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.
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.
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.)
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.
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.
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
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
https://en.m.wikipedia.org/wiki/Quantum_mechanics
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.
Being continuous is not actually a requirement of being real.
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.
https://simple.m.wikipedia.org/wiki/Planck_length#:~:text=It is about 1.616255,Planck length per Planck time.
That is actually good to know, it answers a lot of questions I’ve had about the universe.
If you want my credentials, the second book is deriving the hydrogen atom.
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