  The Ehrenfests have suggested that the ergodic hypothesis played a much more fundamental role. In particular they have pointed out that if the hypothesis is true, averaging over an (infinitely) long time would be identical to phase averaging with the microcanonical distribution. Thus, they suggested that Boltzmann relied on the ergodic hypothesis in order to equate time averages and phase averages, or in other words, to equate two meaning of probability (relative time and relative volume in phase space.) There is however no evidence that Boltzmann ever followed this line of reasoning. He simply never gave any justification for equivocating time and particle averages, or phase averages, at all. Presumably, he thought nothing much depended on this issue and that it was a matter of taste.