A few questions for people who know how to answer these things and are able to do these kinds of calculations.
What would the distribution of gravity be if we took the total (non dark matter) mass of a galaxy and converted that value into a probability wave centered on the central black hole? Is that a doable calculation? Has this been done before?
I'm wondering if the distribution of gravity would look different and perhaps account for what we think is the dark matter halo that all galaxies seem to have.
It may not be as simple as just taking the total normal mass and thinking of it as a point-like particle however. It may be that the we have to take the total visible mass distribution (which would be a wave itself since there is a much higher density of mass at the center of a galaxy than at it's edges) and apply the probability wave to that. Then apply gravity to that so that we see what the probable gravity would be for that wave.
The reason this might work is that:
Each photon we interact with and which comes from what we think is a specific place (i.e. the galaxy we decide to measure)--each of these photons obeys quantum mechanical laws. We seem to trust that these photons are coming from where we think they are, but there is a good possibility that any particular photon is coming from somewhere else. The somewhere else may be from within the particular galaxy we are measuring, but it may be impossible to tell with certainty--in fact, it probably is impossible to tell for sure because each and every photon is a quantum object.
So, if we treat the galaxy as a quantum system and get a probability wave of its position based on the visual information we receive (photons) we may find that the gravitation we see is actually correct, and not due to some mysterious and unmeasurable dark entity after all. We already know that we can't measure position and momentum at the same time without losing certainty for one of these properties. If we measure the position we lose the accuracy of our measurement of momentum, and if we measure the momentum we lose accuracy of our measurement of position.
I imagine that there are corrections made to our measurement that are meant to account for quantum mechanical effects, but I don't think that a whole galaxy has been treated as a quantum system that has indefinite position. The superposition of the whole galaxy's visual mass distribution would be a waveform and would, in effect, be larger than what we see. I'm wondering what we would see if we apply gravity to that waveform.