http://arxiv.org/abs/quant-ph/0406094.

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Roger Penrose advanced the notion that gravity causes wave function collapse, giving handwavy arguments involving the Schrodinger-Newton equation (one particular flavor of the nonlinear Schrodinger equation).

The references I'm aware of:

  1. Roger Penrose, "On Gravity's Role in Quantum State Reduction", General Relativity and Gravitation 28 5 (1996) 581-600. DOI:10.1007/BF02105068
  2. Roger Penrose, "Quantum computation, entanglement and state reduction", Phil. Trans. R. Soc. Lond. A 356 no. 1743 (1998) 1927-1939. DOI:10.1098/rsta.1998.0256
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Collapse of the State Vector

Phys. Rev. A 85, 062116 (2012)

http://arxiv.org/pdf/1109.6462v4.pdf

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As far as I know, nonlinearities aren't compatible with Lorentz invariance. The overall probability renormalization factor also needs to be rescaled globally, although that might not be a problem if rejecting a probabilistic ontology.

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Can you explain to us what is the probabilistic ontology and what is the issue of global rescaling? –  stupidity Jun 29 '12 at 19:37
    
Well, based on Weinberg proposition for non linear QM, the non linear observables need to be of order one in $\psi$ and $\psi^*$ so non linear operators in the Hamiltonian will be suppresed by factors $n = \int d^3x \;\psi(x)\psi^*(x)$ which is a non-local quantity. –  toot Jul 13 '12 at 17:24
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