A new formalization of Putnam’s proof that time does not flow

Virtually all known attempts to formalize, at least partially, Putnam’s two-stage proof contained in his famous article Time and Physical Geometry, follow Stein’s advice to interpret the relation R as "x is real to y". However, Putnam has explicitly rejected this interpretation, stating that it “misses the issue” he was addressing. The present attempt to formalize the proof regards reality as an absolute property, in accord with Putnam’s intention. The formalization reveals both the strength and the weak point of his reasoning. On the one hand, it shows that the popular assumption that "all and only things that exist now are real" is incompatible with Special Relativity in its standard interpretation. What is more, its weaker version "all things that exist now are real" implies that future things must be real, which clearly contradicts the popular belief in time flow, i.e. in successive becoming of events. Effectiveness of the proof does not depend on the original choice of simultaneity-in-the-observer’scoordinate-system as R. What is more, its transitivity is not demanded, and after some reasonable strengthening of one of the assumptions, not even symmetry. Without this strengthening, it is still proved that Relativity is incompatible with the presentist conception of time flow and compatible at most with its Growing Block Universe version. Even taking into account the local character of Special Relativity does not help, since the formalization can be easily generalized to hold in the framework of General Relativity. On the other hand, the popular view is compatible with Relativity in the Lorentzian interpretation. Thus, what Putnam has really proved is not incompatibility of time flow with Relativity as such, but only with its standard interpretation