The Concept of Entropic Time: A Preliminary Discussion

The deep connection between entropy and information is discussed in terms of both classical and quantum physics. The mechanism of information transfer between systems via entanglement is explored in the context of decoherence theory. The concept of entropic time is then introduced on the basis of information acquisition, which is argued to be effectively irreversible and consistent with both the Second Law of Thermodynamics and our psychological perception of time. This is distinguished from the notion of parametric time, which serves as the temporal parameter for the unitary evolution of a physical state in non-relativistic quantum mechanics. The atemporal nature of the `collapse' of the state vector associated with such information gain is discussed in light of relativistic considerations. The interpretation of these ideas in terms of both subjective and objective collapse models is also discussed. It is shown that energy is conserved under subjective collapse schemes whereas, in general, under objective collapse it is not. This is consistent with the fact that the latter is inherently non-unitary and that energy conservation arises out of time symmetry in the first place.