This paper argues that the path integral formulation of quantum mechanics suggests a form of holism for which the whole (total ensemble of paths) has properties that are not strongly reducible to the properties of the parts (the single trajectories). Feynman’s sum over histories calculates the probability amplitude of a particle moving within a boundary by summing over all the possible trajectories that the particle can undertake. These trajectories and their individual probability amplitudes are thus necessary in calculating the total amplitude. However, not all possible trajectories are differentiable, thus suggesting that they are not physical possibilities, but only mathematical entities. It follows that if the possible differentiable trajectories are taken to be part of the physical system, they are not sufficient to calculate the total probability amplitude. The conclusion is that the total ensemble is weakly non-supervenient upon the physically possible trajectories.

中文翻译：

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路径积分和整体论

本文认为，量子力学的路径积分公式提出了一种整体论的形式，对于该形式，整体（路径的总集合）具有不能强烈还原为部分属性（单个轨迹）的属性。费曼历史求和通过对粒子可以采取的所有可能轨迹求和来计算粒子在边界内移动的概率幅度。这些轨迹及其各自的概率幅度因此在计算总幅度时是必要的。然而，并非所有可能的轨迹都是可微的，因此表明它们不是物理可能性，而只是数学实体。因此，如果将可能的可微轨迹视为物理系统的一部分，它们不足以计算总概率幅度。结论是总系综在物理上可能的轨迹上是弱非随附的。