A Completely Top-Down Hierarchical Structure in Quantum Mechanics

TL;DR

This paper demonstrates that in certain quantum systems, high-order correlations can determine low-order ones, but not the other way around, supporting a top-down hierarchical view in many-body quantum mechanics.

Contribution

It introduces a novel top-down hierarchical framework in quantum mechanics, challenging the traditional bottom-up reductionist approach.

Findings

High-order correlations can determine low-order correlations.

Low-order correlations do not reveal high-order correlations.

Supports a top-down structure in many-body quantum systems.

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 the following paper we answer these questions on the negative for a specific class of systems and measurements. We begin with simple two-particle example, where strong correlations arise between two apparently empty boxes. This leads to new surprising effects within atomic and electromagnetic systems. A general construction based on pre- and post-selected ensembles is then suggested, where the N-body correlation can be genuinely perceived as a global property, as long as one is limited to preforming a small set of measurements which we term "strictly local". We conclude that within time-symmetric quantum mechanics and under certain boundary conditions, high-order correlations can determine low-order ones, but not vice versa. Moreover, the latter seem to provide no information at all regarding the former. This supports a top-down structure in many-body quantum mechanics.