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:
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.
That is not a definition of the real numbers, quantum physics says no such thing, and even if it did the conclusion is wrong
Let’s have a look.
https://en.m.wikipedia.org/wiki/Irrational_number
In mathematics, the irrational numbers (in- + rational) are all the real numbers that are not rational numbers. That is, irrational numbers cannot be expressed as the ratio of two integers. When the ratio of lengths of two line segments is an irrational number, the line segments are also described as being incommensurable, meaning that they share no “measure” in common, that is, there is no length (“the measure”), no matter how short, that could be used to express the lengths of both of the two given segments as integer multiples of itself.
https://en.m.wikipedia.org/wiki/Quantum_mechanics
Quantum systems have bound states that are quantized to discrete values of energy, momentum, angular momentum, and other quantities, in contrast to classical systems where these quantities can be measured continuously.
The conclusion is wrong, i agree. That’s the joke of the meme.
(Keep down voting if it matters to you. I’m only trying to explain a joke. The top post is in agreement with my statement.)
Quantum mechanics still have endless ratios which aren’t discrete. Especially ratios between stuff like wavelengths, particle states, and more
I’m fully aware of the definitions. I didn’t say the definition of irrationals was wrong. I said the definition of the reals is wrong. The statement about quantum mechanics is so vague as to be meaningless.
Come on then, enlighten the average Joe.
Google it? Axiomatic definition, dedekind cuts, cauchy sequences are the 3 typical ones and are provably equivalent.
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A real number is the set of both rational and irrational numbers. Nothing about continuous anything.
It is exactly that though.
Irrationel and rational numbers are both real.
Quantum physics is limited to the quantum, hence the name.
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.
If you want my credentials, the second book is deriving the hydrogen atom.
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.
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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 .
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.
but irrational numbers like pi
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.
Yes please!
https://www.sciencenews.org/article/quantum-physics-imaginary-numbers-math-reality
Nontechnical article explaining the concept.
But that’s imaginary numbers, not irrational numbers.
The issue between quantum physics and irrational numbers is different than the use of imaginary numbers: Irrational numbers have infinite decimals, while quantum physics is quantized.
So because quantum mechanics is well modeled by imaginary numbers, the existence of quantum particles threatens the definition of irrational numbers? That doesn’t make any sense.
Yes, it does not make any sense. If the link above is what it appears from the summary, some students unknowingly attempted to square the circle.
