Conditional probabilities with Dirac observables and the problem of time in quantum gravity

Relational observables, reference frames, and conditional probabilities

We discuss the construction of relational observables in time-reparametrization invariant quantum mechanics and we argue that their physical interpretation can be understood in terms of conditional probabilities, which are defined from the solutions of the quantum constraint equation in a generalization of the Page-Wootters formalism. In this regard, we show how conditional expectation values of worldline tensor fields are related to quantum averages of suitably defined relational observables. We also comment on how the dynamics of these observables can be related to a notion of quantum refere…

弯曲时空中自由标量量子场论的条件概率与经验定律

The conditional probabilities and the empirical laws in a free scalar QFT in curved spacetime

针对弯曲时空量子场论经验定律存在概念模糊性的问题，本文提出用无初始态信息的先验条件概率描述其部分经验定律，给出了自由标量场相关的经验定律示例。

Anthropics and Myopics: Conditional Probabilities and the Cosmological Constant

We re-examine claims that anthropic arguments provide an explanation for the observed smallness of the cosmological constant, and argue that correlations between the cosmological constant value and the existence of life can be demonstrated only under restrictive assumptions. Causal effects are more subtle to uncover.

Conditional probabilities in Ponzano-Regge minisuperspace

We examine the Hartle-Hawking no-boundary initial state for the Ponzano-Regge formulation of gravity in three dimensions. We consider the behavior of conditional probabilities and expectation values for geometrical quantities in this initial state for a simple minisuperspace model consisting of a two-parameter set of anisotropic geometries on a 2-sphere boundary. We find dependence on the cutoff used in the construction of Ponzano-Regge amplitudes for expectation values of edge lengths. However, these expectation values are cutoff independent when computed in certain, but not all, conditional …

Consistent Probabilities in Wheeler-DeWitt Quantum Cosmology

We give an explicit, rigorous framework for calculating quantum probabilities in a model theory of quantum gravity. Specifically, we construct the decoherence functional for the Wheeler-DeWitt quantization of a flat Friedmann-Robertson-Walker cosmology with a free, massless, minimally coupled scalar field, thus providing a complete decoherent histories formulation for this quantum cosmological model. The decoherence functional is applied to study predictions concerning the model's Dirac (relational) observables; the behavior of semiclassical states and superpositions of such states; and to stu…

Conditional Probabilities in the Excursion Set Theory. Generic Barriers and non-Gaussian Initial Conditions

The excursion set theory, where density perturbations evolve stochastically with the smoothing scale, provides a method for computing the dark matter halo mass function. The computation of the mass function is mapped into the so-called first-passage time problem in the presence of a moving barrier. The excursion set theory is also a powerful formalism to study other properties of dark matter halos such as halo bias, accretion rate, formation time, merging rate and the formation history of halos. This is achieved by computing conditional probabilities with non-trivial initial conditions, and th…