Extending quantum mechanics entails extending special relativity

TL;DR

This paper explores how extending quantum mechanics to include ontological models affects the understanding of special relativity, showing that certain nonlocal features can be embedded in Newtonian spacetime and challenging assumptions about Minkowski causality.

Contribution

It introduces a method for ontologically extending quantum mechanics via oblivious embedding in Newtonian spacetime, linking quantum nonlocality with relativistic principles.

Findings

Ontological extension constructed through oblivious embedding

Minkowski spacetime ruled out as the embedding locus

Operational theory remains Lorentz covariant despite ontological non-covariance

Abstract

The complementarity between signaling and randomness in any communicated resource that can simulate singlet statistics is generalized by relaxing the assumption of free will in the choice of measurement settings. We show how to construct an ontological extension for quantum mechanics (QM) through the oblivious embedding of a sound simulation protocol in a Newtonian spacetime. Minkowski or other intermediate spacetimes are ruled out as the locus of the embedding by virtue of hidden influence inequalities. The complementarity transferred from a simulation to the extension unifies a number of results about quantum nonlocality, and implies that special relativity (SR) has a different significance for the ontological model and for the operational theory it reproduces. Only the latter, being experimentally accessible, is required to be Lorentz covariant. There may be certain Lorentz non-covariant elements at the ontological level, but they will be inaccessible at the operational level in a valid extension. Certain arguments against the extendability of QM, due to Conway and Kochen (2009) and Colbeck and Renner (2012), are attributed to their assumption that the spacetime at the ontological level has Minkowski causal structure.