Holism as the significance of gauge symmetries

The thought experiment known as Galileo's ship exemplifies a relational empirical significance of subsystem boosts. The inertial state of motion of the 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. Can gauge transformations in Yang-Mills theory---taken as mere descriptive redundancy---exhibit a similar empirical significance? This question has been debated in the last fifteen years in philosophy of physics. I will argue that the answer is `yes'. To clearly pose the problem, I focus on physical, i.e.: gauge-invariant information. Recent results prove that given two subsystems' physical information, the universal state obtained by the composition of the subsystems is not always uniquely determined \cite{GomesRiello_new}. Moreover, the state's residual variety is encoded in the action of a symmetry group on a subsystem. While for Galileo's ship the variety is encoded in boosts and translations, in gauge theory this variety has the structure of the finite-dimensional Lie group of the theory.