G. J. Milburn, David Poulin
Using an elementary example based on two simple harmonic oscillators, we show how a relational time may be defined that leads to an approximate Schrodinger dynamics for subsystems, with corrections leading to an intrinsic decoherence in the energy eigenstates of the subsystem.
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We provide a synopsis of an effective approach to the problem of time in the semiclassical regime. The essential features of this new approach to evaluating relational quantum dynamics in constrained systems are illustrated by means of a simple toy model.
In the absence of an external frame of reference physical degrees of freedom must describe relations between systems. Using a simple model, we investigate how such a relational quantum theory naturally arises by promoting reference systems to the status of dynamical entities. Our goal is to demonstrate using elementary quantum theory how any quantum mechanical experiment admits a purely relational description at a fundamental level, from which the original "non-relational" theory emerges in a semi-classical limit. According to this thesis, the non-relational theory is therefore an approximatio…
This article contains a local solution to the notorious Problem of Time in Quantum Gravity at the conceptual level and which is actually realizable for the relational triangle. The Problem of Time is that `time' in GR and `time' in ordinary quantum theory are mutually incompatible notions, which is problematic in trying to put these two theories together to form a theory of Quantum Gravity. Four frontiers to this resolution in full GR are identified, alongside three further directions not yet conquered even for the relational triangle. This article is also the definitive review on relational p…
Students Alice and Bob take an examination in their quantum mechanics class, and thereby illustrate some aspects of energy decoherence.
Statistical mechanics from relational complex time with a pure state
本研究提出无需熵最大化或状态计数，仅通过系统与环境最大纠缠纯态的关系复时间演化，即可导出系统的正则密度矩阵，为统计力学提供新的纯态基础。
We study the quantum dynamics of a time reparametrization invariant system with a vanishing Hamiltonian. The evolution of the physical degrees of freedom of the system is described, both at the classical and at the quantum level, in relational terms by the construction of an internal time parameter. We use the Pegg-Barnett phase operator formalism in finite dimensional Hilbert space as an essential ingredient.
Is Exact Markovianity Fundamental Once Time Is Relational?
通过有限分辨率量子钟的关系性表述，推导出相对论开放量子动力学，证明精确马尔可夫演化是有效的而非基本的。
In the first part of this paper we analyze possible quantum computational capacities due to quantum queries associated with equi-partitions of pure orthogonal states. Special emphasis is given to the parity of product states and to functional parity. The second part is dedicated to a critical review of the relational encoding of multipartite states across (space-like separated) space-time regions; a property often referred to as "quantum nonlocality."
Relational mechanics is a reformulation of mechanics (classical or quantum) for which space is relational. This means that the configuration of an $N$-particle system is a shape, which is what remains when the effects of rotations, translations, and dilations are quotiented out. This reformulation of mechanics naturally leads to a relational notion of time as well, in which a history of the universe is just a curve in shape space without any reference to a special parametrization of the curve given by an absolute Newtonian time. When relational mechanics (classical or quantum) is regarded as f…
In a seminal paper (Page and Wootters 1983) Page and Wootters suggest time evolution could be described solely in terms of correlations between systems and clocks, as a means of dealing with the "problem of time" stemming from vanishing Hamiltonian dynamics in many theories of quantum gravity. Their approach to relational time centres around the existence of a Hamiltonian and the subsequent constraint on physical states. In this paper we present a "state-centric" reformulation of the Page and Wootters model better suited to theories which intrinsically lack Hamiltonian dynamics, such as Chern-…
Relational Emergent Time for Quantum System: A Multi-Observer, Gravitational, and Cosmological Framework
该研究提出一个量子系统中时间从相关性涌现的框架，涵盖多观察者、引力和宇宙学领域，预测了非相互作用粒子的可忽略内部时间及高度纠缠系统的时间偏离。
We use the Relational Blockworld (RBW) interpretation of quantum mechanics to resolve the foundational problems therein. As predicted by Smolin, the resolution of these problems is not independent of the problem of unification and the nature of time. Specifically, RBW requires a theory fundamental to quantum physics in which one must explicitly construct dynamical/diachronic entities (objects obtained via trans-temporal identification) from 'relations'. We use discrete graph theory to propose heuristically the nature of this underlying theory, which is based on a self-consistency criterion for…
Certified Private Relational Time from Entanglement
提出“纠缠时钟”概念，通过单态上的离散测量注册定义时间，利用关联符合流实现关系时间，并证明其量子预测超过经典基准，最终通过贝尔测试实现设备无关的私有时间认证。
How do we Observe Relational Observables?
针对微分同胚不变理论中关系可观测量与经验的联系问题，提出需构建适配的观察者图式，转向意识的能动性概念，并指出标准量子参考系不足以建模能动性，需其他内部参考系解释量子语境下的关系可观测量观测。
Evolution With(out) Time: Relational Holography & BPS Complexity Growth in $\mathcal{N}=2$ Double-Scaled SYK
本文在 $\mathcal{N}=2$ 双缩放 SYK 模型中探讨了关系性 holography 和 BPS 复杂度增长，提出了一种新的 Krylov 复杂度度量以探测零能量 BPS 状态，并与 Hartle-Hawking 状态进行对比。
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