Temporal Existence and Ontological Indeterminism in Minkowski Spacetime

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The view that the future is open, i.e., not only epistemically but ontologically indetermined distinguishes, apparently, the present being the edge of being. Correspondingly, since the famous Putnam/Stein-controversy, in philosophy of science the two problems of the compatibility of relativity with dynamic views of time and reality and with ontological indeterminism are considered as being deeply connected. Many authors (like McCall and Belnap) regard indeterminism at least a necessary condition for a dynamic view of time, being thus constitutive either for a growing block or a presentistic universe. But in fact both conceptions might rather be independent (see Esfeld). Taking into account that the meaning of indeterminism depends on the view of natural laws might be helpful in order to clarify its connection to dynamic views of time. Based on the reductive view of natural laws (see Lewis idea of Humean supervenience) indeterminism is surely compatible with eternalism. But the more interesting question arises, how a realistic understanding of natural laws (see Mumfords metaphysics of dispositions) is related to the block universe view. Could an indeterministic universe in that sense be eternal? Or is such a universe dynamical, even if the laws were deterministic?