3 ms·

I think you're suggesting that "real" numbers are an abstraction that is convenient to model with, but aren't actually fully representable in the universe, beca

• ssivark 8y ago
  It's not even necessarily about quantum stuff. The point is that any practical measurement system (even classical ones) can only deal in finite precision numbers. And since that set is of vanishing measure on the real line, there isn't an obvious notion of continuity/smoothness (my knowledge here is limited). That can lead to some surprises. For the more advanced readers: this result reminds me of how Haag's theorem shows (rigorously) that relativistic interacting QFTs can't exist (assuming operators sit at points indexed by real numbers), while in a Wilsonian sense QFTs are perfectly fine, because there's a UV cutoff, and all measurements have a finite resolution.