标题： 广义不确定性关系：理论、示例和洛伦兹不变性 显示英文标题

标题： Generalized uncertainty relations: Theory, examples, and Lorentz invariance

摘要： 在该量子力学框架中，可观测量与厄米特算符相关联，这个框架过于狭窄，无法讨论诸如时间流逝或简谐振子相位等重要物理量的测量。我们引入了一个更广泛的框架，使我们能够推导出通过任意数据对任意测量在$N$个制备相同的量子系统上进行分析时，参数（例如时间流逝）可能被确定的精度的量子力学极限。这些极限以广义的曼德尔斯塔姆-坦姆不确定关系来表示，这些关系涉及生成参数位移的算符（例如，在时间流逝的情况下为哈密顿算符）。这种方法完全避免了将厄米特算符与参数相关联的问题。我们首先用非相对论的不确定性关系来说明一般形式主义，包括空间位移和动量、简谐振子相位和量子数以及时间和能量；其次，用涉及庞加莱群位移和洛伦兹旋转参数的洛伦兹不变不确定性关系来说明。 显示英文摘要

摘要： The quantum-mechanical framework in which observables are associated with Hermitian operators is too narrow to discuss measurements of such important physical quantities as elapsed time or harmonic-oscillator phase. We introduce a broader framework that allows us to derive quantum-mechanical limits on the precision to which a parameter---e.g., elapsed time---may be determined via arbitrary data analysis of arbitrary measurements on $N$ identically prepared quantum systems. The limits are expressed as generalized Mandelstam-Tamm uncertainty relations, which involve the operator that generates displacements of the parameter---e.g., the Hamiltonian operator in the case of elapsed time. This approach avoids entirely the problem of associating a Hermitian operator with the parameter. We illustrate the general formalism, first, with nonrelativistic uncertainty relations for spatial displacement and momentum, harmonic-oscillator phase and number of quanta, and time and energy and, second, with Lorentz-invariant uncertainty relations involving the displacement and Lorentz-rotation parameters of the Poincar\'e group.