来自变形相对论对称性的飞行时间模糊性
Time-of-flight fuzziness from deformed relativistic symmetries
- Università di Napoli “Federico II”（那不勒斯费德里科二世大学）
- INFN, Sezione di Napoli（意大利国家核物理研究所那不勒斯分部）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本研究在κ-庞加莱变形相对论对称性的非对易时空模型中，推导自由粒子的飞行时间模糊性，得到含系统性修正与随机贡献的飞行时间概率分布，为量子引力相关研究提供了新视角。
AI中文摘要：
量子引力中的一个普遍预期是，时空的量子性质会表现为模糊性，导致与时空相关的可观测量测量中出现不可约的不确定性。在本研究中，我们在具有κ-庞加莱变形相对论对称性的非对易时空模型中，推导了自由粒子的飞行时间模糊性。为保留该理论的完整量子结构，我们在对应的非对易世界线空间中开展研究，这为构造量子态和推导表征粒子轨迹参数的概率分布提供了便利框架，使我们能够获得粒子飞行时间的概率分布。我们的结果重现了已知的系统性飞行时间修正，得出了与狭义相对论预期的能量相关偏差，同时预测了飞行时间的一种新的随机贡献。系统性贡献的标度为粒子能量与量子引力能标之比，并随传播距离放大；而随机贡献的标度为量子引力长度标度与传播时间乘积的平方根，再乘以一个取决于粒子速度的 prefactor（ prefactor 译为“ prefactor”，此处保留英文原名）。
英文摘要：
A general expectation in quantum gravity is that quantum properties of spacetime manifest themselves as fuzziness, causing an irreducible uncertainty in the measurement of spacetime-related observables. In this work, we derive the time-of-flight fuzziness for free particles within a noncommutative spacetime model with $κ$-Poincaré deformed relativistic symmetries. To retain the full quantum structure of the theory we work in the corresponding noncommutative space of worldlines. This provides a convenient framework for constructing quantum states and deriving the probability distributions for the parameters characterizing particle trajectories, allowing us to obtain the probability distribution of particle times of flight. Our results reproduce the well-known systematic time-of-flight correction, leading to energy-dependent departures from the special-relativistic expectation, and simultaneously predict a novel stochastic contribution to the time of flight. While the systematic contribution scales with the ratio between the particle energy and the quantum-gravity energy scale and is amplified by the propagation distance, the stochastic contribution scales as the square root of the product of the quantum-gravity length scale and the travel time, multiplied by a prefactor which depends on the particle velocity.
