http://www.sciencemag.org/cgi/content/abstract/329/5990/418" [Broken](adsbygoogle = window.adsbygoogle || []).push({});

Two pillars of modern physics, quantum mechanics and gravity, have so far resisted attempts to be reconciled into one grand theory. This has prompted suggestions that theories about either or both need to be modified at a fundamental level. Sinha et al. (p. 418; see the Perspective by Franson) looked at the interference pattern resulting from a number of slits, to test the "Born rule" of quantum mechanics. They verified that Born holds true—that the interference pattern is built up by the interference from two paths, and two paths only, with no higher-order paths interfering. The result rules out any nonlinear theories of quantum mechanics; thus, any modification of theory will need to take into account that quantum mechanics is linear.

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I wonder about the inherent non commutativity of operators acting on the same degrees of freedom of the wave function in qm. It just seems like that lends itself to a development of relevant tools in non commutative geometry to describe these physical interactions in qm (via Connes). But I don't normally think of non commutative geometries and linearity in the same breath. And to clarify I think they are saying that the operators act as linear maps on the eigenkets in qm. Is this supposed to be globally true?Are there not other spaces where operators do not act as linear transformations on the eigenkets?

Tell me how my thought process is in error please.

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# Quantum Mechanics Born to be Linear?

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