Physical or not, the amplitudes are synchronized instantaneously and hence are non-local.

"How probability works" is not physics nor is it mathematics. Probability theory is concerned with a pattern of abstraction and not of interpreting observations. There is no time or space in probability theory and applications to specific cases happens independent of the theory. "a feature of how probability works" is not a clarification of what is sufficient to make a wave "collapse", which is a legitimate question within the context of physics.