Back to Publications


Completely top–down hierarchical structure in quantum mechanics

Proceedings of the National Academy Science of the U.S.A. 115(46)
Aharonov, Y.Cohen, E.Tollaksen, J. Institute for Quantum Studies,
Chapman University,
Orange, CA, USA

Physics Department,
Centre for Research in Photonics,
University of Ottawa,
ON, Canada
2018 Physics

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 pre- and postselected ensembles is then suggested, wherein the N-body 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.

The article was published in: Proceedings of the National Academy Science of the U.S.A. 115(46): 11730-11735.

Full article

This work was supported (in part) by the Fetzer Franklin Fund of the John E. Fetzer Memorial Trust.