Does gravity induce wavefunction collapse? An examination of Penrose's conjecture

According to Penrose, the fundamental conflict between the superpo-sition principle of quantum mechanics and the principle of general covari-ance 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 nec-essarily 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, an