My question was about the probability governing the chance at a jump. Apparently, it is not constant and takes t as an input. (Otherwise how does it know that it is rising to 1)
Ok, I see, that makes sense. One thing I’d like to know is, does the frequency of transitions correlate to the time it takes for the transition to occur.
I’m not sure. There must be some factor that causes one quantum transition to occur more or less frequently than another. That factor isn’t really hidden because we can measure the frequency of transitions, but as far as I know, we don’t understand it’s nature. That factor, whatever it is, may determine the time it takes for the transition to occur but it’s not necessarily like a memory, but more like a trajectory. Clearly something in the quantum state is changing, so it is a system of some sort.
I think you're asking two somewhat entwined but not-same questions: Consider the case of a mushroom that is actually mycelium and fungi network underground. The actual mushroom top that has spores is at the very very end of the lifecycle. The mushroom fungal network of mycelium actually spans months, years, or even decades before the final "fruiting" part of the mycelium takes place. It's likely that these quantum leaps are much like the fruiting event of a long-time-growing networked-body of sorts. In which case, frequency of fruiting and time it takes to occur would be different for different types of mushroom, or different types of plants, and therefore it's likely that there are probably different "types" of quantic networks that are direct precursors to quantum jerks that only appear instantaneous when your equipment is frame-rated. This, of course, only incurs more questions, like what the heck is this pre-leap quantum body like, and how can back can we actually trace a quantum event, and if everything is broken down into quantum events how can we meaningfully measure development and duration of something seemingly induratable? It'd be like trying to trace back fully grown corn to the seed. Of course, it's likely covered in kernels that will inspire and directly create other corn-phenomena, but the original kernel cracking open is information long gone. Quantum entanglement therefore actually means you're inextricably linking two quantum streams, not quantum events. Using that sort of process, it may be possible to find out where quanta are "produced" if I may use such coarse terminology that harkens back to the natural plowshare of the most simple kind of field.
