The meme wasn’t about imaginary numbers, but irrational numbers like pi or the swuare root of 3. Mathematicaly, those numbers have mever ending decimals that never repeat. But quantum mechanics doesn’t allow for any measurements smaller/more precise than the planck scale. The quantum nature of the universe means that no object in the universe can have an irrational length.
An easy way to picture this is a right triangle. I can make said triangle with two sides that are exactly 1 meter long, all the way down to the planck length. The hypotenuse is theoretically exactly the square root of 2 meteres long, but that is impossible because part of that triangle would have to exist beyond the quantum realm.
Imaginary numbers are a rotational operator.
You don’t need quantum mechanics to observe rotation in the real world.
The meme wasn’t about imaginary numbers, but irrational numbers like pi or the swuare root of 3. Mathematicaly, those numbers have mever ending decimals that never repeat. But quantum mechanics doesn’t allow for any measurements smaller/more precise than the planck scale. The quantum nature of the universe means that no object in the universe can have an irrational length.
An easy way to picture this is a right triangle. I can make said triangle with two sides that are exactly 1 meter long, all the way down to the planck length. The hypotenuse is theoretically exactly the square root of 2 meteres long, but that is impossible because part of that triangle would have to exist beyond the quantum realm.
i is a rotational operator. So equations with i in them have pi encoded into them too.
Trying to expand a quantized rotation into a quantized linear coordinate is attempting to square a circle.