Are indeterministic events temporally irreducible?

If one divides time successively one ends up with Zeno Paradox situations, but I think with indeterminism you have a potentially different problem.

Consider quantum indeterminism -->

1) What happens between the moment a photon makes contact with a window and the next moment it either passes through or becomes one of the "reflected four" out of 100?

2) What happens between the moment a particle is in superposition and the moment it actually ends up in a singular position?

3) What happens between the moments before & after a particle is emitted from an atomic nucleus due to radioactive decay?

So given these all seem like examples of irreducible events, it might be better to think of a "thick present" like the physicist Lee Smolin talks about ->

As Rovelli has emphasized, time is a complex phenomena, and we should be precise and assert exactly which aspects are being claimed to be fundamental. I will be more precise in section 3 below, but let me briefly say here that the aspect of time I assert is irreducible is its activity as the generator of novel events from present events[3]. This activity generates a thick present,by which is meant that two events in the present can be causally related with each other. This thick present is continually growing by the addition of novel events. At the same time other events in the thick present, having exhausted their potential to directly influence the future, slip from the present to join the always growing past. This continual construction of the future from the present, which then becomes past, makes the distinction between past, present and future objective and universal.

All to say if an event is genuinely indeterministic, it arguably has to be irreducible with respect to time?

IEP: Alfred North Whitehead (1861—1947)

Gary L. Herstein

The basic units of becoming for Whitehead are “actual occasions.” Actual occasions are “drops of experience,” and relate to the world into which they are emerging by “feeling” that relatedness and translating it into the occasion’s concrete reality...This focus on concrete modes of relatedness is essential because an actual occasion is itself a coming into being of the concrete. The nature of this “concrescence,” using Whitehead’s term, is a matter of the occasion’s creatively internalizing its relatedness to the rest of the world by feeling that world, and in turn uniquely expressing its concreteness through its extensive connectedness with that world...

Actual occasions are fundamentally atomic in character, which leads to the next interpretive difficulty. In his previous works, events were essentially extended and continuous. And when Whitehead speaks of an “event” in PR without any other qualifying adjectives, he still means the extensive variety found in his earlier works (PR 73). But PR deals with a different set of problems from that previous triad, and it cannot take such continuity for granted. For one thing, Whitehead treats Zeno’s Paradoxes very seriously and argues that one cannot resolve these paradoxes if one starts from the assumption of continuity, because it is then impossible to make sense of anything coming immediately before or immediately after anything else. Between any two points of a continuum such as the real number line there are an infinite number of other points, thus rendering the concept of the “next” point meaningless. But it is precisely this concept of the “next occasion” that Whitehead requires to render intelligible the relational structures of his metaphysics. If there are infinitely many occasions between any two occasions, even ones that are nominally “close” together, then it becomes impossible to say how it is that later occasions feel their predecessors – there is an unbounded infinity of other occasions intervening in such influences, and changing it in what are now undeterminable ways. Therefore, Whitehead argued, continuity is not something which is “given;” rather it is something which is achieved. Each occasion makes itself continuous with its past in the manner in which it feels that past and creatively incorporates the past into its own concrescence, its coming into being.

Thus, Whitehead argues against the “continuity of becoming” and in favor of the “becoming of continuity” (PR 68 – 9). Occasions become atomically, but once they have become they incorporate themselves into the continuity of the universe by feeling the concreteness of what has come before and making that concreteness a part of the occasion’s own internal makeup...

Most authors believe that the sense of “atomic” being used here is similar to, if not synonymous with, “microscopic.” However, there are reasons why one might want to resist such an interpretation. To begin with, it teeters on the edge of the fallacy of simple location to assume that by “atomic” Whitehead means “very small.” An electron, which Whitehead often refers to as an “electronic occasion,” may have a tiny region of most highly focused effects. But the electromagnetic field that spreads out from that electron reaches far beyond that narrow focus. The electron “feels” and is “felt” throughout this field of influence which is not spatially limited. Moreover, Whitehead clearly states that space and time are derivative notions from extension whereas, “To be an actual occasion in the physical world means that the entity in question is a relatum in this scheme of extensive connection” (PR 288 – 9). The quality of being microscopic is something that only emerges after one has a fully developed notion of space, while actual occasions are logically prior to space and a part of the extensive relations from which space itself is derived. Thus it is at least arguably the case that the sense of “atomic” that Whitehead is employing hearkens back more to the original Greek meaning of “irreducible” than to the microscopic sense that pervades physical science. In other words, the “atomic” nature of what is actual is directly connected to its relational holism.