Not all symmetries are on a par. For instance, within Newtonian mechanics, we seem to have a good grasp on the empirical significance of boosts, by applying it to subsystems. This is exemplified by the thought experiment known as Galileo’s ship: the inertial state of motion of a ship is immaterial to how events unfold in the cabin, but is registered in the values of relational quantities such as the distance and velocity of the ship relative to the shore. But the significance of gauge symmetries seems less clear. For example, can gauge transformations in Yang-Mills theory—taken as mere descriptive redundancy—exhibit a similar relational empirical significance as the boosts of Galileo’s ship? This question has been debated in the last fifteen years in philosophy of physics. I will argue that the answer is ‘yes’, but only for a finite subset of gauge transformations, and under special conditions. Under those conditions, we can mathematically identify empirical significance with a failure of supervenience: the state of the Universe is not uniquely determined by the intrinsic state of its isolated subsystems. Empirical significance is therefore encoded in those relations between subsystems that stand apart from their intrinsic states.

并非所有对称性都相同。例如，在牛顿力学中，通过将其应用于子系统，我们似乎很好地掌握了增强的经验意义。以伽利略船的思想实验为例：船的惯性运动状态对舱内事件如何展开无关紧要，但记录在关系量的值中，例如船相对于船的距离和速度岸边。但是规范对称性的重要性似乎不太清楚。例如，Yang-Mills 理论中的衡量转换（仅被视为描述性冗余）能否表现出与伽利略船的推进类似的相关经验意义？这个问题在过去的十五年里一直在物理学哲学中争论不休。我会争辩说答案是肯定的，但仅适用于规范变换的有限子集，并且在特殊条件下。在这些条件下，我们可以从数学上确定伴随性失败的经验意义：宇宙的状态并不是由其孤立子系统的内在状态唯一决定的。因此，经验意义被编码在子系统之间的那些与其内在状态不同的关系中。