A classic formula for pi has been discovered hidden in hydrogen atoms

[G_j]

Last edited Mon Nov 16, 2015, 09:00 AM - Edit history (1)

http://www.sciencealert.com/a-classic-formula-for-pi-has-been-discovered-hidden-in-hydrogen-atoms

For the first time, scientists have discovered a classic formula for pi in the world of quantum physics. Pi is the ratio between a circle's circumference and its diameter, and is incredibly important in pure mathematics, but now scientists have also found it "lurking" in the world of physics, when using quantum mechanics to compare the energy levels of a hydrogen atom.

Why is that exciting? Well, it reveals an incredibly special and previously unknown connection between quantum physics and maths.

"I find it fascinating that a purely mathematical formula from the 17th century characterises a physical system that was discovered 300 years later," said one of the lead researchers, Tamar Friedmann, a mathematician at the University of Rochester in the US. Seriously, wow.

The discovery was made when Carl Hagen, a particle physicist at the University of Rochester, was teaching a class on quantum mechanics and explaining to his students how to use a quantum mechanical technique known as the 'variation principle' to approximate the energy states of a hydrogen atom.

While comparing these values to conventional calculations, he noticed an unusual trend in the ratios. He asked Friedmann to help him work out this trend, and they quickly realised that it was actually a manifestation of the Wallis formula for pi – the first time it had even been derived from physics.

..more..

[valerief]

1. Way cool! nt

[KamaAina]

2. Um, the link is to a story from Politico about Bush* and Nineleven(TM)

[annabanana]

4. here:

http://www.sciencealert.com/a-classic-formula-for-pi-has-been-discovered-hidden-in-hydrogen-atoms

[annabanana]

3. I find this fascinating..

And I don't understand it. It sounds like something science postulated is now even MORE multiple-sourced...

[DetlefK]

5. You can also find pi in the gaussian distribution.

[jberryhill]

6. The Wallis formula....

In the event anyone was curious.

[saturnsring]

12. thanks that clears it up

[jberryhill]

13. Well, I think anyone can see the pattern there

It's kind of a neat series. Multiply them out, and you have half a pi.

Do it twice, and you have a whole pi.

[hifiguy]

18. . . .

[struggle4progress]

7. '... The emergence of the formula probably doesn't signal anything profound about quantum theory,

cautions Bruno Nachtergaele, a mathematical physicist at the University of California, Davis, and editor of the journal in which the paper was published. "You are entitled to be delighted by this," he says, "but one shouldn't look too deep for meaning." In fact, the emergence of the formula may have more to do with the properties of gamma functions than the physics of the hydrogen atom, Nachtergaele says. Special functions such as gamma functions can often be written out in many ways as sums, products, integrals, etc., Nachtergaele says, so it's possible that Friedmann and Hagen's analysis could lead to other notable formulas ...'

Famed number ? found hidden in the hydrogen atom
By Adrian Cho
13 November 2015 11:45 am

[eppur_se_muova]

16. Ayup. nt

[Octafish]

8. Jolly Good Show!

FTI: http://www.dailymail.co.uk/news/article-1027178/Easy-pi-Astrophysicist-solves-riddle-Britains-complex-crop-circle.html

More on pi and H2: http://www.rochester.edu/newscenter/discovery-of-classic-pi-formula-a-cunning-piece-of-magic-128002/

[randome]

9. TLDR.

But it's a pretty picture!
[hr][font color="blue"][center]Aspire to inspire.[/center][/font][hr]

[Rex]

14. Aw how cute, one of your groupies showed up!

Just to let you know they still exist!

[FlatBaroque]

25. Lawnmowers and weed whackers!!

[MisterP]

10. and eventually all sciences and subjects will just collapse back into each other

neo-Scholasticism ahoy!

[hifiguy]

11. That is mind-bendingly cool.

[Rex]

15. But is it just a coincidence or is there a deeper meaning to this discovery?

Wow...just...wow. That it would be found in the most abundant atom in the Universe...very interesting.

[hifiguy]

17. I think the only thing it means standing by itself

is that there is some fundamental deep, and as yet undiscovered, unity to the laws of physics.

If we don't destroy the planet first I think we are only three or maybe four Einsteins away from getting to the Bottom Of It All.

I am currently reading Lee Smolin's books "Time" and "The Trouble With Physics." Fascinating guy, and a director of the Perimeter Institute for Theoretical Physics in Toronto. Brilliant and iconoclastic thinker. He's convinced that string theory is nothing but the mental masturbation of extremely bright people that may or more probably may never offer even a single idea that can be tested or make a prediction about to an observable phenomenon, meaning that ultimately it ain't real science. He makes a hell of a case for that argument. I've read a lot of the non-math writing by major string theorists and it is conceptually lovely and elegant, as its proponents claim. But that might only mean it is really good science fiction and nothing more.

Even more interesting is Smolin's contention that the full implications of Einstein's theories have not yet been worked/thought through, which he considers to be a major error. He's well worth a close read.

And then there's the whole fascinating topic of emergence....

[drokhole]

33. You might enjoy a recent (excellent) article from Nautilus on that very topic...

...also featuring Smolin:

The Battle Between Gravity and Quantum Physics, as Told by Craig Hogan and Lee Smolin

[hifiguy]

36. Thanks!

Though I am thoroughly mathlexic few things fascinate me more than theorietical physics.

[G_j]

37. great term

another mathlexic here

[jeff47]

19. The electrons orbiting hydrogen atoms are in a sphere.

That their orbits would have something to do with pi is not particularly stunning.

It's neat to get the same result from a different direction. But we're still talking about the shapes that led to deriving pi via math.

[Rex]

20. I thought hydrogen has only one electron.

Never gave a second thought to the shapes of the orbits, thanks something new to think about.

[jeff47]

21. Yep, they only have 1 electron.

Orbits don't get non-spherical until you get to P orbitals, which start at 3 electrons.

https://en.wikipedia.org/wiki/Atomic_orbital

It should be noted that the "shape" of an orbital is really a probability cloud. The electron's a point, somewhere within that probability.

[Rex]

22. I see, so elections do not orbit in a spherical pattern in other elements.

But they do in hydrogen, even after adding another atom. Thanks, I am always awed by the incredibly tiny universe and the incredibly large universe.

[jeff47]

23. Some of them do, some of them don't.

You start with the 1S and 2S orbitals. Once those are full, you go through the P orbitals. Once those are full, you go through larger S orbitals. Then you go through larger P orbitals. Then you go through some others....I start losing track at this point.

So, hydrogen has one electron in the 1S orbital. Helium has two electrons, in the 1S and 2S orbitals. And so on.

Chemical bonds are created by atoms sharing these orbitals - the most stable configuration is for each "level" to be full. So hydrogen is desperately trying to react to either fill its 2S orbit or empty its 1S orbit, while helium is stable. Lithium wants to get rid of one electron so it's left with just the 1S and 2S electrons. In Neon, that level of P orbitals is full, so it's stable. And so on through the periodic table.

(This is not 100% precise - the electrons get shared between atoms, but it's a decent enough approximation)

[caraher]

26. Only in the ground state

Excited states of hydrogen most assuredly exist, and with angular momenta that are nonzero. You're mistaking a chemistry rule for ground state electronic configurations for all the possibilities in a hydrogen atom.

If hydrogen atoms only existed in 1S configurations, there could be no electronic transitions resulting in absorption (or emission) of light, a clearly contrary-to-fact condition!

[jeff47]

32. Yes, I left out that complexity since the entire concept of orbitals was new. (nt)

[Mnemosyne]

24. This thread is one of the reasons I still love this place.

I learn so much and there are smart people to further explain confusing concepts.

Thanks G_j!

[Rex]

30. Agree completely.

A wealth of knowledge.

[Mnemosyne]

34. And the more I learn, the more I realize how much I don't know. nt

[Rex]

35. I gave up thinking I knew anything long ago.

There is just too much, so enjoy the knowledge you gain while it lasts imo.

[Mnemosyne]

38. I hear ya'! Damnedable runaway brain though... nt

[Quackers]

27. Kick! These are awesome threads! nt

[byronius]

28. May I be the first to point out that this may simply be a product of bored reality programmers.

Who didn't think anyone would notice if they reused a bit of code.

But some humans spot all the tropes.

[Maedhros]

29. The reasoning for this is somewhat circular.

All of our models for understanding physics use our mathematical system. It's no wonder that we find the footprints of that system inside the models we create.

[Enthusiast]

31. Kicked and recommended!