# Correct results from obsolete theories: Only coincidences?

1. May 10, 2015

### greypilgrim

Hi,
Is it more than mere coincidence that we get the correct energy levels (ignoring relativistic, QFT and spin shifts) of the hydrogen atom using Bohr's model? The assumptions it is based on just don't agree with modern QM.

Since I'm going to be a physics teacher, there's also a didactic aspect to this question. Bohr's model takes a great part in the QM chapter of almost every high school physics textbook, but I assume this is mostly for its simplicity, since you need only high school math. I don't like Bohr's model because of all the contradictions with modern QM, and the answer to above question could decide if I'm going to teach it or not.

Something similar happens regarding black holes: If you set the escape velocity $v=\sqrt{2GM/r}$ from a mass to $c$ and solve it to $r=2GM/c^2$, you get the Schwarzschild radius. This calculation is also done in some textbooks, arguing $r$ is the smallest distance an object with maximum velocity $c$ can escape the mass.

I also highly doubt that it is more than coincidence that those results agree.

2. May 10, 2015

### Drakkith

Staff Emeritus
By ignoring all those 'details' you have reduced the complexity of the atom to one of simple energy levels, which, by nature of hydrogen having only a single electron, can be easily found and computed. In other words, the simplistic nature of the hydrogen atom, in the absence of magnetic fields and other effects you mentioned, reduces the calculations to a simple empirical formula. It's not coincidence, it's a direct consequence. Note that the main success of Bohr's model is in explaining the Rydberg Formula, an empirical formula used to determine the spectral lines of hydrogen. It was, quite literally, specifically built to explain this formula (and a few other things), so it's no surprise that it does so. The model doesn't produce Rydberg's formula as far as I know. It just explains why it works.

A similar thing happens for a black hole. The Schwarzchild radius is a simplification that only applies to a non-rotating, spherically symmetric object, which doesn't exist in the real world. (All real stellar objects have some degree of asymmetry and rotation, even if just a tiny amount)

If you're going to teach it to students, be sure to explain that this is a simplified model that only works in a few very specific circumstances and is only meant to introduce them to the idea of Quantum Physics, not to be an accurate representation of what an atom is like. It was superseded long ago by the formulation of the theory of Quantum Mechanics and several different atomic and molecular models. (Valence shell theory and molecular orbital theory are two that I've learned recently)

3. May 10, 2015

### Staff: Mentor

As a teacher, you will mostly teach what the curriculum tells you to teach.

Part of the reason old/obsolete theories are taught is as a history and scientific process lesson.

4. May 10, 2015

### ZapperZ

Staff Emeritus
Well, is it any coincidence that from very far, a cow looks like a sphere and can be accurately approximated as such?

That is your decision to make. However, is there a problem if you clearly point out to the students way in the beginning that this is a highly simplified idea (tell them about the cow) and that there are more accurate means to describe the hydrogen atom? As Russ pointed out, often times, this is done simply to show the historical context. There is no way an average high-school student can understand the actual QM formulation.

Zz.

5. May 10, 2015

### greypilgrim

Fortunately, in my country curricula are very open, giving teachers a lot of freedom about what they want to teach. It depends on the school, but my curriculum will probably only tell me to cover something from modern physics, letting me decide if it be QM, relativity, nanophysics or whatever.

Ok, it makes some sense if you look at it that way. Most textbooks though start with the postulate that the angular momentum must be quantized, some of them justifying this by saying that the de-Broglie-wave of the electron circling the proton must interfere constructively with itself. From all we know about the electron today, such an explanation is just plainly false.
Essentially, it explains the discrete nature of the energy levels with the discrete nature of the angular momentum, which it cannot explain. What do we win by that?

Well, my question basically is if those theories really are approximations or just plain nonsense that coincidentally happen to yield the correct results. If the latter is true, I don't think the mere fact that a theory gives the correct results qualifies it to be taught over and over again, if everything else about that theory is just not in agreement with modern day physics.

Another example: If you use $E=mc^2=hf$ to ascribe a mass to a photon and then use Newtonian physics to compute the deflection of light passing a massive body, you get only half the (experimentally verified) value from a proper GR computation, which is probably why most textbooks don't do this. I'm sure it would be different if this simple computation gave the correct value, but it wouldn't change the fact that SR and Newtonian physics are simply not powerful enough to explain the deflection of light.

6. May 10, 2015

Staff Emeritus
Those aren't your only options. You can have a theory that is right in some respects and wrong in some respects, which gets some things right and some things wrong. A good example is the Drude model of metals - "electrons in a metal behave as a gas" which is one word away from the modern view: "electrons in a metal behave as a quantum gas".

7. May 10, 2015

### cosmik debris

Physical theories are models, each model has a domain of applicability. For example Newton's models work very well for low velocity low mass dynamics. Outside of this domain one needs to apply a different model, that of Relativity; it doesn't make the Newtonian model wrong just outside of its domain. The more complicated model should still give the answers of the simpler model as long as the conditions for the simpler model are met.

8. May 10, 2015

### greypilgrim

I understand your arguments about the applicability of theories. I'm not like going to teach my students only GR because it essentially replaces Newtonian physics (at least outside the quantum scale). But I don't think this reasoning applies in this specific example of the Bohr model.
Is Bohr's model really simpler? Yes the math is, but the underlying postulates make much stronger assumptions (and unjustified or even contradictory ones) than the modern QM description.

Last edited: May 10, 2015
9. May 10, 2015

### SteamKing

Staff Emeritus
The old saying goes, "A stopped clock is right twice a day."

Of course, this saying was current before digital timepieces.

10. May 10, 2015

### Drakkith

Staff Emeritus
It seems to me that it is those assumptions which make it simpler in the first place. Not to mention the model is MUCH easier to understand for most people since they already intuitively understand that one object can revolve around another like a planet revolves around a star. (Or a tether-ball around a pole)

11. May 11, 2015

### ShayanJ

What's the purpose of teaching QM to high school students? Its certainly not to make them do some serious theoretical work. Also, honestly, hydrogen atom is just an example of applying QM. So I think now that the OP is free to choose what to teach and what not to teach, he can put aside hydrogen atom and just explain in detail experiments like double slit and Stern-Gerlach! Of course not with the full QM and all the math. But only bringing into attention what classical mechanics predicts, what QM predicts and what actually happens. I myself understood QM by thinking deeply about these experiments.