One-dimensional physical quantities

In the present paper, we present operational definitions of the physical quantities distance, mass and time. Attempts to formulate a well-based operational definition of physical entities were first proposed in the end of the 19-th century by Hermann von Helmholtz and Otto Hölder. The problem consists in finding how to associate a number (the value of the entity) with a non-numerical entity (the entity itself). The paper presents a modern reading of the above mentioned authors. Paraphrasing Feynman in his classic work on path integrals, “there is a pleasure in recognizing old things from a new point of view”.

本文提出了距离、质量与时间三类物理量的操作定义（operational definition）。为物理实体构建具备坚实基础的操作定义的尝试，最早由赫尔曼·冯·亥姆霍兹（Hermann von Helmholtz）与奥托·赫尔德（Otto Hölder）于19世纪末提出。该问题的核心在于探索如何将数值（即物理实体的量值）与非数值的物理实体本身建立对应关联。本文对上述两位学者的相关研究进行了现代视角下的重读与阐释。正如费曼在其关于路径积分（path integral）的经典著作中所言：“以全新视角审视旧有事物，自有其独到乐趣。”