  There are various reasons to believe that quantum theory could be an emergent
phenomenon. Trace Dynamics is an underlying classical dynamics of non-commuting
matrices, from which quantum theory and classical mechanics have been shown to
emerge, in the thermodynamic approximation. However, the time that is used to
describe evolution in quantum theory is an external classical time, and is in
turn expected to be an emergent feature - a relic of an underlying theory of
quantum gravity. In this essay we borrow ideas from Trace Dynamics to show that
classical time is a thermodynamic approximation to an operator time in quantum
gravitational physics. This prediction will be put to test by ongoing
laboratory experiments attempting to construct superposed states of macroscopic
objects.
