Decompositional Equivalence: A Fundamental Symmetry Underlying Quantum Theory

Abstract

Decompositional equivalence is the principle that there is no preferred decomposition of the universe into subsystems. It is shown here, by using a simple thought experiment, that quantum theory follows from decompositional equivalence together with Landauer's principle. This demonstration raises within physics a question previously left to psychology: how do human -or any -observers identify or agree about what constitutes a "system of interest"?

Building the Observer into the System: Toward a Realistic Description of Human Interaction with the World

“…The invisibility of internal component boundaries to outside observers, previously termed decompositional equivalence [64], has significant consequences for decoherence and particularly for quantum Darwinism [65,66,67]. If the classical information acquired by outside observers of a composite system does not depend on the placement of subsystem boundaries within that system, then it cannot depend on interactions defined at those boundaries.…”

“…It is natural for an observer who knows no more about what is being observed than the observational outcomes obtained thus far to represent the source of these outcomes, whatever it is, by a linear superposition of the observed outcomes. As distinct outcomes can indicate either distinct states or distinct systems, this representation can be interpreted as either a superposition of states or as a superposition of systems; the two interpretations are entirely equivalent [67]. While the former is by far the more familiar, the latter is implicit in Feynman diagrams and is even more evident in more abstract representations, such as the amplituhedron [112], in which particles and even spacetime are elided altogether.…”