  The collapse of a quantum state can be understood as a mathematical way to
construct a joint probability density even for operators that do not commute.
We can formalize that construction as a non-commutative, non-associative
collapse product that is nonlinear in its left operand as a model for joint
measurements at timelike separation, in part inspired by the sequential product
for positive semi-definite operators. The familiar collapse picture, in which a
quantum state collapses after each measurement as a way to construct a joint
probability density for consecutive measurements, is equivalent to a
no-collapse picture in which L\"uders transformers applied to subsequent
measurements construct a Quantum-Mechanics--Free-Subsystem of Quantum
Non-Demolition operators, not as a dynamical process but as an alternative
mathematical model for the same consecutive measurements. The no-collapse
picture is particularly simpler when we apply signal analysis to millions or
billions of consecutive measurements.
