AI 中文总结
利用钍 - 229 核时钟测试时间 - 能量不确定性原理修正，推导非局部时间 - 能量不确定性原理，通过直接时钟 - 能量通道得出\(E_M\)不同尺度下限，表明核时钟为非局部性提供了从理论到实验室界限的实验途径。
AI 中文摘要
新的钍 - 229 核时钟为测试时间 - 能量不确定性原理的修正是否正确提供了新的实验系统。本文推导了非局部时间 - 能量不确定性原理，并将已发表的钍 - 229 核时钟数据作为非局部尺度\(E_M\)的首个探测器。因实验非为测试非局部量子场理论设计，所得约束被视为激励性界限而非确定性排除。利用直接时钟 - 能量通道，得到\(E_M\)在数十兆电子伏特尺度的保守下限，当前乐观数据估计达数百兆电子伏特尺度。考虑钍 - 229 跃迁已知的核敏感性增强，在吉电子伏特范围有更强的模型相关界限，核尺度参考能量情形可达太电子伏特范围。结论是核时钟已为从非局部时间 - 能量不确定性到非普朗克非局部性的可测量实验室界限提供了实验途径。
英文摘要
In this paper we derive the nonlocal Time-Energy uncertainty principle and then apply the published $^{229}$Th nuclear clock data as a first probe of the nonlocality scale \(E_M\). By using the direct clock-energy channel, we find conservative lower bounds on \(E_M\) at the tens of MeV scale, with optimistic present-data estimates reaching the hundred MeV scale. Including the known nuclear sensitivity enhancement of the $^{229}$Th transition gives us stronger model dependent bounds in the GeV range, while nuclear-scale reference-energy scenarios can reach the TeV range. The conclusion we draw from this is that nuclear clocks already provide an experimental route from nonlocal time--energy uncertainty to measurable laboratory bounds on non-Planckian nonlocality. We explore the idea of using a squeezed-state experiment with the $^{229}\mathrm{Th}$ nuclear clock to test the time--energy structure of nonlocal quantum field theory. The idea is reasonably obtainable within the near future of nuclear clock experiments. One would prepare an ensemble of thorium nuclei in a coherent superposition of the nuclear ground state and the low-lying isomeric clock state, entangle the participating nuclei through a collective interaction, and generate a family of spin-squeezed states with a tunable squeezing parameter $r$. Then a phase-controlled analysis pulse will rotate the selected collective nuclear quadrature into a measurable ground-isomer population difference. Near a strongly polarized collective state the normalized operators $J_y/\sqrt{S}$ and $J_z/\sqrt{S}$ obey the same approximate canonical algebra as the phase and amplitude quadratures of a squeezed optical mode. We use this experiment to either probe or bound the nonlocal energy scale $E_M$.
Comments45 pages, 1 figure. Fist paper is 17 pages, and the second paper is 28 pages
