But probability isn't the same as saying a system is random. Classical systems follow probability and this doesn't imply things happen randomly. As for the 'it's entirely random' claim, clearly it isn't. One such method of decay of a system is by associating the rate of decay with its motion. This is far from saying there is no physical parameters which are not directly affecting the decay rate. This type of radiation which will lead to a decay if it can, is called Larmor radiation. And changing the decay rate of a system, by altering further physical situations, further adds evidence it is a dynamical property - associated to a system, in dynamical ways.
It says the system behaves as if it were random. Physical circumstances - and measurement frames - often affect probability distributions. The decay rate is a calculation, based on a probability distribution. What's your point?
No where does probability mean strictly it must behave randomly. Take a wave function, where does it explicitly say in the physics text books that probability HAS to be random? I'll answer that for you.. no where. In fact, deterministic probability fields have been suggested and they take the form of pilot waves.
My point is, the abuse of physics here. Probability doesn't have to imply random systems. Not in physics it doesn't.
In its axioms. Randomness is assumed, in the axioms of probability theory. So to correct your statement: Everywhere does probability mean strictly it must behave randomly. "Deterministic probability fields"? Good luck with that. The only known ways you can handle the violations of Bell's Inequality predicted by theory and observed by research are 1) QED - probability, intrinsic randomness 2) discarding Relativity and/or the standard formulations of logic employed so far by science in general.
Don't you understand its a contradiction to think wave functions imply randomness, when in definition, you can get deterministic cases? In mathematics, we don't say a system is this or that when both solutions are actually valid. If you can create a deterministic theory of a wave function (which people have actually done) then no, a wave function doesn't HAVE to mean it is random. Does that make any sense?
And if a wave function doesn't have to be random, then no, it doesn't make as the only argument to satisfy randomness.
You can't get a deterministic cause, normally. You can get a deterministic approximation, a very useful deterministic simplification and model, or the like, involving causes. I suggested pondering the 2nd Law, or thermodynamic events and entities (air pressure, for example). In the case of radioactive decay you would need to discard Relativity Theory and/or standard formal logic, to get even that. Quantum phenomena violate Bell's Inequality. Now if you want to go out into the ether and speculate on probability - the mathematics of it - being our way of perceiving a cause invisible to our senses or mental abduction alike, the reasoning and mathematics acting as a virtual sensory organ (in extension of its similar role in other arenas), so that you do have a causal determinism here with probability as the cause (and your "deterministic probability field" foreshadows sense), then I'm on board.
I always found this following as an interesting and peculiar analogue which demonstrates the phenomenon of the guiding wave phenomenon https://www.quantamagazine.org/flui...erministic-pilot-wave-quantum-theory-20140624
Of course. What's the "cause"? And how do you plan to handle the Bell violations, while keeping your cause/effect analysis coherent? You might be, say, discarding Relativity, or standard logic, or the requirement that "cause" always precede effect. You have several choices. Or you might be joining me in recognizing that pilot wave as a way of visualizing or imagining a probability distribution as a "cause". Btw: this refers to all physical situations, including the bouncing oil drop. You don't need to get hung up on the quantum stuff to see the issue.
In an illustrative way. There isn't one, and attempting to provide one can enlighten. Meanwhile: And this: still hang.
When a coin is tossed, probability is the best available tool to predict its outcome. But at the same time various forces are also working with the coin to decide its outcome. It may be the similar case with Radioactive Decay also.
It may conceivably be shown to be so one day, but there is no evidence for this to date. According to current physics it is a random process. More here: https://en.wikipedia.org/wiki/Radioactive_decay
Then let me rephrase: according to current physics there is no evidence of any force working. Therefore, applying Ockham's Razor, modern physics does not recognise any such force.
Violations of Bell's Inequality impose severe requirements on any proposed "force", to the point that it would not fulfill the ordinary intuitive comprehension of the meaning of the word - which is the major value, generally, as "forces" are seldom rigorously valid entities. Coin tosses never violate Bell's Inequality, and are otherwise well behaved and easily simplified systems - so essentially or rigorously invalid concepts such as "force" can be used to usefully simplify descriptions of what's happening.