“Indeed, we can consider using invariance groups as a way of specifying a structure (rather than specifying a structure in some other fashion, and then examining its invariances).” (p. 57) #Dewar #invariance #group #structure
„The key difference from Newtonian spacetime, then, is that there is no ‘persistence of space over time’: since there is no notion of a vector being ‘purely temporal’, we cannot say of two points in G0 that they differ by a purely temporal vector, and hence correspond to the same point of space at two different times. (By contrast, since we do have a notion of purely spatial vectors, we can say of two points of G0 that they differ by such a vector and hence correspond to two different points of space at the same time; this is precisely the relation that foliates G0.).“ (p. 55) #Dewar #spacetime