## Sunday, June 09, 2013 ... /////

### Bohr model: 100 years ago

One hundred years ago, in July 1913, when the author was 28 years old, Philosophical Magazine received Niels Bohr's manuscript on his model of the atom. Happy birthday. Both 25-page papers are available in English here:

On the Constitution of Atoms and Molecules I
On the Constitution of Atoms and Molecules II
Bohr's model was wrong in details – and he should have been able to see it – but the papers clarified many aspects of nuclear and atomic physics. Bohr referred to Rutherford, Thomson, and others. But only after Bohr's paper, nuclear physics started to be carefully distinguished from atomic physics. For example, Rutherford received the 1908 Nobel prize in chemistry. These days, we would surely not think that nuclear physics is chemistry.

Bohr's model was essentially classical physics with the ad hoc assumption that the periodic orbits were restricted: $\oint p\,dq$ had to be in $2\pi\hbar\ZZ$. Quite accidentally, this assumption implied that the allowed total energy of the electron in an otherwise Keplerian orbit around the nucleus agrees with the energy extracted from the hydrogen emission and absorption spectrum (or from quantum mechanics that wasn't born yet).

Today, we know it was a coincidence. The correct spectrum must be extracted from quantum mechanics that was developed more than 10 years later (perhaps, they should have seen it faster?). The hydrogen atom happens to be sufficiently simple and solvable and its energy levels $E_0/n^2$ just happen to agree with the levels that you obtain by the classical model restricted with a simple additional constraint.

The second Bohr's paper is dedicated to more complicated applications of Bohr's theory to other atoms and molecules. He should have seen that those things couldn't really work. Already the helium atom is a messy object and the classical three-body problem – with a nucleus and two electrons – is in some sense even messier than the quantum mechanical problem because the trajectories really don't want to be periodic.

We should also notice that Bohr had to overcome some additional steps towards quantum mechanics that was born in the mid 1920s. These steps went beyond the quantization of the orbital parameters. In particular, he had to realize that the transitions during which photons are emitted are governed by a nearly quantum logic. The electron that is changing its state of motion must be guaranteed that the new orbit will be allowed – it will obey the quantization rule for the orbital parameters. This requirement is almost directly extracted from the experimental data on spectroscopy but because it contradicts the classical logic so much (in classical physics, you would need an electron that plans the future, a mechanism that is sort of acausal, while the transition is perfectly causal in quantum mechanics), Bohr had to be courageous to propose it.

After some time, the correct theory was found and the reason why Bohr's theory looked good was understood. Some patience was needed. We should learn a lesson or two from these historical episodes.

Of course, many questions remained open even after 1925. For example, what is the glue that holds the nucleus together?

No, it has nothing to do with QCD or Gross or Wilczek or Politzer. Check the video above about the newest research which finally told us what is the answer. ;-) Via Honza U.

#### snail feedback (21) :

I thougt it was the Holy Spirit . Wrong theory.

Funny. A few hours ago, I wrote a YouTube comment over there (an unimportant reply to someone) that the neutrons were held together by the holy spirit.

:-) Jesus Christ, Holy Spirit, God... Always laughable when Religion wants to venture into Science...

No, "old spooky", as he likes to be known, is responsible for the expansion of the universe

Mark 10:40 - chirality. Coincidence? I think not. LOL!

Ha ha, does this Fischer guy really believe what he says :-D?

If Jesus Christ is a new force particle, can this be seen at the LHC ...?

Dear Dilaton, sure, the LHC collisions are almost predominantly collisions between the messengers who communicate the strong nuclear force.

So Jesus Christ has already been colliding against another Jesus Christ two quadrillion times. This is quite some masochism but don't forget that this man and Son of God has to sacrifice enough to save all the mankind, Earth, Universe, and more.

Have you seen this ? In Swaziland witches are not allowed to fly with their broom above 150 metres :-)
Not a joke :
http://www.trutv.com/library/crime/blog/2013/05/17/swaziland-witches-banned-from-flying-over-150-meters/index.html

So, coincidences do happen, Lubosh?

Well quite clearly the holy trinity, J.C., G*d and the Holy Spirit were simply an archaic form of representing the SU(3) group. Since in most cases G*d interacts through angels that are emissaries, and good angels don't switch sides and bad angels do switch sides, then the good angels are the Cartan generators of the group and the bad angels are the non-Cartan generators of the group. This is all obvious and has been known for thousands of years before Gross, Wilczek and Politzer were even born...didn't you all go to Sunday school?

That's cool - but Nancy Pelosi says obamacare will be an 'exciting adventure' . At least Mr Fischer isn't trying to extract thousands from my account, and does not seem to be getting the IRS to go after me.

Yes Lubos can you explain the nature of the 'coincidence' between the electron energy and hydrogen spectrum a little? I usually find many more ways for a mistake to produce a wrong result, versus the rare comedy of errors that that brings you to the right spot by dumb chance. Was it that Bohr's ad-hoc restrictions were chosen for just that purpose (in order to bully the output into the form he needed)?

Bohr may have got it wrong 100 years ago but once he learned about QM he was one of the first to grasp the profound significance of the new insight into nature. There are tons of smart people, including more than a few accomplished physicists, who don’t get it even today.
Lubos’ untiring efforts to correct this situation are bearing fruit, hopefully. But I have always been an optimist.

My favorite Bohr story:
A visitor to Bohr’s office noticed a horseshoe hanging on the wall and commented, “I didn’t think you believed on that sort of superstition, Professor
Bohr.”
Bohr replied, “Oh, I don’t but I understand that it works whether you believe in it or not."

Right, they happen all the time, the fundamental laws of Nature are probabilistic, after all.

But if we know that someone achieved something purely by a coincidence, it makes no sense to reward him for that because such a reward won't increase the chances that something nice will happen in the future.

Right. My take, however, is somewhat different. The coincidences happen not because of probabilistic nature of Nature, but due to some laws or formulae being very simple to be guessed right. So I think (and prove) that success of renormalization is a fluke precisely of this sort. Most of possible theories are non renormalizable just because the "fix" is too hard to guess (arxiv.org/abs/1110.3702).

LOL :-D!

So am I not the only one always thinking about such geeky stuff, when sporadicaly sitting in church ( in particular when our choir I am a member of has something to contribute)... :-P ?

Thinking geeky physics stuff while listening to a sermon always makes me chuckle by myself, which leaves my neighbors completely clueless, probably thinking I am nuts :-D !

Once I have seen in another church a hymn book, where the authors obviously wanted to be particularly cool; it explicitely mentioned some scientific topics such as cosmology, and even unified field theories !!! How that made me almost rolling on the floor :-D...

And if I got it right, concerning the unified field theories they wore not thinking about LQG or something, but this point was not further clarified in the hymn-book.

I do think about it, in bible stories I see smart people trying to find a language to explain things they know to be true, but just lacking the tools because of the times they are in. I can't help but believe that when J.C. was asked why he spoke in parables, he secretly wanted to say, "Because you're a bunch of m*r*ns"

Eloheim asked via defunct Blogger built-in comment system (BTW how do you do that, folks? It should be impossible):

Yes Lubos can you explain the nature of the 'coincidence' between the electron energy and hydrogen spectrum a little? I usually find many more ways for a mistake to produce a wrong result, versus the rare comedy of errors that that brings you to the right spot by dumb chance. Was it that Bohr's ad-hoc restrictions were chosen for just that purpose (in order to bully the output into the form he needed)?

Bohr knew the result he wanted to get - the 1/n^2 spectrum of the atom. It followed almost directly from the C(1/m^2-1/n^2) form of the frequencies that were reverse engineered from the spectroscopic data by numerologists such as Balmer. So Bohr was solving an inverse problem - find a set of physical laws that produces E0/n^2 as the set of results or "allowed energies". This reverse problem doesn't have a unique solution - there are many candidate laws that produce the same simple answer to a particular question. They include the old Bohr model of the atom as well as the full-fledged quantum mechanics. Bohr just happened to guess the first as the first guess while QM was found 12 years later. Bohr's first guess was only giving the right answer for the hydrogen spectrum - and details, e.g. degeneracy of states, were already wrong even for the hydrogen.