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arXiv:1004.2004

Multipartite macroscopic locality and macroscopic non-contextuality

Miguel Navascués

Published Apr 12, 2010• 0 citations
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Abstract

The author cannot grant that Quantum Mechanics satisfies the axioms described here when repeated measurements are at stake. This does not compromise the validity of the conclusions of the previous article "A glance beyond the quantum model", Proc. Roy. Soc. Lond. A 466, 881-890 (2009).
DOI
10.48550/arxiv.1004.2004

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We consider the manifold-valued, stochastic extension of the Schrödinger equation introduced by Hughston (Proc.Roy.Soc.Lond. A452 (1996) 953) in a manifestly covariant, differential-geometric framework, and examine the resulting quantum evolution on some specific examples of Kähler manifolds with many symmetries. We find conditions on the curvature for the evolution to be a `collapse process' in the sense of Brody and Hughston (Proc.Roy.Soc.Lond. A458 (2002) 1117) or, more generally, a `reduction process', and give examples that satisfy these conditions. For some of these examples, we show that the Lüders projection postulate admits a consistent interpretation and remains valid in the nonlinear regime.
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In a previous paper, Hayden and I ( Deutsch & Hayden 2000 Proc. R. Soc. Lond. A 456 , 1759–1774. ( doi:10.1098/rspa.2000.0585 )) proved, using the Heisenberg picture, that quantum physics satisfies Einstein's criterion of locality. Wallace and Timpson ( Wallace & Timpson 2007 Found. Phys. 37 , 951–955. ( doi:10.1007/s10701-007-9135-7 )) have argued that certain transformations of the Heisenberg-picture description of a quantum system must be regarded as leaving invariant the factual situation being described, and that taking this into account reveals that Einstein's criterion is violated after all. Here, I vindicate the proof and explain some misconceptions that have led to this and other criticisms of it.