Zero chance events

A standard thing in the philosophy of science to say such stochastic explanation questions is that one can given an answer in terms of the objective chance of the event, even when these chances are less than 1/2.

But consider the question: Why did this atom decay exactly at t₁?

Here, the objective chance may well be zero. And surely that an event had zero chance of happening does nothing to explain the event. After all, that the decay at t₁ had zero chance does not distinguish the atom’s decaying at t₁ from the atom’s turning into a square circle at t₁. And to explain something we minimally need to say something that distinguishes it from an impossibility.

Here, I think, the causal powers theorist can say something (even though I may just want to reject the presuppositions; see the Response to Objection 2, below). Stochastic systems have a plurality of causal powers for incompatible outcomes. The electron in a mixed-spin state may have both a causal power to have its spin measured as up and to have its spin measured as done. Normally, some of the causal powers are apt to prevail more than others, and hence have a greater chance than others. But even the weaker causal powers are there, and we can explain the event by citing them. The electron’s spin was measured as, say, up because it had a causal power to that outcome; had it been measured as, say, down, that would have been because it had a causal power to that outcome. We can give further detail here: we can say that one of these causal powers is stronger than the other. And the stronger causal power has, because it is stronger, a higher chance of prevailing. But even the weaker causal power can prevail, and when it does, we can explain the outcome in terms of it.

This story works just fine even when the chances are zero. The weaker causal power could be so weak that the chance associated with it has to be quantified as zero. But we can still explain the activation of the weaker causal power.

So, going back to the decay, we can say that the atom had a causal power to decay at t₁, and that’s why it decayed at t₁. That causal power was of minimal strength, and so the chance of the decay has to be quantified as zero. But we still have an explanation.

The causal powers story about the atom encodes information that the chances do not. The chances do not distinguish the atom’s turning into a square circle from the atom’s decaying exactly at t₁. The causal powers do, since it has a power to decay but no power to turn into a square circle.

Objection 1: Let’s say that the atom has twice as high a chance of decaying over the interval of times [0, 2] as over the interval of times [0, 1]. How do we explain that in terms of causal powers, given that there are equally many (i.e., continuum many) causal powers to decay at precise times in [0, 2] as there are causal powers to decay at precise times in [0, 1]?

Response: It could be that just as the causal power story carries information the chance story does not, the chance story could carry information the causal power story does not, and both stories reflect aspects of reality.

Another story could be that there are causal powers associated with intervals as well as points of times, and the causal power to decay at a time [0, 2] is twice as strong as the causal power to decay at a time in [0, 1]. There are difficulties here, however, with thinking about the fundamentality relations between the powers associated with different intervals. I fear that there is no avoiding an infinite sequence of causal powers that violates causal finitism, and I am inclined to reject the possibility of exact decay times—and hence reject the explanatory question I started this post with. I don’t see much hope for a measurement of an exact time after all. But someone with other commitments about finitism could have a story.

Objection 2: This is just like a dormitive power explanation of opium making someone sleepy.

Response: Opium’s dormitive power is fundamental or not. If opium has a fundamental dormitive power, then the dormitive power explanation is perfectly fine. That’s just the kind of explanation we have to have at the fundamental level. If the dormitive power explanation is not fundamental, then the explanation is correct but not as informative as an explanation in terms of more fundamental things would be.

Likewise, the power to decay at t₁ either is or is not fundamental. If it is fundamental, then the explanation in terms of the power is perfectly fine. If it is not, then there is a more fundamental explanation. But probably the more fundamental explanation will also involve minimal strength powers with zero activation chances, too.