Contemporary ‘common sense’ thinks of the world as a collection of material objects extended in three-dimensional space and enduring in a separate Newtonian time. Special Relativity unifies Newtonian space and time into space-time. It does not recognize any special universal ‘now’ of time. Instead, it states that objects consist, not of 3D entities enduring in time, but as 4D world lines existing and extended from the big bang to the big crunch.
For example, the earth is not a spheroid circling the sun, but a stationary hyperhelix wound around the world lines of the sun. Thus the buildings of imperial Rome still stand — it is just that we cannot see them any more. The buildings of future cities already exist — but we cannot see them yet. It should be noted, however, that there is no more a distinguished present in Newtonian physics than there is in special relativity, so all times must be treated symmetrically in regard to the distribution of matter. So, if one wants to account for our psychological impression that there is a ‘now’ in time and moreover that time in some way flows, we must look elsewhere than contemporary physics, whether Newtonian or Relativity, to find it.