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I give a brief introduction to many worlds or "no wave function collapse" quantum mechanics, suitable for non-specialists. I then discuss the origin of probability in such formulations, distinguishing between objective and subjective notions of probability.

Quantum gravitational effects suggest a minimal length, or spacetime interval, of order of the Planck length. This in turn suggests that Hilbert space itself may be discrete rather than continuous. One implication is that quantum states with norm below some very small threshold do not exist. The exclusion of what Everett referred to as maverick branches is necessary for the emergence of the Born Rule in no collapse quantum mechanics. We discuss this in the context of quantum gravity, showing that discrete models (such as simplicial or lattice quantum gravity) indeed suggest a discrete Hilbert space with minimum norm. These considerations are related to the ultimate level of fine-graining found in decoherent histories (of spacetime geometry plus matter fields) produced by quantum gravity.

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. Derivations of the Born rule which originate in decision theory or subjective probability (i.e. the reasoning of individual observers) do not resolve this problem, because they are circular: they assume, a priori, that the observer occupies a non-maverick branch. An ab initio probability measure is sometimes assumed to explain why we do not occupy a maverick branch. This measure is constrained by, e.g. Gleason’s theorem or envariance to be the usual Hilbert measure. However, this ab initio measure ultimately governs the allocation of a self or a consciousness to a particular branch of the wave function, and hence invokes primitives which lie beyond the Everett wave function and beyond what we usually think of as physics. The significance of this leap has been largely overlooked, but requires serious scrutiny.

We suggest that it might be possible to resolve the vacuum energy problem by assuming the reality of a many worlds interpretation of quantum mechanics. The suggested resolution is that the enormous theoretical prediction for the vacuum energy density is actually the value distributed across all the parallel universes in a superposition. It is assumed that branching of all the universes into a larger superposition is a physical process which is extremely rare, but which has occurred sufficiently often since the Big Bang that the discrepancy for the experimentally measured value of the energy density can be explained.

Non-collapse interpretations of quantum mechanics set themselves the task of developing a self-consistent and empirically adequate version of quantum mechanics that does not make use of the projection postulate (or collapse of the wavefunction). Only unitary evolution is allowed in these interpretations, so that superpositions are always maintained during evolution—even in measurements. In this paper we discuss how this deterministic mathematical scheme can be brought into accordance with the usual statistical predictions of quantum mechanics. In particular, we investigate how the Born probability rule fits in.