  Collapse models possibly suggest the need for a better understanding of the
structure of space-time. We argue that physical space, and space-time, are
emergent features of the Universe, which arise as a result of dynamical
collapse of the wave function. The starting point for this argument is the
observation that classical time is external to quantum theory, and there ought
to exist an equivalent reformulation which does not refer to classical time. We
propose such a reformulation, based on a non-commutative special relativity. In
the spirit of Trace Dynamics, the reformulation is arrived at, as a statistical
thermodynamics of an underlying classical dynamics in which matter and
non-commuting space-time degrees of freedom are matrices obeying arbitrary
commutation relations. Inevitable statistical fluctuations around equilibrium
can explain the emergence of classical matter fields and classical space-time,
in the limit in which the universe is dominated by macroscopic objects. The
underlying non-commutative structure of space-time also helps understand better
the peculiar nature of quantum non-locality, where the effect of wave-function
collapse in entangled systems is felt across space-like separations.
