Where could I find the proof that “as quantum amplitude of a piece of the wavefunction goes to zero, the probability that I will ‘find myself’ in that piece also goes to zero” is equivalent to the Born rule?
Quantum Mechanics In Your Face talk by Sidney Coleman, starting slide 17 near the end. The basic idea is to try to operationalize how someone might test the Born rule—they take a bunch of quantum measurements, one after another, and they subject their data to a bunch of randomness tests and so on, and then they eventually declare “Born rule seems true” or “Born rule seems false” after analyzing the data. And you can show that the branches in which this person declares “Born rule seems false” have collective amplitude approaching zero, in the limit as their test procedure gets better and better (i.e. as they take more and more measurements).
Where could I find the proof that “as quantum amplitude of a piece of the wavefunction goes to zero, the probability that I will ‘find myself’ in that piece also goes to zero” is equivalent to the Born rule?
Quantum Mechanics In Your Face talk by Sidney Coleman, starting slide 17 near the end. The basic idea is to try to operationalize how someone might test the Born rule—they take a bunch of quantum measurements, one after another, and they subject their data to a bunch of randomness tests and so on, and then they eventually declare “Born rule seems true” or “Born rule seems false” after analyzing the data. And you can show that the branches in which this person declares “Born rule seems false” have collective amplitude approaching zero, in the limit as their test procedure gets better and better (i.e. as they take more and more measurements).
I was assigned this reading for a class once but only skimmed it—now I wish I’d read it more closely!