  According to Penrose, the fundamental conflict between the superposition
principle of quantum mechanics and the principle of general covariance of
general relativity entails the existence of wavefunction collapse, e.g. a
quantum superposition of two different space-time geometries will collapse to
one of them due to the ill-definedness of the time-translation operator for the
superposition. In this paper, we argue that Penrose's conjecture on gravity's
role in wavefunction collapse is debatable. First of all, it is still a
controversial issue what the exact nature of the conflict is and how to resolve
it. Secondly, Penrose's argument by analogy is too weak to establish a
necessary connection between wavefunction collapse and the conflict as
understood by him. Thirdly, the conflict does not necessarily lead to
wavefunction collapse. For the conflict or the problem of ill-definedness for a
superposition of different space-time geometries also needs to be solved before
the collapse of the superposition finishes, and once the conflict has been
resolved, the wavefunction collapse will lose its physical basis relating to
the conflict. In addition, we argue that Penrose's suggestions for the collapse
time formula and the preferred basis are also problematic.
