  The cosmological constant problem is principally concerned with trying to
understand how the zero-point energy of quantum fields contributes to gravity.
Here we take the approach that by addressing a fundamental unresolved issue in
quantum theory we can gain a better understanding of the problem. Our starting
point is the observation that the notion of classical time is external to
quantum mechanics. Hence there must exist an equivalent reformulation of
quantum mechanics which does not refer to an external classical time. Such a
reformulation is a limiting case of a more general quantum theory which becomes
nonlinear on the Planck mass/energy scale. The nonlinearity gives rise to a
quantum-classical duality which maps a `strongly quantum, weakly gravitational'
dynamics to a `weakly quantum, strongly gravitational' dynamics. This duality
predicts the existence of a tiny nonzero cosmological constant of the order of
the square of the Hubble constant, which could be a possible source for the
observed cosmic acceleration. Such a nonlinearity could also be responsible for
the collapse of the wave-function during a quantum measurement. We conclude by
suggesting that the idea for the origin of dark energy proposed in this paper
can be tested indirectly in the laboratory by a detailed examination of the
process of quantum measurement.
