  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.
