A formal proof of the Born rule from decision-theoretic assumptions
David Wallace
Abstract
I develop the decision-theoretic approach to quantum probability, originally proposed by David Deutsch, into a mathematically rigorous proof of the Born rule in (Everett-interpreted) quantum mechanics. I sketch the argument informally, then prove it formally, and lastly consider a number of proposed ``counter-examples'' to show exactly which premises of the argument they violate.
arXiv comments
36 pages. To appear (under the title "How to prove the Born rule") in Saunders, Barrett, Kent and Wallace, "Many Worlds? Everett, Quantum Theory, and Reality" (Oxford University Press)
I believe in Many-Worlds, the update step falls out of decoherence "for free." Because you are also in superposition after the measurement, the "you have measured 1" part of your wavefunction of course measures amplitude 1. That doesn't give you the Born rule though - I believe…
Here's a blog post I wrote about this recently: http://blog.rongarret.info/2019/07/the-trouble-with-many-wor... The TL;DR is that the critics are correct. Deriving the Born rule begs the question because it makes an unjustified assumption (branching indifference) and also…
I believe in Many-Worlds, the update step falls out of decoherence "for free." Because you are also in superposition after the measurement, the "you have measured 1" part of your wavefunction of course measures amplitude 1. That doesn't give you the Born rule though - I believe…
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