Written by: Stephen Hsu
Primary Source: Information Processing
I am a Quantum Engineer, but on Sundays I have principles. — J.S. Bell
My own conclusion … there is no interpretation of quantum mechanics that does not have serious flaws. — Steve Weinberg
I wrote this paper mainly for non-specialists: any theorist should be able to read and understand it. However, I feel the main point — that subjective probability analyses do not resolve the measure problem in many worlds quantum mechanics — is often overlooked, even by the experts.
The measure problem in no-collapse (many worlds) quantum mechanics
We explain the measure problem (cf. origin of the Born probability rule) in no-collapse quantum mechanics. Everett defined maverick branches of the state vector as those on which the usual Born probability rule fails to hold — these branches exhibit highly improbable behaviors, including possibly the breakdown of decoherence or even the absence of an emergent semi-classical reality. An ab initio probability measure is necessary to explain why we do not occupy a maverick branch. Derivations of the Born rule which originate in decision theory or subjective probability do not resolve this problem, because they are circular: they assume, a priori, that we reside on a non-maverick branch.
To put it very succinctly: subjective probability or decision theoretic arguments can justify the Born rule to someone living on a non-maverick branch. But they don’t explain why that someone isn’t on a maverick branch in the first place.
It seems to me absurd that many tens of thousands of papers have been written about the hierarchy problem in particle physics, but only a small number of theorists realize we don’t have a proper (logically complete) quantum theory at the fundamental level.