How so? I also find randomness profound but not sure what you mean but not belonging in the materialized world. Particle decay/Radiation is a pretty random process I believe?

Possibly connecting random events to time, which is not material.

The transformation of a particle into two more basic particles is absolutely material.

Some confusion? I was saying "time is not material".

In my conception time is made out of events, and the events are I suppose all material, and all have probabilities. So maybe time follows inevitably from matter. But I think it exists in its own right as a phenomenon that isn't material. There are such things. Knowledge is another one.

Noether's Theorem states that it is fundamental to our real world - or else the apparent, fundamental symmetries of our physics are wrong.