Symmetry and measurement: a foundation for semi-local quantum physics

这一提议涉及描述（亚）原子物质的量子理论，以及描述万有引力和高速运动的爱因斯坦相对论。现代物理学的这些基本组成部分并不容易组合在一起。这个项目在这些重要主题之间的边界上处理了几个问题。量子理论和狭义相对论结合在量子场论（QFT）中，量子场论是粒子物理学的一个非常成功的模型，在欧洲核子研究中心进行了引人注目的测试。然而，它的数学基础是不完整的，量子理论与广义相对论（量子引力）的结合是科学中最大的开放问题之一。量子论和相对论之间的一个紧张关系涉及测量。学生们了解到，量子测量会导致瞬时态坍缩，但相对论告诉我们，不同的观察者对“瞬时”的含义存在分歧。因此，QFT中测量的描述一直受到不一致和悖论的困扰，例如，典型的测量允许不可能比光信号更快。项目团队成员最近取得的重大进展提供了一个度量框架，它与相对性完全兼容，并且没有困扰早期工作的问题。这一提议将在量子引力测量中显著地推广这些想法。在这一点上，对称性进入了。物理学家和数学家喜欢对称，因为它通常可以简化问题，并产生非常令人愉快的数学结构。然而，广义相对论具有如此多的对称性，以至于出现了一个严重的问题：没有局部的物理可观测量。一种解决方案是利用对称性的颗粒，引入“关系可观测性”，我们中的一个人已经在有效量子引力中实现了这一点。我们将把它们整合到上述测量的一般框架中，在理论思想和实施之间架起桥梁（在实践中无法测量的观察结果几乎没有用处）。我们提议的另一个主题是对称和边界之间的关系，特别是时空中的边界。例如，黑洞的视界代表了一个有效的边界：经典信息可以流入，但不能流出。然而，霍金表明，当量子理论被考虑在内时，黑洞的辐射就好像它们是热的，甚至可以完全蒸发。现在，输出的信息比输入的信息要无序得多。“丢失的信息”发生了什么是一个著名的未解决问题，有人认为与对称性相关的自由度可能是关键。这些自由度并不局限于大部分时空，而是存在于时空的边界上，在视界上，也存在于无限远处的边界上。另一个例子是，带电粒子，例如电子，总是伴随着一团“软光子”，这种“软光子”可以延伸到无限远。这再次说明了边界自由度的重要性，以及它们可能与整体混合的复杂方式。我们提议的长期目标是超越QFT中定位的传统思想，为“半局部量子物理”构建一个框架，该框架可以像处理远离边界的绝对定位一样轻松地处理边界和关系可观测值。虽然这一建议是基础科学发现，但其长期影响可能包括技术应用。量子信息理论正迅速从实验室转移到大规模的地面系统，甚至是星载系统和卫星系统。这些发展将量子信息理论带入了相对论领域，因此，一个清晰的框架，结合对QFT测量的操作理解，可能成为分析此类技术的标准工具。

This proposal concerns quantum theory, describing (sub)atomic matter, and Einstein's theories of relativity, describing gravitation and high speed motion. These fundamental building blocks of modern physics do not fit easily together. This project tackles several problems at the boundary between these important subjects. Quantum theory and special relativity are combined in quantum field theory (QFT), a hugely successful model for particle physics tested spectacularly at CERN. However its mathematical foundations are incomplete and the combination of quantum theory with general relativity (quantum gravity) is one of the biggest open problems in science.One tension between quantum theory and relativity concerns measurement. Students learn that quantum measurement causes an instantaneous state collapse, but relativity teaches that different observers disagree on what "instantaneous" means. Consequently, the description of measurement in QFT has been plagued by inconsistencies and paradoxes suggesting, for example, that typical measurements allow impossible faster than light signalling. Significant recent progress by members of the project team has provided a measurement framework that is fully compatible with relativity and free of the problems afflicting earlier work. This proposal will significantly generalise these ideas for measurements in quantum gravity.At this point, symmetry enters. Physicists and mathematicians like symmetry because it can often simplify problems and produces very pleasing mathematical structures. However general relativity has so much symmetry that a serious problem occurs: there are no local physical observable quantities. One solution is to work with the grain of the symmetry, introducing "relational observables", which have been implemented by one of us in effective quantum gravity. We will integrate them into the general framework for measurement mentioned above, bridging between the theoretical idea and its implementation (an observable that cannot be measured in practice is of little use).Another theme in our proposal is the relation between symmetry and boundaries, particularly boundaries in spacetime. For example,the event horizon of a black hole represents an effective boundary: classical information can flow in, but not out. However, Hawking showed that when quantum theory is taken into account, black holes radiate as if they are hot and can even evaporate entirely. Now, the information that comes out is much less ordered than the information that enters. What happens to the `lost information' is a famous unsolved problem and it has been suggested that degrees of freedom related to symmetries may hold the key. These degrees of freedom are not localised within the bulk of spacetime but rather live on the boundaries of spacetime, at the horizon and also a boundary at infinity. Another example is that charged particles, e.g. electrons, are always accompanied by a cloud of `soft photons' that reaches to infinity. Again, this exemplifies the significance of boundary degrees of freedom, and the complicated way in which they may be mixed up with the bulk.The long-term goal of our proposal is to move beyond traditional ideas of localisation in QFT to build a framework for "semi-local quantum physics" that can handle boundary and relational observables just as easily as those with absolute localisation away from boundaries.While this proposal is fundamental discovery science, its long term impact may include technological applications. Quantum information theory is rapidly moving from the laboratory into large scale terrestrial and even space-borne and satellite systems. These developments put quantum information theory into the relativistic realm and so a clear framework incorporating an operational understanding of measurement in QFT could become a standard tool for analysing such technologies.