  The random motion of a pollen grain in a glass of water is only apparently
so. It results from coarse-graining an underlying deterministic motion - that
of the molecules of water colliding with the grain. Not observing degrees of
freedom on smaller scales can make deterministic evolution appear
indeterministic on larger scales. In this essay we attempt to make the case
that quantum indeterminism arises in an analogous manner, from coarse-graining
a deterministic (but non-unitary) evolution at the Planck scale. The underlying
evolution is described by the theory of trace dynamics, which is a
deterministic matrix dynamics from which quantum theory and its indeterminism
are emergent. One consequence of the theory is the Karolyhazy uncertainty
relation, which implies a universal upper bound to the speed of computing, as
noted also by other researchers.
