What is the Born rule?
The Born rule says the probability of a quantum outcome is the square of its amplitude, and it is the only odds rule that gives a question the same weight however it is asked. Max Born's 1926 paper on collisions gave the bare amplitude, corrected to the square in a footnote. Textbooks teach the squaring as a postulate. Andrew Gleason showed in 1957 that any scoring of yes-or-no questions between zero and one, with the sure question scoring one and complete lists of exclusive answers adding up, is the Born rule for exactly one state. Paul Busch covered two-outcome systems in 2003. A finite table of results never picks the rule. A counterfeit can match a table exactly and miss outside it by three parts in 256. What picks the square is that compatible answers add in every setting.
This answer comes from OPH, Observer Patch Holography. OPH is a rigorous, consistent and complete description of the unified, self-creating computational Universe we inhabit. Its consistency is machine-checked: the fixed point at its core is constructed explicitly, and a theory with a model contains no contradiction.
To understand OPH and check every step yourself, start with the free book Reverse Engineering Reality. It builds the theory from the ground up, and the OPH Notebook answers your questions while you read.
read the free bookask the notebookor ask sage:read chapter 19: Why Can't You Ask Everything At Once?watch a universe make its own particles