1. Jan 20, 2007

### arcnets

Hiya,
I'm about to teach the photoelectric effect in class. Everybody knows that observations contradict the classical prediction. Which is: Stopping voltage schould go up with light intensity. OK.
But I have a problem: What EXACTLY is the classical prediction? I mean, is there a formula that says "stopping voltage as a function of light intensity should be so and so..." and how do I derive this from classical first principles?

thx,
arcnets

2. Jan 20, 2007

### ZapperZ

Staff Emeritus
Look at the wave theory of light. The higher the intensity, the larger the amplitude of the wave, resulting in higher energy.

Zz.

3. Jan 21, 2007

### arcnets

Yes OK, I know that. So the electrons start to oscillate because they're in an oscillating field. The stronger the light, the stronger the oscillations, OK. But oscillation doesn't mean they get out of the metal, does it?

4. Jan 21, 2007

### ZapperZ

Staff Emeritus
It is the energy content of the incoming radiation here that is the issue.

Zz.

5. Jan 22, 2007

### arcnets

Yes, it is indeed. But I actually did this experiment. I had .6 Watts of light being absorbed by the cathode (caesium), so the upper limit for photocurrent is .3 Amperes, since an electron needs ~2 eV to escape.
What I actually measured was 1.5 x 10^-7 Amperes of photocurrent. So the best part of the radiation energy obviously goes into heat.
I mean, how can I use (in class) any argument involving conservation of energy, when such a large fraction of the impingent energy goes into heat, and not photocurrent (= when there's so much friction)?
I think it has to do s.th with statistical energy distributions, like Maxwell-Boltzmann (since Fermi-Dirac was unknown at the time), but how?

6. Jan 22, 2007

### ZapperZ

Staff Emeritus
Er... you do know that there is something called "quantum efficiency", don't you?

Not every photon that hits the cathode will liberate an electron. In fact, for metals, the QE is almost always less than 0.001%. What happens to the other photons that do not liberate electrons? Many get reflected (metals tend to be shinny, and QE measures the TOTAL number of photons hitting the surface, not just those that actually get absorbed). The rest are absorbed by the lattice of the material and becomes heat.

Zz.

7. Jan 23, 2007

### arcnets

Yes, Ok. Sorry if I explained badly. My goal was to look at the photoelectric effect from a purely classical point of view, and make a classical prediction.
A quantitative prediction *without* using photons.

Then to show (in class) by experiment that this prediction is wrong.

It must be possible...

8. Jan 23, 2007

### ZapperZ

Staff Emeritus
But... but... what's wrong with showing them the "standard" results that show why it is wrong? I mean, increasing the intensity of the light source is equivalent to increasing the amplitude of the wave, so classical wave indicates that you have more energy. Yet, the stopping potential that you use is STILL the same experimentally, whereas the classica wave indicates that you are putting in more energy and thus, more energetic electrons should be liberated. Isn't this what all of the standard photoelectric effect experiments try to show?

Zz.

9. Jan 25, 2007

### arcnets

I think I understand why you scratch your head. Maybe I make it more complicated than it is.
Well. I did some classical calculation. First, I calculated the amplitude of the electric field produced by the light (.6 Watts over 1 cm^2). I came up with 24.000 V/m which is quite weak. In such a field, an electron should only oscillate with a max elongation of ~.3x10^-15 m and a max velocity of ~1 m/s. That is a very weak oscillation - by far not strong enough to leave the metal.
Now the wave enters the metal to a depth of ~3x10^-9 m, that's the Skin depth. All the absorbed energy should go into this thin layer. So the oscillations should get stronger with time. Let's say 10% of the incident energy is absorbed. It should then take ~1s until the electron energy reaches ~2eV which is needed for escape.
That's the first contradiction with experiment: photocurrent starts in fact immediately.
Now I calculated the amplitude of such a strong oscillation, and came up with 2x10^-10 m. But that's comparable to the inter-atom distance. So at this point, the electrons should already be heavily interacting, distributing the energy among them.
This gives us a statistical ensemble (or, electron gas at a certain temperature) where some electrons have a very high energy and others do not. The value of 2 eV is then just an average. There should be much more energetic electrons (not so many, but there should.)
So there shouldn't exist a finite stopping voltage, shouldn't it? Some electrons should always come through...

Or maybe there's an error somewhere, don't really know.

10. Jan 25, 2007

### ZapperZ

Staff Emeritus
What is the shortcoming of doing this via qualitative comparision?

I mean, we KNOW what classical wave picture tells us when we increase the intensity. So you make one change there. But when the stopping potential doesn't increase accordingly, without doing any quantitative analysis, we can already see that something isn't kosher.

If you are teaching students the photoelectric effect for the first time, all of these quantitative analysis will do nothing but bury the message, because the students will be bogged down in the technical details. A simple comparision, in this case, would have been sufficient, and a lot more transparent.

Zz.

11. Jan 28, 2007

### arcnets

OK, the lesson is tomorrow, let's see what happens. Thanks a lot for your input ZapperZ.

12. Jan 29, 2007

### vanesch

Staff Emeritus
I would like to point out that this "classical theory cannot explain the photo-electric effect" is very standard in the teachings of modern physics, but personally, I think this is not a good pedagogical idea.
What one should teach, is that quantum theory CAN explain the phenomenon. It is extremely difficult to show that "classical theory cannot", and - as illustrated by the questionings of the OP - such "impossibility proofs" are usually just rethoric argumentation based upon visibly erroneous toy models in the "wrong" theory. In other words, the illustration quickly becomes an argument against a straw man. Moreover, this has the perverse effect on the bright student, who can see through the silliness of the argument develloped, that ALL argumentation is going to be of this low quality, and drawn to the extreme, that scientists are just a bunch of crowd-deluding demagogues or something of the kind.

It is extremely difficult to demonstrate that *all thinkable models* based upon classical EM theory are *necessarily contradicted* by one single experimental result. You could have things like parametric resonance, mode coupling, ... so many unexpected things that can happen in a classical mechanical system that it would be very difficult to rule out the applicability, in all generality, of classical theory. The energy of the EM wave could be "focussed" onto one or a few electrons, you could think of so many different models.

In fact, if one accepts that matter is quantized, then the rudimentary properties illustrated by these basic experiments are entirely in agreement with a semi classical treatment where the EM radiation IS treated classically. It is in the fine details that differences can be observed, but not in such a basic experiment.

So, purely logically speaking, it is totally ERRONEOUS to conclude from the photo-electric effect as demonstrated by a basic experiment, that the EM field must be quantized. This is unfortunately some kind of mantra through which physics students must go when learning about modern physics, and I think it can only do damage. It is not because the conclusion is correct (the EM field is quantized) that the REASONING is correct.

What is, IMO, much more productive, is to demonstrate that a *simple quantum model* CAN explain the observed effects, without saying that it is classically impossible. The only classical models which are ruled out, are very very naive and simplistic models, which are in any case easily disqualified with other experimental observations ; in other words, the only classical models we rule out, are models which are already known to be irrealistic.

13. Jan 29, 2007

### ZapperZ

Staff Emeritus
But vanesch, we have gone through this before. First of all, without invoking any complex scenario such as the stochastic classical E&M plus the "quantization of matter", the classical EM wave cannot explain all of the observation of the photoelectric effect. Secondly, the introduction of "matter is quantized" is rather vague. The conduction electrons (if that is what you meant by quantized matter, though I don't see how that would be relevant), which are the ones involved in the standard photoelectric effect, are not in any quantized state at all. The conduction band is continuous, and so is the photocurrent being detected, which after all, is all we care about and can talk about.

And in fact, if we do want to bring in all the various complexities and then show that, ah hah! Classical EM can explain the standard photoelectric effect, then I'd say why hasn't it able to explain ALL of the photoemission observation beyond just the highly simplified photoelectric effect. Remember, as I've pointed out before, the standard photoelectric effect is nothing more than a highly special case where a bunch of things are ignored. A theory that can explain a whole lot more than a special case is always accepted as being the more accurate description. To continue to cling on the classical scenario is like claiming that to the Bohr model is valid just because it works for the hydrogen atom. Should we just continue to tell the students to hang on to the planetary model of the atom just because it works for ONE special, highly simplified case?

I don't think so...

Note that we are ignoring the abundance of experimental observations of the validity of the photon model from various EPR-type experiments and the which-way experiments. Not a single one of those experimental results have even hinted at any contradiction to such a scenario. So what is being taught is correct as of now. The students are not being taught something that is wrong. To me, considering I remembered as a student how difficult and confusing all of these new information were, it is the most pedagogically sound technique to do.

Zz.

14. Jan 29, 2007

### vanesch

Staff Emeritus
I think you missed my point (again - last time we also had this discussion). I'm absolutely not implying that classical EM is somehow correct. I'm only indicating that setting up a simple photo electric effect experiment in a freshman lab, in which the only thing one really measures is the onset of the photocurrent from a certain stopping voltage onward, and that this threshold voltage is rather independent on the intensity of the EM beam, BY ITSELF, together with a simple argument about "how the stopping voltage should be somehow a function of intensity in a classical model" from which ought to follow that ANY CLASSICAL MODEL based upon a non-quantized EM field is now definitively falsified is AN ERRONEOUS FORM OF REASONING. It doesn't mean that the conclusion is right or wrong, but the approach is false.

First of all, it is very difficult to claim that ANY classical model (no matter how involved) should have a reaction to an EM field which ejects particles at high EM intensities with low frequency (which is the core of the argument). As I said, it is only in simplistic models (individual electrons, linked with breakable springs or something of the kind) that this is evidently true. There could simply be a mechanism which acts as a high pass filter and which preferrably converts EM radiation into heat below a cutoff frequency in a complicated mechanical system. There's no way to exclude such a thing a priori in a mechanical system with so many degrees of freedom. If you allow for JUST ANY model (and you have to, if you pretend to prove that ALL OF THEM must fail), fairly complicated dynamics is possible. So instead of making a totally unsubstantiated claim, I think it is better to keep one to what has ACTUALLY been demonstrated with said experiment.

Next, your argument about the conduction band doesn't hold IMO. The fermi level of the conduction band is still negative as compared to a free electron. So applying Fermi's golden rule using classical EM on such a quantum system, will only transport electrons hv up, and if this hv is below the dE needed to get free, it will not result in a free state, but rather in a population "higher up" in the conduction band. If the thermal phenomena which restore the Fermi distribution are fast enough, then the build-up of this population will be neglegible, so that "a second step" is almost impossible. And all this, using the band model of a simple solid, but a classical EM potential (using Fermi's golden rule). So this model can ALSO explain the onset of the photocurrent from a certain potential onward, which is a proof that not all (semi)-classical models are ruled out BY JUST THIS SINGLE EXPERIMENT, and hence that all reasoning that tries to show this, must be erroneous.

True, but then the REASONING that SIMPLY THIS EXPERIMENT invalidates all classical models is an erroneous reasoning: you have to bring in a lot of other results, and you have to consider a lot more possibilities for the classical models. So the CORRECT reasoning is simply, that after a lot of experimenting, and after a lot of modeling, the scientific community came to the conclusion that they never managed to get a satisfactory classical model explaining ALL experimental results, while the quantum model does so easily. And we come to what I think is important to stress: that the quantum model works WELL ; not that the classical model DOESN'T work. This is NOT demonstrated with the simple photoelectric effect, and the naive toy model. The only thing that is demonstrated by only that experiment is that ONE SINGLE NAIVE classical model DOESN'T WORK.

No, that's not what I'm saying. The problem is that this one special, highly simplified case has been singled out as PROOF. THIS is false.

Absolutely, but as you say yourself, it is a WHOLE HOST OF EXPERIMENTS and a whole host of theoretical reasoning which made people come to this conclusion ; it is not JUST this single freshman lab which did so. So one mustn't claim that, SOLELY BASED UPON THIS SINGLE RESULT, that the EM field MUST be quantized.

To put it in carricature: drop a big stone, and drop a small stone. Both fall at about the same rate. This shows that the Ptolomean model of the solar system is erroneous, and that the sun is the center of the solar system, and not the earth...

Clearly the conclusion is correct. There are myriads of observations which confirm this without doubt. It would be silly to teach the Ptolomean system in all its detail to students. But the experiment with the stones didn't show this. The experiment with the stones illustrated something valid about Newton's laws, and are one building block in setting up Newtonian mechanics. We should stress, with such an experiment, that Newton's laws can predict this. But we shouldn't, by erroneous reasoning, claim that THIS experiment has invalidated beyond doubt, once and for all, the Ptolomean view on the solar system.

EDIT: again, the question is pedagogical. What's the use of pedagogy in physics ? The use is 1) to teach students a bunch of material which they have to know and be able to apply 2) to teach them the correct ways of reasoning in science: to be critical, open to alternatives, not be gullible, etc...

Well, if you teach them about the photo-electric effect, and show them how it can be explained using the quantization of the EM field, then they have gained something on 1). If you show them an erroneous reasoning about how this rules out classical models, then you have HURT 2).

Last edited: Jan 29, 2007
15. Jan 29, 2007

### ZapperZ

Staff Emeritus
But this argument is similar to what ether fanatics are using nowadays. They have hijacked the name, but have put in all the different variations to the properties of the "ether". If we use your argument, we can't use the MM-experiment to show that it "disproves" the existence of the ether. Yet, in reality, it is the classical ether that has been well-defined in the 19th century that we are dealing with, NOT the "future, yet-to-be-determined ether" that it is disproving. I see nothing wrong with making such a claim. You are faulting the conclusion of an experiment that disproves the understanding of classical EM fields the way it is understood at that level based on an infinite possibility of what could be formulated in the future. If that is the case, then the word "falsify" would never appear in physics.

Hang on. Aren't you flipping back and forth here? By using "hv", aren't you already using the photon model? Secondly, if you have a cw light source, shouldn't the classical wave be able to cause an emission eventually no matter how low the frequency is? Even slightly below the work function should cause such an effect.

Note that even when one CAN cause emission using light with photon energy less than the work function, the emission spectrum isn't trivial. In fact, multiphoton photoemission spectrum clearly indicates the absorption of energy in discrete clumps, something that I've pointed out before and which has no "semi-classical" anything being associated with it.

The problem here is the mixing of different worlds. A "semi-classical" model is nothing more than an ad hoc simplification when one either does not have, or cannot yet formulate, a truer model. We do that all the time, but we very seldom argue that such a model actually reflects what is going on.

I see no loss in accuracy by saying such a thing. Again, if I transpose the experiment, I can also use your words and argue for not falsifying the Bohr model based on some toy model that does not work for some other element. The classical model does NOT work, not if you have the energy of the EM wave as dependent on the intensity. With only the work function of the material and the nature of the light source, the photoelectric model works while the classical wave model does not. Under the SAME, leveled ground, without invoking any quantum mechanics, we clearly see which one is valid. In terms of being pragmatic, I haven't see anything that has caused a detriment to the understanding of physics by invoking that.

Zz.

16. Jan 29, 2007

### vanesch

Staff Emeritus
This is another discussion, but it is true of course that the MM experiment does NOT disprove the Lorentz-Fitgerald ether ; only the more "standard" one which doesn't have any length contraction or time dilatation. The MM experiment only shows agreement with SR (AND with the Lorentz ether - only, the latter concept becomes *superfluous* when introducing a Minkowski spacetime, but is not erroneous as such: it is an unobservable preferred foliation of spacetime).

I think that any erroneous claim of proof is a wrong thing to do in science (not necessarily in politics, for instance ), because it hurts its basic value system.

No, no, much simpler than that. The argument doesn't prove conclusively that a classical system with 10^23 charged particles, which can also undergo other interactions, exposed to standard EM radiation, CAN NEVER GIVE RISE to the behavior which is compatible with the observed threshold effect. As such, one has to prove a theorem, concerning this class of systems. These theorems are extremely rare, and surely, no clear proof is given.

It is very difficult to falsify a CLASS of theories and models. One can falsify a SINGLE model which makes precise predictions ; sometimes one can even prove a theorem concerning a certain class of systems, and if the conclusions of that theorem are falsified, then this whole class is falsified. But to my knowledge, no such theorem exists for an arbitrary system of charged particles with other interactions, exposed to an EM field.

Most of science is about "models which are not yet falsified" and which work well. Absolute claims are usually just rethorical exaggerations - as in this case.

No, the hv condition comes from the Fermi golden rule, applied to a quantum system to which a PERIODIC POTENTIAL is applied as a perturbation, and which gives you the transition probability. It turns out that there needs to be a matching between the energy difference of the quantum states of the considered system, and the frequency of the perturbation: the match needs to be dE = hv. This is exactly why semi-classical models can MIMIC certain photon-properties, without necessitating the quantisation of the thing that gives you the periodic potential.

I don't know. But actually, that IS the case: consider cold emission with a STATIC but strong electric field (ZERO frequency and nevertheless emission: does this falsify the photon model now ?? )

Yes, yes, yes. I agree. But that is (1) NOT the experiment that is done in the freshman lab and (2) this doesn't prove that there *cannot* exist a classical, or semi-classical model with similar behaviour. The point is NOT to show that these models are false, the point is to show that the model with a quantized EM field WORKS WELL.

Of course. But remember that we had set out to PROVE that there COULDN'T BE ANYTHING ELSE but a fully quantized EM field in order to explain the simple freshman experiment on the photo-electric effect. I was pointing out that the PROOF was erroneous. Like a mathematics professor can point out to a student that he makes an erroneous proof of a correct theorem, because he forgot a lot of subtleties. I think it does no student a good service to present erroneous proofs of correct conclusions.

The "workfunction" is a very derived concept, including a lot of subtleties, which needs to be derived from a more complete quantum model. If I tell you that the "classical model" contains a high-pass filter which doesn't allow the EM energy to be given to an electron below, then that's just as good. And the simple "photon model" you give doesn't work for cold emission: there, you suddenly have to invoke the semi-classical approach with a classical field and classical potential, because in the static field, there are no "energetic photons" which can eject electrons.

If anything, it causes gullibility of textbook material and narrow-mindedness. Being aware of the limitations of an argumentation is one of the principal properties of a good scientist - as was our OP.

17. Jan 29, 2007

### ZapperZ

Staff Emeritus
But to be fair, I've seen many instances in which a few textbooks are careful about what they say that is being falsified. I can't remember which books at the moment, but I do remember reading Tippler's Modern Physics text where he clearly was focusing on a simple wave model and showing why, without considering the nature of the material, that THAT model simply won't fit into the photoelectric effect observation. One can also look at Millikan's work to see that he clearly had a particular classical model in mind when he tried to falsify the Einstein model.

I'm guessing that you would be satisfied if we "qualify" what exact classical model that we are falsifying. However, it is my opinion that we do not lose any accuracy in the teaching of physics by stating that the "classical model" that the students know of at that level does not work when applied to the photoelectric effect. There are many things we teach the students that do not apply when we extend it further. You don't see me jumping up and down shouting "LIARS!" when people claim that for photon energies lower than the work function, we will never get photoelectrons, which is claimed in the standard photoelectric theory. Considering that I have personally done experiments that violate such a thing, I would be justified to be irked by such claims. However, I know within what context this is being used, and when these students 'grow up' to become physicists, they'll learn that there are many caveats to things that they were taught in elementary physics. That is why I don't go around chastising physics texts for still making that statement.

This is rather confusing. At the simplest level (which is what the photoelectric effect is supposed to be), there are no "periodic potential". Within the conduction band, even if one considers the periodic potential due to the ions, the Bloch states do not come into play at the middle of the band, where the continuous band is all that matters. The periodicity only comes in at the edge of the band which opens a gap at the end of the brillouin zone. So if you want to be accurate as far as the material's quantum property is concerned, the periodic potential does not come into play at all here.

18. Jan 30, 2007

### vanesch

Staff Emeritus
Ah ? Things are improving then

Well, I don't see the use of that (but at least, it wouldn't be an erroneous claim). As I said, what counts, is that the photon model DOES work - not so much that another model doesn't. When teaching classical mechanics, one doesn't go through the pain, usually, to show that the Ptolomean model doesn't work (this is actually quite difficult, because there is an equivalent between the perturbation expansion of the Kepler motion, and the set of epicycles in the Ptolomean model! So a simplistic reasoning to show that the Ptolomean system doesn't work would probably be erroneous). Usually, in courses on classical mechanics, one is satisfied with showing that the Newtonian model does work.

It could be a fun exercise to work out exactly what would be the predictions of a specific model - but then what value has this, apart from a futile application of classical physics ? Its falsification would only be a falsification of a specific toy model.

It is simply a limitation of the model. We are used to that - it is one of the basic ingredients of doing physics. There's a difference between saying that a specific model has a limited scope of applicability, and saying that a specific experiment has ruled out definitively an entire class of theories. Nevertheless, it would indeed be a good thing to point out that the elementary photon model used, has its limitations also - as you point out yourself.

Well, look at our OP's (justified) worries. It is, IMO, much less erroneous to present a specific model, and to show that for certain experiments, it does give good results, than to make grandiose claims about general classes of theories based upon erroneous reasoning.

Again: I think it is a good thing to say that the elementary photon model CAN explain the photo-electric effect (thus implicitly re-inforcing the "case for the quantization of the EM field"). It might be a good idea too to show that a simple classical model can't do so, although this is IMO not necessary. However, I think it is a bad idea to say something which is not true, and which will never be true: that this result definitively shows that the EM field must be quantized. This result, by itself, doesn't. This is only so when bringing in many many more experimental results - which are even incomprehensible at that point of teaching. I stress this, because I think that it is very important for a scientist to distinguish precisely between those things that have been shown to be right, and how exactly, and those things which are suggestive, but hypothetical. If one starts, during the education, to be very sloppy on that, one hurts one of the basic qualities of a good scientist.

In a course on quantum theory, I don't see immediately the need to show the falsity of classical theory. As with classical mechanics, the argumentation is not (as it was eventually, historically) to show that ptolomean celestial mechanics is wrong: the idea is to show the applicability of classical mechanics. In the same way, I think it would be much easier, bring less confusion and polemics, if one limited oneself to show that the quantum model DOES work.

I wasn't talking about spatial periodicity, but temporal periodicity. The dipole term of a charge in a classical EM wave is of the lambda cos(omega.t) kind, which is the hamiltonian perturbation. Working out first order time-dependent perturbation theory for this term leads to Fermi's golden rule, which specifies a condition on the transition probability which is exactly that the energy difference between initial and final states should be +/- hbar omega, thus MIMICKING the "photon energy".

Sure ; I only wanted to show that the "argumentational easiness by which one discards the classical model" in the photo-electric effect, applied in the other sense, would discard the photon model. Both kinds of reasoning are wrong! But in the latter, the conclusion is wrong too, and in the former, the reasoning is wrong but the conclusion is right, so it is more difficult to see the error.

Hey, but you don't know out of what population you draw this ! Maybe we would have had 10 times more excellent physicists if textbooks were more accurate :tongue: