The inconsistency of linear dynamics and Born's rule

TL;DR

This paper argues that linear objective collapse theories cannot naturally produce Born's rule without additional assumptions, highlighting an inconsistency in their formulation when explaining quantum-to-classical transition.

Contribution

It demonstrates that deriving Born's rule from linear collapse theories is impossible without hidden assumptions, challenging their validity in explaining quantum measurement outcomes.

Findings

Linear collapse theories cannot produce Born's rule without extra assumptions.

Previous proofs of Born's rule in such theories rely on hidden assumptions.

Objective collapse theories must be non-linear to be consistent with Born's rule.

Abstract

Modern experiments using nanoscale devices come ever closer to bridging the divide between the quantum and classical realms, bringing experimental tests of objective collapse theories that propose alterations to Schr\"{o}dinger's equation within reach. Such objective collapse theories aim to explain the emergence of classical dynamics in the thermodynamic limit and hence resolve the inconsistency that exists within the axioms of quantum mechanics. Here, we show that requiring the emergence of Born's rule for relative frequencies of measurement outcomes without imposing them as part of any axiom, implies that such objective collapse theories cannot be linear. Previous suggestions for a proof of the emergence of Born's rule in classes of problems that include linear objective collapse theories are analysed and shown to include hidden assumptions.