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Penrose has been advocating the view that the collapse of the wave functionis rooted in the incompatibility between general relativity and quantummechanics. On the basis of conceptual analysis, he arrived at an estimate forthe collapse time. To better understand his estimate, in this paper we presenta thought experiment, which singles out the role of time-dilations in massivesuperpositions. First we investigate the behavior of a hypothetical clockcontaining a component which can be in a superposition of states. The clockcontains a massive object, whose only purpose is to introduce a curvature ofspace time into the problem. We find that a state of this massive object with asmaller radius, but with the same mass, experiences a larger time dilation.Considering a coherent superposition of the large and small object, introducesan ambiguity in the definition of a common time for both states. We assert thatthis time ambiguity can be thought to affect the time evolution of a state indifferent ways and that the relative phase difference between these differentinterpretations can be calculated. We postulate that the wave function collapsewill occur when this phase difference becomes of order unity. An absoluteenergy scale enters this equation and we recover Penrose's estimate for thecollapse time by equating the absolute energy scale to the rest mass of theobject.

A clock containing a massive object in a superposition of states; what makes Penrosian wavefunction collapse tick?