Replacing faulty nineteenth century physics by its orthodox quantum successor converts the earlier materialist conception of nature to a structure that does not enforce the principle of the causal closure of the physical. The quantum laws possess causal gaps, and these gaps are filled in actual scientific practice by inputs from our streams of consciousness. The form of the quantum laws permits and suggests the existence of an underlying reality that is built not on substances, but on psychophysical events, and on objective tendencies for these events to occur. These events constitute intrinsic mind-brain connections. They are fundamental links between brain processes described in physical terms and events in our streams of consciousness. This quantum ontology confers upon our conscious intentions the causal efficacy assigned to them in actual scientific practice, and creates a substance-free interactive dualism. This putative quantum ontology has previously been shown to have impressive explanatory power in both psychology and neuroscience. Here it is used to reconcile the existence of physically efficacious conscious free will with causal anomalies of both the Libet and Einstein–Rosen–Podolsky types. This article is a sequel to Stapp [2005, Journal of Consciousness Studies12(11), 43–58] but strives to be largely self-contained.