论文标题
贝尔的轨迹定理
Bell's theorem for trajectories
论文作者
论文摘要
在经典理论中，粒子的轨迹完全通过动态定律的完整初始条件来确定。基于此，我们为经典粒子的动力学（即贝尔的轨迹不平等）制定了无关定理，并在量子场景中讨论了其可能的违规行为。然而，从某种意义上说，轨迹不是量子测量的结果，因为它没有可观察到的量子，因此没有对贝尔对轨迹的不平等的“直接”实验测试。然而，我们通过考虑我们的通用不平等的特殊情况来展示如何克服这个问题，该案例可以通过时间进行实验测试。量子力学确实违反了这种不平等，并且在整个时间间隔内，不仅在特定的奇异瞬间都存在违规行为。我们将违规解释为暗示在地方现实主义理论中不能预先确定的轨迹（或至少其碎片）。
In classical theory, the trajectory of a particle is entirely predetermined by the complete set of initial conditions via dynamical laws. Based on this, we formulate a no-go theorem for the dynamics of classical particles, i.e., a Bell's inequality for trajectories, and discuss its possible violation in a quantum scenario. A trajectory, however, is not an outcome of a quantum measurement, in the sense that there is no observable associated with it, and thus there is no "direct" experimental test of the Bell's inequality for trajectories. Nevertheless, we show how to overcome this problem by considering a special case of our generic inequality that can be experimentally tested point-by-point in time. Such inequality is indeed violated by quantum mechanics, and the violation persists during an entire interval of time and not just at a particular singular instant. We interpret the violation to imply that trajectories (or at least pieces thereof) cannot exist predetermined, within a local-realistic theory.
