The conceptual relation between objective becoming and the direction of time is explored by discussing an ontologically asymmetric notion of causation. It is claimed that such a notion, in terms of which Stein defined objective becoming in Minkowski spacetime, has either a purely metaphysical status or is reducible to physical concepts. In the former case, it is adequate for Stein's purpose but irrelevant to physical theories. In the latter, the causal asymmetry can be related to irreversible physical processes only in (...) an extrinsic way. This dilemma creates additional difficulties both to a unified theory of the direction of time and to the project of making room for becoming in the physical world. (shrink)