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Yes, there are non-deterministic parts in physics. For example atomic decay. While we can measure and work with half-life times for large amounts of radioactive atoms, the decay of a single, individual atom is unpredictable. So in a way, you can get your desired dose of vagueness by controlling how many atoms you monitor. The less, the more.
Or another example from the same field: There are atoms for which we believe they are stable, although they theoretically could decay. But we never observed it. So maybe they are in fact stable, or maybe they decay just slower than we have time. Or only when we don't look. Examples would be Helium-4 or Lead-208.
I also like the idea, inspired by Douglas Adams, that the universe itself could be a weird and random fluctuation, which just happens to behave as if it was a predictable, rationally conceivable thing. That actually, it's all a random chain of junk events, and we're fooled into spottings some patterns. This apparence could last forever or vanish the very next moment, who knows. Maybe it's all just correlation and there is zero causation. As far as I know, we'll never be able to tell. So fundamentally, all of it is a vague guess, supported by mountains of lucky evidence.
(Edit: Author name corrected)
Bismuth-209 was for a long time considered to be the heaviest stable primordial isotope, it had been theorized for a while that it might technically decay, but no one proved that until 2003, it has a half-life of over a billion times the current age of the universe, and so for all practical purposes can be treated as if it is stable.
I'm no physicist, so I very well be way out of my element, but I would personally not be the least bit surprised if it turned out every atom was technically unstable, but since the decay is so incredibly slow we may never be able to accurately detect it. Using the lead-209 example you gave, if it ever is proven to be unstable, the half life should be at least 10^25^ (10,000,000,000,000,000,000,000,000/ten septillion) times longer than the age of the universe. Smarter people than myself probably have some ideas, but I couldn't imagine how you could possibly attempt to measure something like that.
Oh wow, thanks for the details! 10^25^ years ... no, times ... yeah, crazy. I mean, that's beyond homeopathic. Since I learned about this topic as an interested layman, I somehow assumed everything can decay, and we simply call the things "stable" which do so very slowly. Which can mean as many atoms decay over the course of a billion years as there are medically effective molecules in homeopathic "medicine"; none.
Also https://en.wikipedia.org/wiki/Proton_decay
Good answer! Thanks for that. Also, good use of 'apparence' - not a word i see often.
Apparently Bismuth-209 has what is considered an "alpha decay" with a half life longer than the lifetime of the universe - whatever that means. So yeah, entered into some fuzzy physics there.
The standard model predicts that hydrogen-1 is the only stable nuclide because electroweak instantons allow three baryons (such as nucleons: protons and neutrons) to decay into three antileptons (antineutrinos, positrons, antimuons, and antitauons), which imply the instability of any nuclide with a mass number of at least three; or for two baryons to decay into an antibaryon and three antileptons, which would imply that deuterium could decay into an antiproton and 3 antileptons.
This is very rarely discussed because the nuclides that can only decay through baryon anomalies would be predicted by the standard model to have ludicrously long half lives (to my memory, something roughly around 10^150 years, but I might be wrong).
Hydrogen-1 is stable in the standard model, as it lacks a mechanism for (single) proton decay.