A cognitive basis for physical 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.