Completely Top–Down Hierarchical Structure in Quantum Mechanics

Authors

Yakir Aharonov, Chapman UniversityFollow
Eliahu Cohen, University of Ottawa
Jeff Tollaksen, Chapman UniversityFollow

Document Type

Article

Publication Date

11-13-2018

Abstract

Can a large system be fully characterized using its subsystems via inductive reasoning? Is it possible to completely reduce the behavior of a complex system to the behavior of its simplest “atoms”? In this paper we answer these questions in the negative for a specific class of systems and measurements. After a general introduction of the topic, we present the main idea with a simple two-particle example, where strong correlations arise between two apparently empty boxes. This leads to surprising effects within atomic and electromagnetic systems. A general construction based on preand postselected ensembles is then suggested, wherein the Nbody correlation can be genuinely perceived as a global property, as long as one is limited to performing measurements which we term “strictly local.” We conclude that under certain boundary conditions, higher-order correlations within quantum mechanical systems can determine lower-order ones, but not vice versa. Surprisingly, the lower-order correlations provide no information whatsoever regarding the higher-order correlations. This supports a top–down structure in many-body quantum mechanics.

Comments

This article was originally published in Proceedings of the National Academy of Sciences of the United States of America, volume 115, issue 46, in 2018. DOI: 10.1073/pnas.1807554115

Recommended Citation

Aharonov Y, Cohen E, Tollaksen J (2018) Completely top-down hierarchical structure in quantum mechanics. Proc Natl Acad Sci USA 115:11730-11735. doi: 10.1073/pnas.1807554115

Peer Reviewed

1

Copyright

The authors

Creative Commons License

This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.