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Joined 1 year ago
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Cake day: July 2nd, 2023

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  • No, by our current understanding there is no length smaller than a Planck length, and any distance must therefore be divisible by an integer. That is, the length is made up of discrete quanta. Pi, or any other irrational number, is by definition not divisible by an integer, or it would be a ratio, making it rational. This has nothing to do with the accuracy or precision of our measures.



  • My only guess as to what this could mean is that since quantum mechanics is quantum, i.e. discrete, the universe therefore cannot be continuous as the reals are. But this is a category error. Just because you could never find an object that is, say, exactly pi meters long, does not mean that the definition of pi is threatened. There’s nothing infinite that we can observe, but infinity is still a useful concept. And it works both ways; just because quantum mechanics is our best model of the universe doesn’t mean the universe is therefore quantum. 150 years ago everyone believed the universe was like a big clockwork mechanism, perfectly deterministic, because Newtonian physics are deterministic. And who knows, maybe they were right, and we just don’t have the framework to understand it so we have a nondeterministic approximation!