Decompositional equivalence

TL;DR

This paper formalizes the Principle of Decompositional Equivalence in physics, demonstrating its implications for the invariance of physical laws and challenging assumptions in quantum measurement interpretations.

Contribution

It introduces a formalization of Decompositional Equivalence and shows its implications for the limits of experimental verification and the assumptions in quantum mechanics.

Findings

Finite experiments cannot confirm pointer states refer to the same system

Extra-theoretical assumptions are stronger than classicality assumptions

Standard quantum interpretations are logically inconsistent

Abstract

Both classical and quantum mechanics assume that physical laws are invariant under changes in the way that the world is labeled. This Principle of Decompositional Equivalence is formalized, and shown to forbid finite experimental demonstrations that given pointer states |p1> and |p2> refer to the same physical system S. It is then shown that any extra-theoretical assumption that given pointer states |p1> and |p2> with indistinguishable coefficients in a Schmidt basis for the universe refer to the same physical system S is stronger than the assumption of classicality. Standard interpretations of quantum mechanics make such as assumption in analyzing measurement; hence they are logically inconsistent.