A quantum formalism for events and how time can emerge from its foundations

Abstract: Although time is one of our most intuitive physical concepts, its understanding at the fundamental level is still an open question in physics. For instance, time in quantum mechanics and general relativity are two distinct and incompatible entities. While relativity deals with events (points in spacetime), with time being observer-dependent and dynamical, quantum mechanics describes physical systems by treating time as an independent parameter. To resolve this conflict, in this work, we extend the classical concept of an event to the quantum domain by defining an event as a transfer of information between physical systems. Then, by describing the universe from the perspective of a certain observer, we introduce quantum states of events with space-time-symmetric wave functions that predict the joint probability distribution of a measurement (observation) at $ (t, {\vec x}) $. Under these circumstances, we propose that a well-defined instant of time, like any other observable, arises from a single event, thus being an observer-dependent property. As a result, a counterfactual asymmetry along a particular sequence of events within a stationary quantum state gives rise to the flow of time as being successive "snapshots" from the observer's perspective. In this proposal, it is the many distinguishable states in which the observer stores information that makes the existence of time possible.