Scholars Award: Observables in Hamiltonian Dynamics

该奖项支持物理学哲学中的一个技术项目。PI拥有物理学、历史学和科学哲学博士学位，他将解决广义相对论的哲学基础中的一个问题，即该理论的两个公式的等价性。其中一种更接近量子力学的标准公式，更有利于找到可行的量子引力理论。然而，这一表述似乎暗示变化是一种幻觉;可观测量（这一表述指定为真实的物理量）不随时间而变化。该理论的另一种表述更符合常识;（在该表述中的）可观测量确实随时间而变化。尽管如此，这两种理论表述之间的这种差异近乎自相矛盾;说它们是等价的，这意味着什么，我们并不清楚。 PI建议通过提供一个新颖的和令人信服的论据来解决这种紧张局势，为局部变化的观测量的新定义解决时间问题，同时保持两种制剂的等效性。 除了将他的研究成果发表在三篇计划中的期刊文章（最终出版一本书）之外，PI还计划通过一系列的六次公开讲座和他在剑桥的相关教学，使他的工作能够被广泛的受众所了解。这个项目研究了广义相对论的哈密顿公式与拉格朗日公式的等价性，以解决时间问题。自20世纪50年代中期以来，哈密顿广义相对论一直与物理上真实的观测量缺乏变化有关，而更基本的拉格朗日处理（爱因斯坦方程），就像常识一样，表现出变化的观测量。许多著名的物理学家都对这种不可接受的情况发表了评论，但由于种种原因，还没有找到一个适当的解决办法。人们提出了两个新的可观测量定义，一个是由PI提出的，另一个是由脑桥、索尔兹伯里和桑德迈尔提出的。PI试图采取关键的下一步，采取最近提出的可观测量的定义并测试它们，通过研究它们是否正确地使各种理论的等效公式在其观测内容中等效。该项目将揭示量子引力的研究计划，展示广义相对论和粒子物理学之间相互作用的成果，并展示综合科学史和科学哲学对当前科学的效用。

This award supports a technical project in the philosophy of physics. The PI, who has a PhD in both Physics and History and Philosophy of Science, will address an issue in the philosophical foundations of the General Theory of Relativity concerning the equivalence of two formulations of the theory. One tends to be preferred because it is much closer to how quantum mechanics is standardly formulated, which is better for the purposes of finding a viable theory of quantum gravity. However, that formulation seems to imply that change is an illusion; observables (what the formulation designates as real physical quantities) do not change with time. The other formulation of the theory is more in line with common sense; observables (within that formulation) do change with time. Nevertheless, this difference between the two formulations of the theory borders on the paradoxical; it is not clear what it means to say that they are equivalent. The PI proposes to resolve this tension by giving a novel and compelling argument for a new definition of observables that vary locally resolving the problem of time while maintaining the equivalence of the two formulations.  In addition to publishing the results of his research in three planned journal articles (and eventually in a book), the PI plans to make his work accessible to a wide audience through a series of six public lectures and through his relevant teaching at Cambridge.This project examines the equivalence of the Hamiltonian formulation of General Relativity with the Lagrangian formulation to resolve the problem of time. Hamiltonian General Relativity has been associated with a lack of change in physically real observables since the mid-1950s, whereas the more fundamental Lagrangian treatment (Einstein's equations), like common sense, exhibits changing observables. Many leading physicists have commented on this unacceptable situation, but for various reasons an adequate solution has not been found. Two new definitions of observables have been proposed, one by the PI and another by Pons, Salisbury, and Sundermeyer. The PI seeks to take the crucial next step, of taking the recently-proposed definition of observables and testing them, by studying whether they correctly render equivalent formulations of various theories equivalent in their observational content. The project will shed light on research programs in quantum gravity, exhibits the fruitfulness of interaction between General Relativity and particle physics, and shows the utility of integrated history and philosophy of science for current science.