量子引力中的时间与因果性
Time and causality in quantum gravity
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中文总结 AI 辅助
本文从经典到量子理论审视时间概念，比较量子引力各方法对时间问题的处理，指出该问题在弱引力领域已显现，而非仅限普朗克尺度。
中文摘要 AI 辅助
量子引力中的时间问题通常被视为将量子理论应用于广义相对论的结果。这些笔记采取了更广阔的视角。我们首先考察时间如何进入经典力学、相对论、量子理论和量子场论，区分三个主要方面：因果顺序、时间持续和当下。这一分析表明，与时间相关的概念困难并非仅在引力被量子化时才出现。因果结构、时钟、可观测量和测量之间的张力已经存在于构建量子引力的理论之中。然后，我们审视了量子引力主要方法中对时间问题的回应。这些方法包括正则量子化和Wheeler-DeWitt量子化、路径积分和历史表述、微扰和背景依赖方法、因果集以及扭量理论。我们根据这些方案是否保留外部时间、是否通过量子化使时间成为问题、或将因果或时间结构纳入其基础来对它们进行比较。特别强调了量子基础和相对论量子信息引发的问题。最后，我们考察线性化引力和弱引力量子系统。这一领域表明，时间问题并不局限于普朗克尺度物理，而是在试图提供接近平坦几何时空的预测性和操作性有意义的量子描述时就已经出现。
英文摘要
The problem of time in quantum gravity is often presented as a consequence of applying quantum theory to general relativity. These notes adopt a broader perspective. We first examine how time enters classical mechanics, relativity, quantum theory, and quantum field theory, distinguishing three principal aspects: causal order, temporal duration, and the present. This analysis shows that the conceptual difficulties associated with time do not arise only when gravity is quantised. Tensions between causal structure, clocks, observables, and measurement are already present in the theories from which quantum gravity is constructed. We then survey responses to the problem of time across the principal approaches to quantum gravity. These include canonical and Wheeler-DeWitt quantisation, path-integral and histories formulations, perturbative and background-dependent approaches, causal sets, and twistor theory. The programmes are compared according to whether they retain an external time, render time problematic through quantisation, or incorporate causal or temporal structure into their foundations. Particular emphasis is placed on questions arising from quantum foundations and relativistic quantum information. We conclude by examining linearised gravity and weak-gravity quantum systems. This regime shows that the problem of time is not confined to Planck-scale physics, but arises already in attempts to provide a predictive and operationally meaningful quantum description of spacetime near flat geometry.
发表机构
- University of Patras（帕特雷大学）
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