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Extensions of Born’s rule to non-linear quantum mechanics, some of which do not imply superluminal communication

Helou, Bassam and Chen, Yanbei (2017) Extensions of Born’s rule to non-linear quantum mechanics, some of which do not imply superluminal communication. Journal of Physics Conference Series, 880 . Art. No. 012021. ISSN 1742-6588. doi:10.1088/1742-6596/880/1/012021.

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Nonlinear modifications of quantum mechanics have a troubled history. They were initially studied for many promising reasons: resolving the measurement problem, formulating a theory of quantum mechanics and gravity, and understanding the limits of standard quantum mechanics. However, certain non-linear theories have been experimentally tested and failed. More significantly, it has been shown that, in general, deterministic non-linear theories can be used for superluminal communication. We highlight another serious issue: the distribution of measurement results predicted by non-linear quantum mechanics depends on the formulation of quantum mechanics. In other words, Born's rule cannot be uniquely extended to non-linear quantum mechanics. We present these generalizations of Born's rule, and then examine whether some exclude superluminal communication. We determine that a large class do not allow for superluminal communication, but many lack a consistent definition. Nonetheless, we find a single extension of Born's rule with a sound operational definition, and that does not exhibit superluminal communication. The non-linear time-evolution leading to a certain measurement event is driven by the state conditioned on measurements that lie within the past light cone of that event.

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Chen, Yanbei0000-0002-9730-9463
Additional Information:© 2016 The Authors. Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Published under licence by IOP Publishing Ltd.
Group:Astronomy Department
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Record Number:CaltechAUTHORS:20170822-064232533
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Official Citation:Bassam Helou and Yanbei Chen 2017 J. Phys.: Conf. Ser. 880 012021
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:80662
Deposited By: Ruth Sustaita
Deposited On:22 Aug 2017 16:18
Last Modified:15 Nov 2021 19:37

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