Space, and Spacetime, are Emergent Features of the Universe: they Arise as a Result of Non-Local Dynamical Collapse of the Wave-Function

Space, and Spacetime, are Emergent Features of the Universe: they Arise as a Result of Non-Local Dynamical Collapse of the Wave-Function 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.