Randomness from the point of view of an agent can be defined as having incomplete information. It is about the strongest state of belief that can be justified. But don't let your intuition fool you that having incomplete information means it is possible to have complete information. As a simple example, consider the position of a certain particle floating freely in space at 1 second in the future to be the thing of interest. It is NEVER possible for any agent to have enough information to know this. If this is in a large vacuum, the uncertainty becomes greater as the amount of time in the future increases.
The reason this is so is that there is uncertainty in the position and uncertainty in the velocity. You need to have perfect knowledge of BOTH to know where the particle will be at a certain time in the future. But Heisenburg says that you can't be precise about both. The more precisely you know one thing, the less precise your knowledge of the other. There is a fairly happy medium where both are a bit imprecise that minimises future uncertainty about the position, but this is always at least some minimum amount (that can easily be calculated for a given particle and given time interval).
The strong characteristic of quantum randomness (say about the position of a particle at some time) is that it applies to all of agents who are in the causal past of some point in space-time.
I'm very aware that experiments prove that agents can never access complete information, but im not aware of any experiment that show that the information do not exist regardless to agents.
do you understand what i mean by that?
It is the experiments that violate Bell's inequality that prove that there is no possibility of recovering determinism - the randomness is absolute.
absolutely inaccessible for an agent? or just absolutely random regardless of any agents?
The experimental evidence is often consistent with no effect, and cheats and errors have been detected in a lot of experiments that do appear to provide evidence, so it is best to be slow to believe any that do.>>>
The entire field is full of experiments that have been badly constructed and wrongly interpreted, leading to evidence both positive and negative, although most these days seem to be tilted towards "proving" no effect whilst those say in the very early 1970s seemed to genuinely show that effects existed. Of course, that's before everything was logged online. But forgetting human experiences and experiments, there are enough examples of effects that can only realistically be explained as telepathy in animals to make one realise that what we have now is an intellectual industry devoted to demonstrating logical positivism, and that in the face of newer experiments that are just starting to come through. These things occur in waves or trends. I suspect we'll see a new type of experimentation. But to set up a really well done experiment would cost millions of pounds and at best it could only demonstrate things that can be explained as statistical freaks.