  There are four reasons why our present knowledge and understanding of quantum
mechanics could be regarded as incomplete. Firstly, the principle of linear
superposition has not been experimentally tested for position eigenstates of
objects having more than about a thousand atoms. Secondly, there is no
universally agreed upon explanation for the process of quantum measurement.
Thirdly, there is no universally agreed upon explanation for the observed fact
that macroscopic objects are not found in superposition of position
eigenstates. Fourthly, and perhaps most importantly, the concept of time is
classical and hence external to quantum mechanics : there should exist an
equivalent reformulation of the theory which does not refer to an external
classical time. In this paper we argue that such a reformulation is the
limiting case of a nonlinear quantum theory, with the nonlinearity becoming
important at the Planck mass scale. Such a nonlinearity can provide insights
into the problems mentioned above. We use a physically motivated model for a
nonlinear Schrodinger equation to show that nonlinearity can help in
understanding quantum measurement. We also show that while the principle of
linear superposition holds to a very high accuracy for atomic systems, the
lifetime of a quantum superposition becomes progressively smaller, as one goes
from microscopic to macroscopic objects. This can explain the observed absence
of position superpositions in macroscopic objects [lifetime is too small]. It
also suggests that ongoing laboratory experiments maybe able to detect the
finite superposition lifetime for mesoscopic objects, in the foreseeable
future.
