Common sense quantum mechanics
Related to: Quantum physics sequence. TLDR: Quantum mechanics can be derived from the rules of probabilistic reasoning. The wavefunction is a mathematical vehicle to transform a nonlinear problem into a linear one. The Born rule that is so puzzling for MWI results from the particular mathematical form of this functional substitution. This is a brief overview a recent paper in Annals of Physics (recently mentioned in Discussion): Quantum theory as the most robust description of reproducible experiments (arXiv) by Hans De Raedt, Mikhail I. Katsnelson, and Kristel Michielsen. Abstract: > It is shown that the basic equations of quantum theory can be obtained from a straightforward application of logical inference to experiments for which there is uncertainty about individual events and for which the frequencies of the observed events are robust with respect to small changes in the conditions under which the experiments are carried out. In a nutshell, the authors use the "plausible reasoning" rules (as in, e.g., Jaynes' Probability Theory) to recover the quantum-physical results for the EPR and Stern–Gerlach experiments by adding a notion of experimental reproducibility in a mathematically well-formulated way and without any "quantum" assumptions. Then they show how the Schrodinger equation (SE) can be obtained from the nonlinear variational problem on the probability P for the particle-in-a-potential problem when the classical Hamilton-Jacobi equation holds "on average". The SE allows to transform the nonlinear variational problem into a linear one, and in the course of said transformation, the (real-valued) probability P and the action S are combined in a single complex-valued function ~P1/2exp(iS) which becomes the argument of SE (the wavefunction). This casts the "serious mystery" of Born probabilities in a new light. Instead of the observed frequency being the square(d amplitude) of the "physically fundamental" wavefunction, the wavefunction is seen as a math
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