A retrospective view of the Umkehreinwand and Wiederkehreinwand

Do these objections show that there are inner inconsistencies in the statistical interpretation Several respected investigators answer this question in the affirmative even today.148 A careful consideration of the geometrical properties of the tf-curves (as given above) is needed in order to understand how Boltzmann in his elucidations of the //-theorem could assign to these H- 

That H almost always immediately decreases from any higher value (in the sense of the H-theorem). 

That this holds both in the direct and reverse time directions (as Loschmidt demands it—Section 7a). 

As soon as we clear up all the misunderstandings in this respect (see the discussion of Section 14b), we have to agree with Boltzmann that we can find no inner inconsistencies this way at all.149 

It is true that to each phase r in the set of phases in question we can find a phase r in such a way that r and r assign the gas model the same configurations but opposite velocities.161 However, the statement that 

---