  At present, there are two possible, and equally plausible, explanations for
the physics of quantum measurement. The first explanation, known as the
many-worlds interpretation, does not require any modification of quantum
mechanics, and asserts that at the time of measurement the Universe splits into
many branches, one branch for every possible alternative. The various branches
do not interfere with each other because of decoherence, thus providing a
picture broadly consistent with the observed Universe. The second explanation,
which requires quantum mechanics to be modified from its presently known form,
is that at the time of measurement the wave-function collapses into one of the
possible alternatives. The two explanations are mutually exclusive, and up
until now, no theoretical reasoning has been put forward to choose one
explanation over the other. In this article, we provide an argument which
implies that the collapse interpretation is favored over the many-worlds
interpretation. Our starting point is the assertion (which we justify) that
there ought to exist a reformulation of quantum mechanics which does not refer
to a classical spacetime manifold. The need for such a reformulation implies
that quantum theory becomes non-linear on the Planck mass/energy scale.
Standard linear quantum mechanics is an approximation to this non-linear
theory, valid at energy scales much smaller than the Planck scale. Using ideas
based on noncommutative differential geometry, we develop such a reformulation
and derive a non-linear Schr\"{o}dinger equation, which can explain collapse of
the wave-function. We also obtain an expression for the lifetime of a quantum
superposition. We suggest ideas for an experimental test of this model.
