This would be a lot simpler if you weren't avoiding my questions. I have asked you whether you have understood and accept the derivation of the dominant eigenstate as the best possible description of the state of a system that the observer is part of. I have also asked if you have read my blog from the beginning, because I need to know where your confusion about what I am saying comes from.

The Stern Gerlach experiment goes like this in my theory: The superposition of the spins of the silver atoms must be collapsed already at the moment the beam splits up, because a much later collapse would create a continuous position distribution. That also means a Copenhagen-like act of observation cannot happen any later, specifically not at a screen. This is a good indication that not observation itself forces the silver atoms to localize but something else, that relates to observation but is not the act of looking at it. In the system that contains the experiment and the observer, the observer would always "see" a state that belongs to the dominant eigenstate of the objective state operator of that system. It doesn't really matter if in that system the observer is entangled with the spin state or not. As soon as you apply the field to separate the silver atoms you also create an energy difference (which is also flight time dependent and scans through a rather large range of possible resonant frequencies). The photons in the environment that are out of the observer's direct observation and unknown to him begin to interact with the two spin states, and some do in a way that creates spin flips, with absorption and stimulated emission, or just shake the atom a little bit. The sum of these interactions can create a total unitary evolution that creates two possible eigenvectors of the state operator, one containing each spin z-eigenstate and a probability for each to be the dominant eigenstate that goes conform with the Born rule. That includes the assumption that the photon states from the environment are entirely unknown. The scattering process I give in my blog shows that such a process is possible and has the right outcome. The dominant eigenstate of the system containing the observer is then the best description of reality that this observer can come up with. Or in other words, he sees either spin up or down and their trajectories.

If you accept the fact that an internal observer can only ever know the dominant eigenstate then state jumps with unknown/random outcome are a necessary consequence. That the statistics of those jumps is the Born rule for events that involve unknown photons is also a direct consequence. And all that follows just from unitary evolution of the global state and the constraints by locality and unitarity on the observer. So please tell me which of the derived steps you do not accept, so that we can focus on it. And please point me to exactly where in the blog the offending statement is.