What physical properties would a universe have if governed by classical physics with a Galilean space-time?
The answer depends on what type of mechanical system makes up this hypothetical universe. Let us consider the simplest possible model: suppose that all of space is (or is filled with) an ideal elastic solid. Disturbances of equilibrium can yield transverse and compressional waves. Historically this model was used to derive the classical properties of light. Variable density results in wave refraction. If anything resembling matter can exist in such a medium, it must take the form of standing or soliton waves whose energy is localized within a limited region. If matter itself consists of waves, then it is not possible to measure the characteristic wave speed. All distance measurements (even with rulers made of soliton waves) would be equivalent to wave propagation time measurements. The wave speed can be nothing more than a conversion factor relating units of distance and units of time. This is the key feature of Special Relativity: that the speed of light is simply a constant factor. O
