# Insights Some sins in physics didactics - comments

1. May 7, 2015

### vanhees71

Last edited: May 9, 2015
2. May 7, 2015

### Greg Bernhardt

Great first entry vanhees71!

3. May 7, 2015

### Ken G

Fascinating, so the photoelectric effect did not really demonstrate light was a particle, it merely showed that the electron cannot resonate with the radiation field unless there are frequency components present that can lift the electron past the work function. IIRC, Planck derived his famous function using similar thinking, he didn't imagine the high frequencies were underoccupied because of light quanta, only because electrons could only give energy to the field in quantized bits.

4. May 8, 2015

### Drakkith

Staff Emeritus
Nice article!

5. May 8, 2015

### vanhees71

Exactly! Planck didn't like Einstein's "light quanta hypothesis". In contradistinction to that he was an immediate follower of Einstein's special relativity resolution of the puzzle concerning the lack of Galilei invariance of Maxwell electrodynamics, and he wanted to get Einstein to Berlin very much. Together with von Laue and other Berlin physicist he made Einstein an irresistable job offer, including the post of a director of the Kaiser-Wilhelm-Institut für Theoretische Physik, which consisted only of Einstein himself at the time, which meant minimal effort of time for him. In addition, and this was the most attractive feature of the offer for Einstein, he was free from any teaching duties but still being a professor at the University. For this, of course, Planck needed the agreement of the faculty, and in his letter of recommendation, he stated that Einstein was a genius, and one should not take it against him that he sometimes got over the line into speculation, particularly concerning his "light-quanta hypothesis".

Ironically the opposite was true for the Nobel-prize committee. For them (both spacial and general) relativity was too speculative to ground his nomination for the prize, and they rather gave it for the light-quanta hypothesis. He got the prize for 1921 in 1922, and I guess the main reason was the discovery of the Compton effect, which convinced many physicists of the time about the reality of light quanta, then also dubbed with the modern name "photon". That's the more ironic, because at this time there was neither non-relativistic quantum theory nor quantum-field theory, which latter was introduced only in 1927/28 by Dirac and in 1929 by Jordan et al.

So, in some sense you can say that Einstein got his Nobel for the only theory he discovered that has not survived (completely) the development of modern quantum theory. In my opinion if you have to name only one achievement of Einstein's to theoretical physics to justify his Nobel prize, then it's General Relativity. You could have awarded him for many other things, including his tremendous capability in statistical physics (already the 1905 Brownian Motion paper would have deserved the prize). Einstein, of course, well deserved the prize (if not him, who else?), but that it was given for his light quanta, is really funny ;-).

6. May 8, 2015

### Ken G

It was as though they had given him the Nobel prize for general relativity including a built-in cosmological constant, then regretted it when universal expansion was discovered, then been vindicated when dark energy was inferred! Of course, if we ever discover a need for a lumineferous ether, we'll be glad they gave it to him for the light-quantum hypothesis over special relativity...

7. May 8, 2015

### vanhees71

Interesting, where have you heard that the Nobel committee first wanted to give it for GR? I've never heard this, but only that they hesitated to give the prize for relativity at all. So there's no Nobel for the discovery of GR at all!

It's pretty funny with Nobel prizes anyway. A said case of negligence is Lise Meitner, who for sure should have gotten the prize together with Otto Hahn since she was the one who gave the correct interpretation of Hahn's results in terms of fission of Uranium nuclei. Hahn didn't have a clue! The reason seems to be that Siegbahn's influence in the Nobel-prize decisions prevented the Nobel prize for Meitner, whom he didn't like due to his antisemitic attitude.

8. May 8, 2015

### Ken G

I don't know what deliberations they had, I just mean that giving him the Nobel for the interpretation of the photoelectric effect could have proved disastrous if it had not turned out that light was quantized, merely the process of adding energy to the electromagnetic field inherited the required resonances from quantum mechanics. Then they might have felt they had made a mistake-- only to be vindicated later by quantum field theory! I was commenting that something quite similar to that might have happened had they given him the Nobel for GR with a cosmological constant in it, since then Hubble's observations would have made it look like they had been premature-- only to be vindicated later by dark energy. It just shows our many ups and downs with all of Einstein's great ideas.
Yes, she tops the list of Nobel snubs: http://www.scientificamerican.com/slideshow/10-nobel-snubs/

9. May 8, 2015

### zonde

I don't think that you show what you promise here:
"In the next section we shall use this modern theory to show, what’s wrong with Einstein’s original picture and why it is a didactical sin to claim the photoelectric effect proves the quantization of the electromagnetic field and the existence of “light particles”, now dubbed photons."
What you show (I assume your mathematical argument is correct) is that modern wave model can accommodate quantized energy transfer in photoelectric effect.

But Einstein's model is certainly good for didactical purposes because - in science it is important that proposed model gives testable prediction, that this prediction is tested and it is confirmed. In that sense explanation of photoelectric effect from perspective of photons is good example.
But of course claiming that such confirmation "proves" particular model can totally spoil positive side of such example. But this is very general objection and is not very specific to particular case.

10. May 8, 2015

### Ken G

I can give an example of what I think vanhees71 is talking about, because I've taught students about the photoelectric effect, and this is what I used to say. I said that if light was just an electromagnetic wave, and not a particle, then you should be able to crank up the intensity of a red light until it is knocking off electrons out of the metal. The idea is, if it's just the strength of the electric field that is jostling the electrons around, you should be able to compensate for low frequency by having a high intensity. But if you have to knock the electron out in a single "quantum event," then you need enough energy per quantum of light, since you only get to use one such quantum before the metal has in some sense reabsorbed the electron.

vanhees71
is saying my explanation was a didactic sin-- first of all, if you have a strong enough field, it could be a DC field and still get electrons out, so it's just not true that low frequency couldn't work. But what is really going on is that the field amplitude is always way too low to knock the electron out in a single period of the oscillation, so you need a kind of resonant accumulation of the effect, and that can be completely accomodated by a wave picture for the light. The need for a resonance, comes from the quantum mechanics of the electron, so is a "first quantization" issue, it does not require the light come in quanta, so is not a "second quantization" issue.

I see his argument as correct, so much so in fact that I am smacking my head and saying "doh" for ever repeating the everyday argument that the photoelectric effect proved that light had to come in quanta. It was basically a coincidence stemming from the existence of a time period in which we did not understand the quantum mechanics of the electron, that we ever thought that way, so we don't need to re-enter a mistaken mindset every time we bring up the photoelectric effect! vanhees71 is saying that once we understood the quantum mechanics of the electron, we had cause to reject Einstein's explanation of the photoelectric effect, but since quantum electrodynamics came along in short order, that rejection never actually happened. It's a bit like Einstein's cosmological constant, which did encounter a period of rejection, but it was not long lived! I think the case can be made that two of Einstein's most famous suggestions, that light is quantized and that there is a cosmological constant, both turned out to be true for reasons other than the ones that motivated his suggestions! So not to take too much away from the Great One, but it could be concluded that on both those counts, he got lucky.

11. May 8, 2015

### ShayanJ

I just see one loophole here. Its true that when we go to QM, it turns out that some phenomena that are impossible in CM, become possible. But we often find out that those strange phenomena have a relatively low probability to happen and that explains why we weren't measuring them before. So I think someone should actually do some calculations using the semi-classical theory of the photoelectric effect and find the amplitude for the immediate emission of electrons(with some proper definition of immediate) and compare that with experiments. I think it may be too low to account for the experimental value. I'm not saying it will be, but I'm just thinking that only because such an explanation is possible, doesn't give us the conclusion. Maybe such explanation is still inadequate!

12. May 8, 2015

### strangerep

Have you studied the quantum optics textbook of Mandel & Wolf? They perform careful calculations along these lines, both for the semi-classical case, and also the full quantum case.

13. May 8, 2015

### ShayanJ

Oh...So I guess the amount of agreement is satisfactory!

But I still can argue that this isn't a sin in education. Because in a QM course, photoelectric effect is described as a step in the historical development of QM. Historical development means what phenomena inspired scientists to suggest a particular theory. So as far as historical development is concerned, it doesn't matter photoelectric effect actually proves the existence of photons or not, it just matters that Einstein thought as such. In fact no one could predict such a semi-classical description! So I think its not a sin.

14. May 9, 2015

### Ken G

All I can say is, after reading this, I will from now on say that the photoelectric effect was incorrectly interpreted as evidence that the radiation field comes in quanta, when in fact it was merely evidence that getting an energy E into an electron often requires resonant coupling to some electromagnetic power at frequency E/h. A radiation field that doesn't oscillate at that frequency is therefore not good at doing it. However, it turns out that radiation is regarded as quantized anyway.

Incidentally, I'm not even sure you need to quantize the radiation field to get spontaneous emission. It seems to me a classical treatment of the radiation field can work for that as well, if you simply let the Fourier mode that perturbs the electron be the electromagnetic field that the electron itself creates, in the spirit of the bootstrap effect sometimes used to analyze the radiative reaction force. Which leaves us with the question-- what is the best observational evidence that the radiation field needs to be quantized? The Compton effect? Even photon shot noise could conceivably be modeled as stochastic amplitude variations in a classical field, I would think. Maybe there's even some way to get the Compton effect with a classical field, if such stochastic amplitude variations are included?

15. May 9, 2015

### ShayanJ

I remember @ZapperZ once said that multiphoton photoemission and angle-resolved photoemission can only be explained in terms of photons.

16. May 9, 2015

### zonde

Simply ban the word "proved" from your lexicon whenever you are talking about science. However when teaching something you want to present your subject as solid as possible so there is sort of conflict with inconclusive statements that science can make.

In science cause for rejecting some model is falsification of it's predictions. You could rather say that:
Once we understood the quantum mechanics of the electron, we had no cause to reject (pathced) wave model because of the photoelectric effect.

17. May 9, 2015

### vanhees71

What I wanted to say is that one must not teach students "old quantum theory" as if it was still considered correct. The photoelectric effect, at the level of accuracy described in Einstein's paper, does not show that the electromagnetic field is quantized, as shown by the standard calculation provided in my Insights article (the only thing, I've never found is the argument given there, why one can omit the interference term between the two modes with $\pm \omega$ of the em. field, which are necessarily there, because the em. field is real).

I've not calculated the cross section to the end, because I thought that's an unnecessary complication not adding to the point at the level of the (in my opinion false) treatment in introductory parts of many QM1 textbooks. You can do this quite easily yourself, using as an example the analytically known hydrogen wavefunctions for the bound state and a plane-wave free momentum eigenstate for the continuum state. Then you integrate out the angles and rewrite everything in terms of energy instead of $\vec{p}$. You can find the resul in many textbooks, e.g., Sakurai, where this example is nicely treated.

Of course, what I've calculated is the leading-order dipole approximation. Perhaps one should ad a paragraph showing this explicitly, but I don't know, whether one can add something to a puglished insight's article. There are also some typos :-(.

So here is the derivation. What we need is the right-hand side of Eq. (15), i.e., the matrix element in the Schrödinger picture (which coincides by assumption with the interaction picture at $t=t_0$). First of all we note that in the interaction picture
$$\dot{\hat{\vec{x}}}=\frac{1}{\mathrm{i} \hbar} [\hat{\vec{x}},\hat{H}_0]=\frac{1}{m} \hat{\vec{p}}.$$
Thus we have
$$\langle E (t_0)|\hat{\vec{p}}(t_0)|E_n(t_0) \rangle=\frac{m}{\mathrm{i} \hbar} (E-E_n) \langle E(t_0)|\hat{\vec{x}}|E \rangle.$$
Now if you plug this into (20) then due to the energy-conserving $\delta$ distribution and making use of the fact that this piece relevant for the absorption (photoeffect) transition rate only comes from the positive-frequency piece $\propto \exp(-\mathrm{i} \omega t)$ in $\vec{A}$, you find that what enters is in fact
$$\alpha^2 \propto |\vec{E}_0 \cdot \langle E(t_0)|\hat{\vec{x}}(t_0) E_n(t_0) \rangle|^2,$$
and this is nothing else than the electric-field amplitude times the dipole-matrix transition matrix element.

The whole calculation also shows that there's no absorption of frequency modes of the em. field if $\hbar \omega$ is smaller than the binding energy of the initial state of the electron and that the rate of absorption processes is proportional to the intensity of the external field (for small fields so that perturbuation theory is still applicable).

For those who like to print the article, I've put it on a new website, I've just created:

http://fias.uni-frankfurt.de/~hees/pf-faq/

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

### Ken G

I agree with all of your more careful restatements, yet you are saying the same thing. We have taken vanhees71's points here.

19. May 9, 2015

### atyy

As zonde says, the issue is general. An observation cannot prove a theory. At best, it can prove a theory within a well-defined model class, eg. in classical Mendelian genetics or in Wilsonian renormalization where one considers the "space of all possible theories".

However, although the photoelectric effect does not prove that the electromagnetic field is quantized, now that we do know the electromagnetic field is quantized, can Einstein's explanation be considered correct?

20. May 9, 2015

### vanhees71

I'd say no, although you can doubt this in some sense: Of course, the photoeffect must also be describable in terms of QED. The setup, most similar to the semiclassical one in my article, is to use a free atom and a coherent state of the em. field as "initial state" and a free electron of momentum $\vec{p}$, another coherent state of the em. field, and a free proton in the final (asymptotic) state. You should get the same, or a very similar, result as in the semiclassical treatment. In some sense you can indeed say, Einstein's picture is not that wrong, because the corresponding transition-matrix element describes the processes as absorption of one photon out of the coherent field (and even more, because it includes the change of the state of the em. field due to the interaction with the atom in 1st-order perturbation theory).

Nevertheless, at this level of accuracy of the description and just making a measurement to demonstrate the validity of Eq. (1) from Einstein's paper, does not "prove" the necessity of a quantization of the em. field, because there is this semiclassical calculation, leading to this formula (1).