On Wednesday, May 13, 2020 at 12:30:44 AM UTC-5, Brent wrote: > > > > In any case though, I don't see the form of the Born rule as something > problematic. It's getting from counting branches to probabilities. Once > you assume there is a probability measure, you're pretty much forced to the > Born rule as the only consistent probability measure. > > Brent > >
Once one approaches the domain of 'quantum phenomena' as a probability/measure theorist would do, then all roads (formulations of the underlying measure space) should lead to Born. A measure theory on the appropriately-defined measure space underlies both probability theory and what has been called quantum-probability theory. *Schwinger’s picture of Quantum Mechanics* https://arxiv.org/pdf/2002.09326.pdf *A gentle introduction to Schwinger’s formulation of quantum mechanics: The groupoid picture* https://www.researchgate.net/publication/325907723_A_gentle_introduction_to_Schwinger's_formulation_of_quantum_mechanics_The_groupoid_picture *Quantum measures and the coevent interpretation* https://arxiv.org/abs/1005.2242 cf. *Probabilities on Algebraic Structures* Ulf Grenander review: https://projecteuclid.org/download/pdf_1/euclid.aoms/1177700302 *Derivation of the Schrödinger equation from the Hamilton-Jacobi equation in Feynman's path integral formulation of quantum mechanics* J.H.Field https://arxiv.org/abs/1204.0653 *Feynman’s path integral formulation of quantum mechanics is based on the following two postulates* [11]: *1. If an ideal measurement is performed to determine whether a particle has a path lying in a region of spacetime, the probability that the result will be affirmative is the absolute square of a sum of complex contributions, one from each path in the region.* *2. II The paths contribute equally in magnitude but the phase of their contribution is the classical action (in units of ¯h) i.e. the time integral along the path.* [11] Feynman R.P. 1948 Rev. Mod. Phys. 20 367. @philipthrift -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/79de99c0-727c-48c0-87dc-e0fb9dfe0c00%40googlegroups.com.
