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!
We could make an object that is exactly pi meters long. Make a circle of 1 meter in diameter, and then straighten it out. We would not be able to measure the length more accurately than we can calculate it (that might be the largest understatement ever) but to the tolerance with which we could make a 1 meter diameter circle, you should have the same tolerance to the circumference being pi.
I mean, you only need 39 digits of pi to calculate the circumference of a circle with a diameter the size of the universe to the width of a hydrogen atom. So no matter how detailed you get it’s impossible to determine if a circles circumference is anywhere close to exactly pi.
To ops point, you could set up your thing theoretically and we can math out that it should be pi. But we could not make that object.
There is no fact about reality that can ever threaten facts about mathematics. Mathematic definitions exist independent of reality.
Kurt Gödel:
In fact, you can build a system of definitions that very clearly doesn’t exist in real world, like hyperbolic geometry.
I know those words, Someone please explain .
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.
But irrational numbers aren’t the same as imaginary numbers. Also, there are irrational imaginary numbers. And quantum physics loves using imaginary numbers. So that sentence in the image is nonsense, right?
The definition of irrational numbers is that they are the real numbers that are not rationel. So we need to look at the definition of real numbers. A real number is a number that can be used to measure a continuous one dimensional quantity.
Quantum physics says that reality is not continuous. Particles make “discrete” jumps instead of moving continuously. So irrational numbers can’t exist.
They don’t make “discrete jumps” as in teleportation. They exist stable in discrete energy levels, but that doesn’t imply things don’t move continuously.
ORLY?
Please take your evening off to explain to the common man how electrons are distributed without restoring to quantisation.
That’s not what I said?
They’re “stable” energy states. That’s all.
And that they might still move continuously. Which is impossible to prove (see Planck length).
Edit: Corrected my statement based on the reply
That’s not what Planck length is. It’s the minimum resolvable accuracy not measurement. Meaning we can’t prove something was somewhere specific beyond the Planck length. Not that it’s the building size of the universe.
it is a common misconception that it is the inherent “pixel size” or smallest possible length of the universe.[1] If a length smaller than this is used in any measurement, then it has a chance of being wrong due to quantum uncertainty
That is actually good to know, it answers a lot of questions I’ve had about the universe.
