The emergence of time under interaction of system and environment

The nature of time has fascinated not only physicist for many centuries, but even today no conclusive answer exists about its origin. Is it fundamental or emergent?

The so-called “relational approach" is based on a static description of the world and introduces time for a system as emergent through separation from the environment. We show how time and dynamics in time emerge for a system from correlations with the rest of the world, the environment, it is embedded in. By retaining arbitrary couplings between system and environment, we are able to bridge the gap between two major strands of research for the relational approach to time, which are either unable to deal with interactions or require semiclassical approximations. As a result, we derive the time-dependent Schrödinger equation for the system from a static global state and provide the analytically exact form for an effective environment-dependent potential governing the time-dependence of the system.

Analytical and numerical examples will be provided to illustrate and confirm our approach to time which reduces to either of the two previous lines of research with the appropriate approximations. Moreover, we find a close conceptual connection to the theory of decoherence.