Is a time symmetric interpretation of quantum theory possible without retrocausality?

TL;DR

This paper investigates whether a time-symmetric interpretation of quantum theory can exist without retrocausality, proposing alternative assumptions and analyzing their implications for quantum causality and Bell inequalities.

Contribution

It introduces the assumption of $$-mediation as an alternative to the quantum state reality assumption and reformulates the argument for time symmetry without retrocausality.

Findings

Replacing the quantum state assumption with $$-mediation is plausible.

The assumptions imply a timelike Bell causality criterion.

It shows the impossibility of a non-retrocausal, time-symmetric ontology.

Abstract

Huw Price has proposed an argument that suggests a time-symmetric ontology for quantum theory must necessarily be retrocausal, i.e. it must involve influences that travel backwards in time. One of Price's assumptions is that the quantum state is a state of reality. However, one of the reasons for exploring retrocausality is that it offers the potential for evading the consequences of no-go theorems, including recent proofs of the reality of the quantum state. Here, we show that this assumption can be replaced by a different assumption, called $\lambda$-mediation, that plausibly holds independently of the status of the quantum state. We also reformulate the other assumptions behind the argument to place them in a more general framework and pin down the notion of time symmetry involved more precisely. We show that our assumptions imply a timelike analogue of Bell's local causality criterion and, in doing so, give a new interpretation of timelike violations of Bell inequalities. Namely, they show the impossibility of a (non-retrocausal) time-symmetric ontology.