I have been reading with interest the debates here on whether the wave function/density state actually collapses or not, or whether it is subjective Bayesian or objective with actual complex numbered values for each component. I have been struck, though, by the implicit assumption made by all camps that something like the wave function/density state actually exists, whether subjective or objective. What if it does not? That would render all of these debates moot.
The wf/ds is a highly abstract theoretical inference of what is measured experimentally. All one measures are correlations between definite measured outcomes. Pragmatically, it has been found such correlations can pretty much only be calculated accurately within the Dirac/von Neumann two stage framework where one first postulates some abstract wf/ds evolving unitarily alternating with a collapse during measurement to the eigenspaces of some 'measured observable' according to the Born rule, whatever that really means. This makes no ontological assumptions per se; it is just what anyone needs to go through to calculate the measured correlations.
Many worlds people argue wf/ds is objective with no collapse and all the branches co-exist. Copenhagenists argue for collapse. But what if the wf/ds doesn't exist? Then they are both wrong and missing the point. Other than the fact the only time wf/ds shows up is in abstract symbolic calculations, why its existence be assumed?
Here, the situation differs from classical probability distributions. The probabilities are still linear for the density state, but not the wave function, but negative probabilities appear and that makes all the difference. In classical Bayesian updating, there is some leeway in when the updating happens because the different updates evolve independently and the original distribution always evolves as a nonnegative weighted sum of the individual independent contributions. In the quantum density state case, destructive interference due to oscillations between positive and negative 'probabilities' exist and the different outcomes can no longer be said to be in any way independent. Decoherence does not really explain it away because the suppression of interference is not exact, takes time, and is potentially reversible in principle. What if the density state does not exist?