A cognitive basis for physical time

TL;DR

This paper proposes a formalization of time inspired by Kant, distinguishing between sequential time and relational time, to reconcile differences between relativity and quantum theory and improve understanding of time in physics.

Contribution

It introduces a dual-component formalization of time with sequential and relational aspects, aligning physical theory with human cognition and addressing the problem of time in quantum gravity.

Findings

Time as a sequential flow is separate from time as a measure of distance.

A formal model with an evolution parameter and an observable for time.

Reconciliation of relativity and quantum theory perspectives on time.

Abstract

The treatment of time in relativity does not conform to that in quantum theory. In the context of quantum gravity this is called "the problem of time". A crucial difference is that time $t$ may be seen as an observable in relativity theory, just like position $x$, whereas in quantum theory $t$ is a parameter, in contrast to the observable $x$. Aiming to resolve the discrepancy, a formalization of time in the spirit of Kant's Copernican revolution is suggested, where it is required that the treatment of time in physics agree with our cognition. This leads to reconsideration of the notions of identity and change of objects, as well as the nature of physical states and their evolution. The formalization has two components: sequential time $n$ and relational time $t$. The evolution of physical states is described in terms of $n$, which is updated each time an event occurs. The role of $t$ is to quantify distances between events in space-time. There is a space-time associated with each $n$, in which $t$ represents the knowledge at time $n$ about temporal distances between present and past events. A universal ordering of events in terms of $n$ can be postulated even though distances $t$ are relativistic. In short, it is argued that time as a sequential flow of events should be separated from time as a measure of distance between events. In physical models, these aspects of time can be expressed as one evolution parameter and one observable, respectively.