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!
There is no fact about reality that can ever threaten facts about mathematics. Mathematic definitions exist independent of reality.
In fact, you can build a system of definitions that very clearly doesn’t exist in real world, like hyperbolic geometry.
Sometimes we find that obscure pure mathematics does describe reality when no one expected it to. Riemannian geometry is one such example.
Complex numbers, and a bunch more things too
Kurt Gödel:
What? You use these words, but I do not think they mean what you think they mean.
Quantization is probably the result of vibrational modes, that doesn’t mean irrational numbers don’t exist, just that we can’t measure an infinitely precise value. Tau and root-two exist, they arise naturally in the most basic geometric shapes.
This sounds really interesting but I’m afraid it’s a bit high level for me. Can you explain how vibrations would cause quantisation? I’d also be happy with a link to the correct Wikipedia article or a paper which explains it. :)
This text book seems to cover the idea. https://phys.libretexts.org/Bookshelves/College_Physics/College_Physics_1e_(OpenStax)/30%3A_Atomic_Physics/30.06%3A_The_Wave_Nature_of_Matter_Causes_Quantization I guess I’m drawing my ideas mainly from the Bohr model.
The premise here is completely wrong.
I know those words, Someone please explain .
Yes please!
