Take radioactive decay. We can predict what percentage of the atoms of a lump of uranium will produce an alpha particle in the next month, say, but there is no way of predicting which particular atoms will do so. Nothing happens to the atoms that do that doesn't happen to the ones that don't. The emission of an alpha particle from an atom of a radioactive element is an event without a cause.
I did some research into this and I see that other forums argue about how "causeless" it is.
It seems I again disagree. But since we are dealing with science we can argue fact and not anecdotes (until we get to the Ultimate Cause!).
The way I see it (and of course, I stand to be corrected) is that:
One is dealing with large numbers of particles. And they are all non-identical both in terms of their internal state, and their position in time and space.
Science knows why they decay. It accomplishes a lower energy state. The fundamental particles making up a molecule are not in identical states. They are, after all, a complex assembly of quantum wave functions.
Added to this is the known scientific phenomenon of quantum vacuum fluctuations – namely that the temporary appearance of energetic particles in empty space is allowed by the uncertainty principle. This is due to interaction of “quantum waves” in the “empty space”.
When there is a combination of these effects, there is enough energy for decay to occur.
The statistical distribution of these effects on a macroscopic level can be observed - just as the macroscopic effect of molecules of gas in a sealed container can be observed.
With regard to gas molecules we know that the molecules have a distributed pattern of momentum. One cannot predict which molecule will escape at what time though a tiny hole in the container unless an instantaneous snapshot of the entire system can be done, and then incredibly precise calculations done to get to future states.
Even this would not work because one would have to take into account the underlying quantum vacuum fluctuations. To remove the randomness from these particles popping in and out of space one would have to take a snapshot of every underlying quantum wave to predict where the fluctuations would take place.
We know what causes the state of a system to change from one state to the other. And we know that each change has a cause - namely the previous state, and the laws of physics. The fact that precise measurement of any one particle is impossible does not negate the cause and effect chain.
Luckily for us, statistical (quantum) mathematics does work. In fact, works so well that science can move back in time to within an almost infinitesimal amount of time before the Big Bang.
The key is to move back past this singularity at time = 0. Something was there! And something caused the chain of events to start. It may have been another multiverse, but eventually we need a prime cause. One that "just is".
And theists call that God - an entity with intelligence and the ability to "cause" things to start happening.