在不同洛伦兹框架下几何可观测量的非交换性
On the non-commutativity of geometric observables in different Lorentz frames
AI总结：
研究不同洛伦兹框架下几何可观测量的非交换性，揭示其在量子引力中的意义。
摘要：
我们的目标是确定由不同观察者观测的几何可观测量，如物理物体的长度、面积或体积，是否满足泊松交换性。为了说明这一点，我们计算了两个与刚性杆相关的长度，分别由两个不同的测地线（惯性）观察者测量的泊松括号。我们的计算表明，不同观察者测量的几何可观测量通常不满足泊松交换性，即使在闵氏时空内也是如此。这一非平凡的结果为量子引力背景下基本尺度的存在问题提供了有趣的见解。
英文摘要：
Our aim is to establish whether geometric observables, such as length, area or volume of a physical object, viewed by different observers Poisson commute or not. To illustrate this, we compute the Poisson bracket of two lengths associated to a rigid rod and measured by two different geodesic (inertial) observers, one of which is at rest while the other is moving with respect to the rod. Our calculation shows that geometric observables measured by different observers generically do not Poisson commute, not even in Minkowski spacetime. This non-trivial result provides interesting insights into questions related to the presence of a fundamental scale in the context of quantum gravity.
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