A Universe that does not know the time

TL;DR

This paper explores the idea that cosmological time is a quantum observable that does not commute with the cosmological constant, leading to a universe that may be delocalized in time and challenging traditional notions of a universal clock.

Contribution

It proposes a novel quantum framework where cosmological time and the cosmological constant are conjugate variables, suggesting new cosmological scenarios and resolving paradoxes related to time.

Findings

Universe can be 'delocalized' in time due to quantum properties.

A sharply defined clock time implies an indeterminate cosmological constant.

Backward quantum time transitions could create localized histories.

Abstract

In this paper we propose that cosmological time is a quantum observable that does not commute with other quantum operators essential for the definition of cosmological states, notably the cosmological constant. This is inspired by properties of a measure of time---the Chern-Simons time---and the fact that in some theories it appears as a conjugate to the cosmological constant, with the two promoted to non-commuting quantum operators. Thus, the Universe may be "delocalised" in time: it does not {\it know} the time, a property which opens up new cosmological scenarios, as well as invalidating several paradoxes, such as the timelike tower of turtles associated with an omnipresent time line. Alternatively, a Universe with a sharply defined clock time must have an indeterminate cosmological constant. The challenge then is to explain how islands of localized time may emerge, and give rise to localized histories. In some scenarios this is achieved by backward transitions in quantum time, cycling the Universe in something akin to a time machine cycle, with classical flow and quantum ebbing. The emergence on matter in a sea of Lambda probably provides the ballast behind classical behaviour.