Correct. This is the part of QM known as Interpretations, for which people cannot agree on a single viewpoint, and hence do not agree on which axiom to add to t

Correct. This is the part of QM known as Interpretations, for which people cannot agree on a single viewpoint, and hence do not agree on which axiom to add to the theory. The measurement / collapse / decoherence / forking-of-worlds / entanglement-with-the-environment is either time-irreversible by definition, or time-irreversible FAPP. For example, Penrose proposes that the gravitational field induces one of these time-irreversible processes: https://en.wikipedia.org/wiki/Penrose_interpretation https://en.wikipedia.org/wiki/Penrose_interpretation