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

对称性与测量：半定域量子物理的基础

• 批准号: EP/Y000099/1
• 负责人: Katarzyna Anna Rejzner
• 金额: $ 59.78万
• 依托单位: University of York
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2023
• 资助国家: 英国
• 起止时间: 2023 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FY000099%2F1
• 关键词: Symmetry; measurement; foundation; semi; local

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.

这个提议涉及量子理论，描述（亚）原子物质，以及爱因斯坦的相对论，描述引力和高速运动。现代物理学的这些基本组成部分并不容易组合在一起。这个项目解决了这些重要主题之间的一些问题。量子理论和狭义相对论结合在量子场论（QFT）中，这是一个非常成功的粒子物理模型，在欧洲核子研究中心（CERN）进行了严格的测试。然而，它的数学基础是不完整的，量子理论和广义相对论（量子引力）的结合是科学中最大的开放问题之一。量子理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状态的坍缩，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，典型的测量不可能比光信号更快。项目小组成员最近取得的重大进展提供了一个测量框架，它与相对论完全兼容，并且没有困扰早期工作的问题。这个提议将显着概括量子引力测量的这些想法。此时，对称性出现了。物理学家和数学家喜欢对称性，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，广义相对论有如此多的对称性，一个严重的问题出现了：没有局部的物理可观测量。一个解决方案是利用对称性的颗粒，引入“关系可观测量”，我们中的一个已经在有效量子引力中实现了。我们将把它们整合到上面提到的测量的一般框架中，在理论思想和它的实现之间架起一座桥梁（一个在实践中无法测量的可观测量是没有什么用处的）。我们建议的另一个主题是对称性和边界之间的关系，特别是时空中的边界。例如，黑洞的事件视界代表了一个有效边界：经典信息可以流入，但不能流出。然而，霍金表明，当考虑到量子理论时，黑洞会像热的一样辐射，甚至可以完全蒸发。现在，出来的信息远没有进入的信息有序。“丢失的信息”会发生什么是一个著名的未解决的问题，有人认为，与对称性有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中，而是存在于时空的边界上，存在于视界上，也存在于无穷远处的边界上。另一个例子是，带电粒子，例如电子，总是伴随着一团“软光子”，它可以到达无穷远。这再次证明了边界自由度的重要性，以及它们可能与体相混合的复杂方式。我们的提案的长期目标是超越量子场论中局域化的传统思想，建立一个“半局域量子物理学”的框架它可以像处理远离边界的绝对局部化一样轻松地处理边界和关系可观测量。发现科学，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进入大规模的地面，甚至空间和卫星系统。这些发展使量子信息理论进入了相对论领域，因此，一个清晰的框架，包括对QFT中测量的操作理解，可能成为分析此类技术的标准工具。