Sunday 31 December 2017

special relativity - Why does nonlinearity in quantum mechanics lead to superluminal signaling?



I recently came across two nice papers on the foundations of quantum mechancis, Aaronson 2004 and Hardy 2001. Aaronson makes the statement, which was new to me, that nonlinearity in QM leads to superluminal signaling (as well as the solvability of hard problems in computer science by a nonlinear quantum computer). Can anyone offer an argument with crayons for why this should be so?


It seems strange to me that a principle so fundamental and important can be violated simply by having some nonlinearity. When it comes to mechanical waves, we're used to thinking of a linear wave equation as an approximation that is always violated at some level. Does even the teensiest bit of nonlinearity in QM bring causality to its knees, or can the damage be limited in some sense?


Does all of this have any implications for quantum gravity -- e.g., does it help to explain why it's hard to make a theory of quantum gravity, since it's not obvious that quantum gravity can be unitary and linear?



S. Aaronson, "Is Quantum Mechanics An Island In Theoryspace?," 2004, arXiv:quant-ph/0401062.


L. Hardy, "Quantum theory from five reasonable axioms," 2001, arXiv:quant-ph/0101012.





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