Brandon Vogt and Sean Carroll agree that causality requires the flow of time. This Humean claim, which is axiomatic among philosophers of science and at least a few philosophers of time (cf. Brody, Smolin, Unger), is one I’ve found bewildering since grad school. I’ve already wrote at length about how the claim involves an equivocation of the temporal and causal senses of “after” but today I’m going to take another approach.
1.) That any Christian could believe the claim is baffling in the face of all the Christian metaphysics that insist on entities that are caused but not temporal. This includes the human soul but also all the separated substances, and St. Thomas follows most biblical angelologies I am aware of by arguing that creation is mostly composed of the angels (response to objection 5).
2.) Even apart from Christian metaphysics, logical implication and mathematical construction cause conclusions while not requiring temporal duration.
3a.) If we try to say that physical entities differ from logical and mathematical ones precisely in being causal, then what we’re doing is like saying that only winged-things fly and so airline pilots don’t. The claim can avoid being purely verbal only if you do the further work to flesh out what you’re saying. As it happens, I think any attempt to flesh out this sort of claim in a scientifically acceptable sense will collapse into contradiction and nonsense, and this for at least four reasons:
3b.) Even if we could flesh out the sense of how causality exists among the physical and not the mathematical or logical, this only gives rise to the further problem that what we now call science defines its units with both mathematical and logical constructions. Time equals things. It is a variable that is multiplied, divided, added, shifted around in an equation, and plotted on a graph. Physical time is therefore formally mathematical and so, ex hypothesi, formally timeless. Notice that this is true before we ever have an Einsteinian block-universe – it’s all there from the beginning by definition. And so if the contemporary physicist starts by trying to separate physical causality from mathematical implication he is guaranteed to end up in contradiction.
3c.) There is nothing odd here – the instantiation of any scientific concept involves contradiction. All of them involve isolation, disregard of complicating factors, idealization, disregard of outlier cases, etc. which is impossible to achieve in a physical system. Note that the sense of impossible I’m using is very strong – I mean logically impossible. An inertially moving body only moves in a straight line if there are no other bodies, but if there were no other bodies it would be unable to move at all (all motion is relative to some other body). Time is the same way: physics uses a notion of time that is infinitely precise since it can determine the error of any given clock, but an infinitely precise measure of time would have no duration and so could not even serve as a measure. Measuring with an infinitely precise time unit is to try to measure out a line in points. Physics is thus non-temporal by definition, since the notion of time it has is contradictory.
3d.) Relativity is seen to require a block universe, but it is not clear whether this is right. Relativity requires that any event that has temporal extension for one observer can be simultaneous for another, i.e. whatever is temporal to one person (i.e. separated from him in time) is not temporal for another. Even if we lay aside the fact of entanglement (!) which requires a single time for any two locations of the universe, it is fallacious to claim that if all events are non-temporal to some observer that there is some observer for whom all events are non-temporal since the first “all” means “any” and the second means “the whole”. But if there is no observer for whom all events are non-temporal, in what sense is the universe “a block”?
What we have, in fact, is another case of what was mentioned in 5. The block universe requires specifying some sense of “now” across all reference frames and then showing that the now of some observers in in front of it or behind it. In other words, it requires positing the existence of a now across all reference frames so as to make it a part of the definition of the denial of a single now. You can watch Brian Greene go through all the steps of the process starting at 21:53 here. All this is fine if we remember that the physical instantiation of scientific concepts involves contradiction, since they are formally tools for knowing and not principles of existence.
3e.) The basic fact in play is the one TOF pointed out a while ago: science moved from being the handmaiden of theology to being the handmaiden of engineering. It makes things that work. Scientists can take off their scientist cap and don a philosopher’s, and then go on to claim that nature is like the things that work, but the “like” always involves some distance from what nature actually is, and it is impossible even in principle to know how great this distance is. The likeness allows us to know something about nature, but saying “this is nature” of any scientific concept will mire the whole concept in contradiction.