When the question of why chancy effects in quantum mechanics lead to statistical regularities is proposed, it is often answered using the law of large numbers.
When you have particles that can be located at with certain probabilities in the double slit experiment, of course, on aggregate you will have effects that seem deterministic. This is similar to how if you define an event that has two possible outcomes with 50% probability each, the law of large numbers dictates that with enough repetitions of this same event, about 50% of them will land on one of the binary outcomes.
But the law of large numbers would only work if the event just discussed is defined to have a probability distribution in the first place. As such, how can this be an explanation of why there is a probabilistic nature to the seemingly uncaused effects in quantum mechanics?
Note that this question is different from asking why certain probabilities exist instead of others, a question that I have asked before. One can presumably use the Schrödinger’s equation and the wave function to explain this.
Neither is this similar to asking why, for example, a radioactive atom decays at a certain time t. For this, atleast we have experiments that may explain why or atleast justify why one should believe this occurs for no (sufficient) cause (as per Bell’s theorem). But even if this does occur for no cause, it has no bearing on why multiple events occurring witj no cause should result in a probabilistic structure in the first place.
Why then is the world probabilistic fundamentally in the first place? Why not chaos? And why does this probabilistic structure evolve in a deterministic way? There is no rule stating that many things that happen with no cause must result in a probabilistic structure. So simply asserting this implication doesn’t work and neither is there any existing physical theorem that points to an answer here.
Are there any philosophers or even scientists that have pondered this or have tried to figure it out, or is this just another one of those things that is chalked up to happening “for no reason”.
(Explain philosophical significance of the question).