Operational quantum theory without predefined time

TL;DR

This paper introduces a generalized quantum theory framework that removes the need for predefined time or causal structure, enabling a description of quantum phenomena with indefinite causal order and potential applications to quantum gravity.

Contribution

It develops a time-neutral, operationally symmetric formulation of quantum theory that generalizes existing frameworks to include indefinite causal structures and boundary-based descriptions.

Findings

Framework compatible with indefinite causal order

Describes events via boundary operators and entangled states

Suggests causal structure as emergent from boundary properties

Abstract

The standard formulation of quantum theory assumes a predefined notion of time. This is a major obstacle in the search for a quantum theory of gravity, where the causal structure of space-time is expected to be dynamical and fundamentally probabilistic in character. Here, we propose a generalized formulation of quantum theory without predefined time or causal structure, building upon a recently introduced operationally time-symmetric approach to quantum theory. The key idea is a novel isomorphism between transformations and states which depends on the symmetry transformation of time reversal. This allows us to express the time-symmetric formulation in a time-neutral form with a clear physical interpretation, and ultimately drop the assumption of time. In the resultant generalized formulation, operations are associated with regions that can be connected in networks with no directionality assumed for the connections, generalizing the standard circuit framework and the process matrix framework for operations without global causal order. The possible events in a given region are described by positive semidefinite operators on a Hilbert space at the boundary, while the connections between regions are described by entangled states that encode a nontrivial symmetry and could be tested in principle. We discuss how the causal structure of space-time could be understood as emergent from properties of the operators on the boundaries of compact space-time regions. The framework is compatible with indefinite causal order, timelike loops, and other acausal structures.