The logical consistency of a description of quantum theory in the context of general relativity, which includes minimal coupling principle, is analyzed from the point of view of Feynman's formulation in terms of path integrals. We will argue from this standpoint and use an argument that claims the incompleteness of the general relativistic description of gravitation, which emerges as a consequence of the gravitationally induced phases of the so-called flavor-oscillation clocks, that the postulates of quantum theory are logically incompatible with the usual minimal coupling principle. It will be shown that this inconsistency could emerge from the fact that the required geometrical information to calculate the probability of finding a particle at any point of the respective manifold does not lie in a region with finite volume. Then we put forth a new quantum minimal coupling principle in terms of a restricted path integral, and along the ideas of this model not only the propagator of a free particle is calculated but also the conditions under which we recover Feynman's case for a free particle are deduced. The effect on diatomic interstellar molecules is also calculated. The already existing relation between restricted path integral formalism and decoherence model will enable us to connect the issue of a quantum minimal coupling principle with the collapse of the wave function. From this last remark we will claim that the geometrical structure of the involved manifold acts as, always present, a measuring device on a quantum particle. In other words, in this proposal we connect the issue of a quantum minimal coupling principle with a claim which states that gravity could be one of the physical entities which results in the collapse of the wave function.
From sources to initial data and back again: on bulk singularities in Euclidean AdS/CFT
