Discrete Hilbert Space, the Born Rule, and Quantum Gravity

薛定谔-牛顿半经典引力场景中的玻恩规则

Born rule in Schroedinger-Newton scenarios of semiclassical gravity

研究薛定谔-牛顿半经典引力模型中玻恩规则的动力学弛豫，发现波包有界或缓慢增长时弛豫发生，快速膨胀时偏离持续，数值模拟证实，为原始量子非平衡提供最小模型。

Many Worlds, the Born Rule, and Self-Locating Uncertainty

We provide a derivation of the Born Rule in the context of the Everett (Many-Worlds) approach to quantum mechanics. Our argument is based on the idea of self-locating uncertainty: in the period between the wave function branching via decoherence and an observer registering the outcome of the measurement, that observer can know the state of the universe precisely without knowing which branch they are on. We show that there is a uniquely rational way to apportion credence in such cases, which leads directly to the Born Rule. Our analysis generalizes straightforwardly to cases of combined classic…

Possibilities for Probabilities

In ordinary situations involving a small part of the universe, Born's rule seems to work well for calculating probabilities of observations in quantum theory. However, there are a number of reasons for believing that it is not adequate for many cosmological purposes. Here a number of possible generalizations of Born's rule are discussed, explaining why they are consistent with the present statistical support for Born's rule in ordinary situations but can help solve various cosmological problems.

Weak Values as Context Dependent Values of Observables and Born's Rule

We characterize a value of an observable by a `sum rule' for generally non-commuting observables and a `product rule' when restricted to a maximal commuting subalgebra of observables together with the requirement that the value is unity for the projection operator of the prepared state and the values are zero for the projection operators of the states which are orthogonal to the prepared state. The crucial requirement is that the expectation value and the variance of an observable should be independent of the way of measurement, i.e., the choice of the maximal commuting subalgebra of observabl…

导航波理论与新物理的探索

Pilot-wave theory and the search for new physics

本文从宇宙学初始条件、量子引力黑洞辐射和短距离运动方程三方面论证导航波理论可引发可观测的 Born 规则偏离，从而揭示超越量子力学的新物理。

Beyond the Born rule in quantum gravity

We have recently developed a new understanding of probability in quantum gravity. In this paper we provide an overview of this new approach and its implications. Adopting the de Broglie-Bohm pilot-wave formulation of quantum physics, we argue that there is no Born rule at the fundamental level of quantum gravity with a non-normalisable Wheeler-DeWitt wave functional $Ψ$. Instead the universe is in a perpetual state of quantum nonequilibrium with a probability density $P\neq\left\vert Ψ\right\vert ^{2}$. Dynamical relaxation to the Born rule can occur only after the early universe has emerged i…

Born-Infeld type Gravity

Generalizations of gravitational Born-Infeld type lagrangians are investigated. Phenomenological constraints (reduction to Einstein-Hilbert action for small curvature, spin two ghost freedom and absence of Coulomb like Schwarschild singularity) select one effective lagrangian whose dynamics is dictated by the tensors g_{μν} and R_{μνρσ}(not R_{μν} or the scalar R).

Quantum gravity and quantum probability

We argue that in quantum gravity there is no Born rule. The quantum-gravity regime, described by a non-normalisable Wheeler-DeWitt wave functional $Ψ$, must be in quantum nonequilibrium with a probability distribution $P\neq\left\vert Ψ\right\vert ^{2}$ (initially and always). A Born rule can emerge only in the semiclassical regime of quantum systems on a classical spacetime background, with normalisable Schrödinger wave functions $ψ$. Conditioning on the underlying quantum-gravitational ensemble yields a nonequilibrium distribution $ρ\neq\left\vert ψ\right\vert ^{2}$ at the beginning of the s…

剪断树枝：在平衡多元宇宙中新兴的分支结构与玻恩法则

Shearing Off the Tree: Emerging Branch Structure and Born's Rule in an Equilibrated Multiverse

研究发现，在平衡多元宇宙中，多世界树的分支结构需重新审视，仅符合玻恩法则的历史才保持退相干，挑战了传统观点。

Baby Universes born from the Void

We propose a novel construction of a third quantised baby universe Hilbert space $\mathcal{H}_{BU}$ for the quantum gravity path integral. In contrast to the original description of $α$-parameters, both the bulk and boundary microscopic parameters are fixed in our proposal. Wormholes and baby universes appear due to refined observables, of the boundary dual quantum field theories, that crucially involve the space of representations of the gauge group. Irreducible representations, on which the path integral factorises, give rise to field theoretic superselection sectors and replace the $α$ stat…

Determinantal Born-Infeld Coupling of Gravity and Electromagnetism

We study a Born-Infeld inspired model of gravity and electromagnetism in which both types of fields are treated on an equal footing via a determinantal approach in a metric-affine formulation. Though this formulation is a priori in conflict with the postulates of metric theories of gravity, we find that the resulting equations can also be obtained from an action combining the Einstein-Hilbert action with a minimally coupled nonlinear electrodynamics. As an example, the dynamics is solved for the charged static black hole.

Born--Oppenheimer decomposition for quantum fields on quantum spacetimes

Quantum Field Theory on Curved Spacetime (QFT on CS) is a well established theoretical framework which intuitively should be a an extremely effective description of the quantum nature of matter when propagating on a given background spacetime. If one wants to take care of backreaction effects, then a theory of quantum gravity is needed. It is now widely believed that such a theory should be formulated in a non-perturbative and therefore background independent fashion. Hence, it is a priori a puzzle how a background dependent QFT on CS should emerge as a semiclassical limit out of a background …

The Born rule in a timeless universe

In canonical quantization of gravity the wave function of the universe is CPT invariant. Thus, if the quantum state of the universe contains a particular history, than it must contain, with the same probability, the time-reversed image of that history as well. In this work, we investigate the meaning of this statement in the context of the conditional probability interpretation of Page and Wootters. Accordingly, we show that a time-reversed history of the universe is consistent with the Page and Wootters mechanism and we derive a time-reversed Schrodinger equation for the evolution of the rest…