Does Galilean relativity imply infinite propagation speed?

[hgandh]

Without assuming a universal speed that is constant in all inertial reference frames, is it a necessary consequence of Galilean symmetry that interactions are instantaneous? If this is the case how can we prove this?

 

[anuttarasammyak]

With the universal maximum speed of c in all IFR, Galilean transform for (t,x,y,z) stands in approximation of v/c $\rightarrow$ 0 namely increasing c to infinity in Lorentz transformation for (t,x,y,z).

I am not certain whether first given infinite c or instantaneous interaction could lead to Galilean transformation.

 

[Ibix]

Without assuming a universal speed that is constant in all inertial reference frames, is it a necessary consequence of Galilean symmetry that interactions are instantaneous?

Galilean symmetry does imply an invariant speed - infinite speed. If you start with the principle of relativity you can derive most of the way to the Galilean and Lorentz transforms. Deciding if your invariant speed is finite or not is the next step that selects which ones you get.

That said, I don't think there's any requirement that anything propagate at that invariant speed. Fluid dynamics, for example, is a form of purely Newtonian physics which yields finite wave speeds in media - so we have finite propagation speeds falling out of Newtonian physics. And in relativistic physics we have the weak interaction which propagates via massive bosons, so slower than light. So it rather looks to me that the existence of an invariant speed doesn't force anything to interact at that speed.