this post was submitted on 20 Jun 2024
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Science Memes

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Irrational (mander.xyz)
submitted 4 months ago by [email protected] to c/[email protected]
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[–] [email protected] -3 points 4 months ago* (last edited 4 months ago) (2 children)

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.

[–] kogasa 12 points 4 months ago (1 children)

That is not a definition of the real numbers, quantum physics says no such thing, and even if it did the conclusion is wrong

[–] [email protected] -1 points 4 months ago* (last edited 4 months ago) (2 children)

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.)

[–] [email protected] 2 points 4 months ago* (last edited 4 months ago)

Quantum mechanics still have endless ratios which aren't discrete. Especially ratios between stuff like wavelengths, particle states, and more

[–] kogasa 2 points 4 months ago (1 children)

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.

[–] [email protected] -1 points 4 months ago (3 children)

Come on then, enlighten the average Joe.

[–] kogasa 2 points 4 months ago

Google it? Axiomatic definition, dedekind cuts, cauchy sequences are the 3 typical ones and are provably equivalent.

[–] [email protected] -2 points 4 months ago (1 children)

A real number is the set of both rational and irrational numbers. Nothing about continuous anything.

[–] [email protected] -1 points 4 months ago (1 children)

It is exactly that though.

Irrationel and rational numbers are both real.

Quantum physics is limited to the quantum, hence the name.

[–] [email protected] 3 points 4 months ago

Being continuous is not actually a requirement of being real.

[–] [email protected] 3 points 4 months ago (1 children)

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.

[–] [email protected] 0 points 4 months ago (2 children)

ORLY?

Please take your evening off to explain to the common man how electrons are distributed without restoring to quantisation.

[–] [email protected] 3 points 4 months ago (2 children)

That’s not what I said?

They’re “stable” energy states. That’s all.

[–] [email protected] 3 points 4 months ago

If you want my credentials, the second book is deriving the hydrogen atom.

[–] [email protected] 1 points 4 months ago* (last edited 4 months ago) (1 children)

And that they might still move continuously. Which is impossible to prove (see Planck length).

Edit: Corrected my statement based on the reply

[–] [email protected] 1 points 4 months ago* (last edited 4 months ago) (1 children)

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%20is%20about%201.616255,Planck%20length%20per%20Planck%20time.

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

[–] [email protected] 1 points 4 months ago

That is actually good to know, it answers a lot of questions I've had about the universe.