Mainly motivated by relativity, a separate time coordinate for every particle in a composite system has occasionally been introduced. A modification of this idea has recently been proposed as a new foundations for non-relativistic quantum theory—a Local Time Scheme, http://dx.doi.org/10.1098/rspa.2014.0283.
Why should we care about yet another quantum foundations?
First, Local Time Scheme (LTS) is purely technical, i.e. non-interpretational and thus potentially of the universal interest. Second, LTS straightforwardly tackles and links some foundational questions in quantum theory. For example: In LTS, closed microscopic (few-particle) systems bear high level of quantum coherence that is otherwise imposed by the unitary Schrodinger dynamics; Closed many-particle systems typically (but not necessarily) bear lower amount of quantum coherence; Certain bipartitions of closed many-particle systems routinely describe ‘quantum measurement’ [in the strong-interaction scenario] and solves the ‘preferred basis problem’ without invoking ‘classical apparatus’ or environmental influence (decoherence) or any interpretation—it suffices that the total system is sufficiently macroscopic; The Scheme provides a plausible interpretation of the Wheeler-DeWitt equation: on the level of the total universe, time does not exist, but on the local level, time does exist.
From the conceptual point of view, Local Time Scheme introduces dynamics as a primitive. The concept of time has been changed and in an ensemble of identical systems is not unique neither is necessarily physically fundamental. Furthermore, LTS allows for the emergent as well as relational physical nature of Time—the prospects, I believe, worth pursuit.