On Symmetries and Springs

Imagine that we are on a train, playing with some mechanical systems. Why can't we detect any differences in their behavior when the train is parked versus when it is moving uniformly? The standard answer is that boosts are symmetries of Newtonian systems. In this article, I use the case of a spring to argue that this answer is problematic because symmetries are neither sufficient nor necessary for preserving its behavior. I also develop a new answer according to which boosts preserve the relational properties on which the behavior of a system depends, even when they are not symmetries.