Why can wave nature of light not explain photoelectric effect?

[savi]

why can't wave nature of light explain photoelectric effect?

 

[Los Bobos]

Simple answer: Classically we cannot explain the threshold frequency. Also in classical case the energy of the emitted electrons would depend on the intensity of light, which is not the case in experiments.

 

[Crosson]

Actually, the true explanation of the photoelectric effect does not involve "photons", in fact the quantum calculations show that light is behaving as a classical wave during this effect! Treating the atom quantum dynamically, we derive the existence of resonant frequencies which are responsible for the "thresholds" which characterize this effect.

Ironically Einstein's nobel prize winning work was bogus, the photoelectric effect does not require photons to be explained.

Beginning in the 1980's experiments done by Aspect et al detected photons for the first (non-bogus) time, for which the team won a nobel prize.

 

[ZapperZ]

Actually, the true explanation of the photoelectric effect does not involve "photons", in fact the quantum calculations show that light is behaving as a classical wave during this effect! Treating the atom quantum dynamically, we derive the existence of resonant frequencies which are responsible for the "thresholds" which characterize this effect.

Ironically Einstein's nobel prize winning work was bogus, the photoelectric effect does not require photons to be explained.

Really?

I'm looking at Photoemission texts such as the one by Huffner, and at no part at all in the physics of XPS, ARPES, RPES, etc., is a "non-photon" scenario ever invoked. Can you show me where such a non-photon scenario is actually used in our modern experiments?

Furthermore, the standard photoelectric effect involves the emission of photoelectrons from solids, typically metals. This means that it is an emission from a many-body system that has formed a collective phenomenon to produce bands, such as the conduction band - the atoms have mostly lost their individual identities. It is different than the phenomenon of photoionization that is from individual atoms and molecules. You do not get "resonances" corresponding to individual atoms. Even in ARPES, you only get the "quasiparticle" peaks corresponding to the band dispersion, not atomic energy level. So I really don't see how one treats the atom "quantum dynamically" and get the same results of a photoemission experiment, when the solid itself defies any description using "the atom".

Beginning in the 1980's experiments done by Aspect et al detected photons for the first (non-bogus) time, for which the team won a nobel prize.

Aspect's team has won the nobel prize? What year was this?

Zz.

 

[tehno]

There is a big step not just from Maxwell to Planck in explaining photoeffect,but also between Planck and Einstein.Planck's breakthrough alone wasn't sufficient to explain it.

 

[vanesch]

Can you show me where such a non-photon scenario is actually used in our modern experiments?

Well, although for more sophisticated photo-electric effects, it is useful to use a quantized EM field, you can look at chapter 9 of Mandel and Wolf (Optical coherence and quantum optics), "Semiclassical theory of photoelectric detection of light" where quite some aspects of the simple photoelectric effect are treated, with a classical EM field and a simple model of an electric dipole interaction with a bound electron.

So, the essential aspects of the photo-electric effect in its most basic form do indeed not need a fully quantized EM field.

 

[ZapperZ]

Well, although for more sophisticated photo-electric effects, it is useful to use a quantized EM field, you can look at chapter 9 of Mandel and Wolf (Optical coherence and quantum optics), "Semiclassical theory of photoelectric detection of light" where quite some aspects of the simple photoelectric effect are treated, with a classical EM field and a simple model of an electric dipole interaction with a bound electron.

So, the essential aspects of the photo-electric effect in its most basic form do indeed not need a fully quantized EM field.

Well, I did ask for where such a scenario is used to explain our modern experiments. In particular, where does such treatement is used in the physics of ARPES, XPS, RPES, multiphoton photoemission, etc? I've worked in ARPES for many years, and no once was there ever any description of everything that we observed that did not use the photon picture.

Let's get this out of the way once and for all. The "standard photoelectric effect" is a very crude and simplistic experiment. I can show you many experiments which "violates" the standard photoelectric effects "observations" (multiphoton photoemission, for example). The more stringent tests come in through those experiments that I have mentioned. There has been, as far as I know, absolute zero attempt to describe such experiments using anything other than the photon scenario. So this is what I'm asking in case I missed it, since people are already selling that alternative method. Can it do as well as what we already have?

Zz.

 

[Parlyne]

Well, I did ask for where such a scenario is used to explain our modern experiments. In particular, where does such treatement is used in the physics of ARPES, XPS, RPES, multiphoton photoemission, etc? I've worked in ARPES for many years, and no once was there ever any description of everything that we observed that did not use the photon picture.

Let's get this out of the way once and for all. The "standard photoelectric effect" is a very crude and simplistic experiment. I can show you many experiments which "violates" the standard photoelectric effects "observations" (multiphoton photoemission, for example). The more stringent tests come in through those experiments that I have mentioned. There has been, as far as I know, absolute zero attempt to describe such experiments using anything other than the photon scenario. So this is what I'm asking in case I missed it, since people are already selling that alternative method. Can it do as well as what we already have?

Zz.

Perhaps a better thing to say would be that the photoelectric effect as described by Einstein can be explained using fully classical light. This is what Mandel and Wolf discuss - that the gross features of the photoelectric effect do not require photons.

That said, there are certainly more detailed experiments that can use the photoelectric effect to demonstrate the need for photons. For example, the semiclassical theory used to derive the gross results without photons predicts that a photocurrent should be shot noise limited. A photon-based treatment allows lower noise, if the photons are created in number states (or, really, and combination with lower noise than a coherent state) and are detected with high efficiency. This effect can actually be seen in a rather simple table-top experiment.

So, photons aren't necessary to get the course photoelectric behavior; but, they are needed to explain the details.

 

[ZapperZ]

Perhaps a better thing to say would be that the photoelectric effect as described by Einstein can be explained using fully classical light. This is what Mandel and Wolf discuss - that the gross features of the photoelectric effect do not require photons.

That said, there are certainly more detailed experiments that can use the photoelectric effect to demonstrate the need for photons. For example, the semiclassical theory used to derive the gross results without photons predicts that a photocurrent should be shot noise limited. A photon-based treatment allows lower noise, if the photons are created in number states (or, really, and combination with lower noise than a coherent state) and are detected with high efficiency. This effect can actually be seen in a rather simple table-top experiment.

So, photons aren't necessary to get the course photoelectric behavior; but, they are needed to explain the details.

Sure, but that certainly does not make the Mandel-Wolf explanation as the true explanation which is what crosson claimed. In fact, I would say that it is not even close to being the true explanation, especially when it is not even used widely in explaining the various photoemission experiments that I have listed.

Zz.

 

[lightarrow]

Perhaps a better thing to say would be that the photoelectric effect as described by Einstein can be explained using fully classical light. This is what Mandel and Wolf discuss - that the gross features of the photoelectric effect do not require photons.

Unfortunately I don't have that book. Can you explain me how that is made? Or point me to some file?

 

[vanesch]

Perhaps a better thing to say would be that the photoelectric effect as described by Einstein can be explained using fully classical light. This is what Mandel and Wolf discuss - that the gross features of the photoelectric effect do not require photons.

That said, there are certainly more detailed experiments that can use the photoelectric effect to demonstrate the need for photons. For example, the semiclassical theory used to derive the gross results without photons predicts that a photocurrent should be shot noise limited. A photon-based treatment allows lower noise, if the photons are created in number states (or, really, and combination with lower noise than a coherent state) and are detected with high efficiency. This effect can actually be seen in a rather simple table-top experiment.

So, photons aren't necessary to get the course photoelectric behavior; but, they are needed to explain the details.

Yes, that was the point. The usual textbook arguments of the "need" for photons are wrong (in that you have "immediate" emission, that there is a threshold in frequency and all that, are usually presented as *necessary conditions* to have photons, and these are the things that are also obtained in the semiclassical approximation, as shown by Mandl and Wolf). This is not so widely known. Of course, for more sophisticated setups, the semiclassical approximation doesn't work well anymore, but these are not the arguments usually brought up in elementary textbooks to require the *need* for photons.

For all clarity, I'm not arguing against photons ! I'm arguing against an erroneous logic that claims the necessity of a certain statement while this doesn't follow from the premisse.

This is a bit as saying that "the proof of the existence of electrons is electric current creating a magnetic field" or something of the kind. True, electrons exist, but this is not demonstrated by the fact that an electric current generates a magnetic field.

 

[ZapperZ]

For all clarity, I'm not arguing against photons ! I'm arguing against an erroneous logic that claims the necessity of a certain statement while this doesn't follow from the premisse.

But vanesch, if you truly are a stickler for accurate phrasing, why didn't you jump all over crosson when he claimed that the alternative scenario is a "true explanation" for the photoelectric effect? I mean, if claiming the photoelectric effect is a "proof" of photons doesn't sit well with you, then claiming the classsical picuture picture as the valid explanation for that phenomenon should also rub you wrong.

In fact, I find such claim to be the "true explanation" to be highly irresponsible. Why? Because there is more of a reason to consider the validity of the photon picture than the classical picture simply from looking at what people use in practice! When it matters the most, it is not the classical picture that is being used. In fact, in none of the experimental descriptions is the Mendel-Wolf scenario is ever, ever used. So how could anyone get away with making such an outrageous claim? There is more validity to claim that the photon picture is the "true explanation" instead simply based on what it can do beyond the naive photoelectric effect experiment.

The best that can be said is that for the photoelectric effect experiment alone, it tends to favor the photon explanation, but the classical light picture still cannot be ruled out.

If someone asks "then why do we accept the photon explanation?", we then point out all the phenomena that goes beyond the simple photoelectric effect and show that the photon picture is used everywhere and that the classical light picture is never used nor formulated for such experiments.

Zz.

 

[vanesch]

But vanesch, if you truly are a stickler for accurate phrasing, why didn't you jump all over crosson when he claimed that the alternative scenario is a "true explanation" for the photoelectric effect? I mean, if claiming the photoelectric effect is a "proof" of photons doesn't sit well with you, then claiming the classsical picuture picture as the valid explanation for that phenomenon should also rub you wrong.

Eh, yes, I re-read that post and that's true. The semi-classical explanation is not a "true" explanation ; it is just good enough.

Any claim of "true explanation" is of course irresponsible, whether it is classical, semi-classical, quantum mechanical or theological

The best that can be said is that for the photoelectric effect experiment alone, it tends to favor the photon explanation, but the classical light picture still cannot be ruled out.

Agree.

Or we could say that the photon picture succeeds in explaining the photo-electric effect, amongst other things.

 

[tehno]

Eh, yes, I re-read that post and that's true. The semi-classical explanation is not a "true" explanation ; it is just good enough.

Good enough for what?
What parts of the photo-electric effect ,in your opinion, "semi-classical" explanation explains and what parts it doesn't explain ?

 

[vanesch]

Good enough for what?
What parts of the photo-electric effect ,in your opinion, "semi-classical" explanation explains and what parts it doesn't explain ?

It doesn't explain those cases where non-classical optical begin and/or end states appear (like those with negative Glauber densities).

I'll quote Mandl and Wolf (on p 439):

It turns out, however, that for many purposes the quantization of the electromagnetic field is not necessary at all, and the response of the photdetector can be understood even if we continue to picture the field in terms of classical electromagnetic waves, provided the photoelectrons are treated by quantum mechanics. The field then simply behaves as an external potential that perturbs the bound electrons of the photocathode. Such an approach is sometimes known as semiclassical (...) and it is substantially simpler than the fully quantized treatment. Of course it has certain limitations and if pushed too far the semiclassical treatment will reveal some internal contradictions. However, that does not detract from its usefulness in many circumstances. As we shall see, for those electromagnetic fields for which an adequate classical description exists, the semiclassical and the fully quantized treatments of the photodetection problem yield virtually identical answers.

 

[tehno]

Actually, the true explanation of the photoelectric effect does not involve "photons", in fact the quantum calculations show that light is behaving as a classical wave during this effect! Treating the atom quantum dynamically, we derive the existence of resonant frequencies which are responsible for the "thresholds" which characterize this effect.

Ironically Einstein's nobel prize winning work was bogus, the photoelectric effect does not require photons to be explained.

Just on the contrary:
The lack of time lags between incident light beam arrival and emmited photoelectron was the key point.
The electron is emmited at instant,that is and was measured experimental fact."Semi-classical" explanation of this aspect of the photoelectric effect,taking only Planck's quantization in the account,turns out to be insufficient there.This is where Einstein steps in:EM field itself must be quantizied too.
Not having said that photon hypotesis explained more elegantly other aspects of the phenomenon,Einstein deserved Nobel solely on the basis of this insight.
Moreover,it was so revolutionary that even Planck or Bohr couldn't believe it at first.
Well,I'm in the process of reading [§],and it is my revelation to be informed that Bohr was,at one stage,more willing to accept breaking the law of energy conservation than Einstein's photons!
As far as concerns me ,that concludes this thread.

Reference:

[§]Max Born;"Physics in My Generation",Pergamon Press,London 1956.

 

[vanesch]

Just on the contrary:
The lack of time lags between incident light beam arrival and emmited photoelectron was the key point.
The electron is emmited at instant,that is and was measured experimental fact."Semi-classical" explanation of this aspect of the photoelectric effect,taking only Planck's quantization in the account,turns out to be insufficient there.

This is one of the typical misunderstandings propagated by textbooks. The classical EM potential applied in perturbation to a "quantum electron" gives immediately rise to a finite emission probability.
It is often argued that the "immediateness" of emission (which has indeed been experimentally established) is an argument for the quantization of the EM field, but this is not correct. It is an argument against an *entirely classical* picture (simply because there's not enough energy transmitted at first sight). Now, when Einstein studied the photo-electrical effect, there was not yet a quantum theory of matter.
But if you apply simply Fermi's golden rule to a classical harmonic potential (as is done in every quantum text that respects itself) you will find that the probability of transition is immediately non-zero.
So you need SOME quantum system to obtain this effect. It can be the matter, or it can be the EM field, or of course as is generally accepted, both. But from the moment that one is quantized, one obtains the basic properties of the photo-electric effect.

This is where Einstein steps in:EM field itself must be quantizied too.
Not having said that photon hypotesis explained more elegantly other aspects of the phenomenon,Einstein deserved Nobel solely on the basis of this insight.
Moreover,it was so revolutionary that even Planck or Bohr couldn't believe it at first.
Well,I'm in the process of reading [§],and it is my revelation to be informed that Bohr was,at one stage,more willing to accept breaking the law of energy conservation than Einstein's photons!

Are you sure about that ? I thought is was in beta-emission that Bohr was ready to give up on energy conservation (because of the undetected neutrino). I didn't know he also was ready to do so for the photo-electric effect.

 

[ZapperZ]

Now, when Einstein studied the photo-electrical effect, there was not yet a quantum theory of matter.
But if you apply simply Fermi's golden rule to a classical harmonic potential (as is done in every quantum text that respects itself) you will find that the probability of transition is immediately non-zero.

How does this fit in into the quantum description of a metal? We don't use a SHO potential for the conduction electrons.

As a side note, what do people mean by the emission of photoelectrons being either immediate or instantaneous? I mean, there is a finite, non-zero response time in such a process, which gets progressively longer as one goes from a metal to a semiconductor (fs to ps time scale).

Zz.

 

[vanesch]

How does this fit in into the quantum description of a metal? We don't use a SHO potential for the conduction electrons.

I meant: the potential of the perturbation, due to a harmonic EM wave. Not the binding potential of the quantum system without it.
If the field is of the form E = E0 exp(i w t - i k x) + cc and we assume only dipolar electric perturbation (W = p.E) then you get a perturbation term which is time-dependent in an exp(iwt) way. I was simply pointing this out as the elementary treatment to reach Fermi's golden rule.

As a side note, what do people mean by the emission of photoelectrons being either immediate or instantaneous? I mean, there is a finite, non-zero response time in such a process, which gets progressively longer as one goes from a metal to a semiconductor (fs to ps time scale).

You are the expert on that, not me !

But there is usually this reference to that old experiment with faint illumination where there isn't enough time for there to be sufficient energy transmitted by the classical beam to get to the energy of one single photo-electron. It is one of the usual textbook arguments to say that the EM field hence must be quantized, but that's not true of course. From the moment that there is the perturbing potential, there is a finite chance of finding the system having undergone a transition.

 

[ZapperZ]

I meant: the potential of the perturbation, due to a harmonic EM wave. Not the binding potential of the quantum system without it.
If the field is of the form E = E0 exp(i w t - i k x) + cc and we assume only dipolar electric perturbation (W = p.E) then you get a perturbation term which is time-dependent in an exp(iwt) way. I was simply pointing this out as the elementary treatment to reach Fermi's golden rule.

That's a dubious model to use. It means that you require a plane-polarized light source. The standard photoelectric effect requries a non-polarized source. Once you polarize it, a number of things can occur, especially on metal where the crystal orientation makes a difference. You can easily no longer get the standard photoelectric effect model. So I am not sure how valid of an explanation that would be using such a form.

Remember, as soon as you put a higher level of complexity to the standard photoelectric effect, you CAN get differing results.

You are the expert on that, not me !

Which is why you never see me mention anything about prompt or instantaneous emission. That's why I'm curous what you guys mean by it, regardless of where it came from.

Zz.

 

[vanesch]

That's a dubious model to use. It means that you require a plane-polarized light source. The standard photoelectric effect requries a non-polarized source. Once you polarize it, a number of things can occur, especially on metal where the crystal orientation makes a difference.

If you know the responses to polarized light, then the unpolarized case should be a statistical mixture, no ?

Now, I would like to lift a misunderstanding which is still propagating here. I take it on your word (because you are the expert, not me, on this), that detailled calculations and angular distributions, and time profiles and anything detailled for specific photo-electric effects on specific materials might need the quantization of the EM field. If you say so, I can accept that.

What I thought what was under discussion here (and a detailled re-reading of the post by crosson made me doubt after the fact that this was what was actually being said, but I initially thought it was), was the following:

- the elementary properties of the photo-electric effect (which are: frequency threshold, "immediate" response and a few others ; the very first empirically known effects, which Einstein was aware of) do not strictly speaking require the quantization of the EM field.
You can, with a simple toy model, also crudely obtain those properties with the EM field acting as a classical perturbing potential on a quantized set of bound electrons. As I said, for more detailled aspects, I take your word for it that the EM quantization makes a difference, but we were talking here about the bare-bones properties of the photo-electric effect (those things that are done in a first or second year course on general physics).

Nevertheless, many textbooks claim the opposite (namely that those bare-bones properties require photons), without them arguing that it are in the detailled and sophisticated aspects of photo-electric effect that one has to look for indications of the quantization of the EM field.

Now, as an argument I referred to Mandel and Wolf, where they do exactly that: they derive the crude (and some not so crude) properties of the photo-electric effect in the semi-classical approximation, with some elementary toy model, which is proof enough that those crude properties do not contradict the semi-classical model. This should be argument enough to point out the reasoning error in many textbooks claiming the impossibility of a semi-classical model producing those elementary properties.

Of course a more correct treatment is using the fully quantized EM field, there is no doubt about that. As to the practical use, I take your word for it (although when reading Mandel and Wolf, one would think that the semiclassical approximation does have some practical use ; but me not being involved in any kind of research, I can only take your word for it).

 

[ZapperZ]

If you know the responses to polarized light, then the unpolarized case should be a statistical mixture, no ?

I don't know. If we are using the classical picture of light, then an unpolarized light should have... what... the superposition of E field in all directions? If you use that, then you really don't have a simple, 1D SHO potential anymore. Then what do you put the "bound electrons" in? A spherically symmetry 3D SHO? Would this be something Mendel and Wolf used? Would such a thing produce the same effect? Or does one consider only a 2D SHO considering that only the in-plane E-field would be the one most responsible for the energy transfer? I don't know and that's why I'm asking. I'm not trying to make this into anything beyond the naive photoelectric effect phenomenon. However, the model must also not go beyond such level, or else, as I've said earlier, you'll start running to a more complex photoemission phenomena which have no "semi-classical" anything so far.

Now, I would like to lift a misunderstanding which is still propagating here. I take it on your word (because you are the expert, not me, on this), that detailled calculations and angular distributions, and time profiles and anything detailled for specific photo-electric effects on specific materials might need the quantization of the EM field. If you say so, I can accept that.

What I thought what was under discussion here (and a detailled re-reading of the post by crosson made me doubt after the fact that this was what was actually being said, but I initially thought it was), was the following:

- the elementary properties of the photo-electric effect (which are: frequency threshold, "immediate" response and a few others ; the very first empirically known effects, which Einstein was aware of) do not strictly speaking require the quantization of the EM field.
You can, with a simple toy model, also crudely obtain those properties with the EM field acting as a classical perturbing potential on a quantized set of bound electrons. As I said, for more detailled aspects, I take your word for it that the EM quantization makes a difference, but we were talking here about the bare-bones properties of the photo-electric effect (those things that are done in a first or second year course on general physics).

Nevertheless, many textbooks claim the opposite (namely that those bare-bones properties require photons), without them arguing that it are in the detailled and sophisticated aspects of photo-electric effect that one has to look for indications of the quantization of the EM field.

However, as I am sure you will agree, if one picture can consistently explain a whole zoo of phenomena, while the other can only explain the most simplistic phenomenon and nothing else, then there is an overwhelming precedent that the one that can explain the most is more than likely the correct description, is it not? I mean, even the old caloric theory of heat had SOME agreement with observations, but you don't see anyone still insisting that we must mention such a thing in thermodynamics textbooks just because it had some successes. This is why I am not that concerned when textbooks cite the photoelectric effect as "evidence" for the validity of the photon picture. While it isn't 100% correct, it is accurate in the sense that it is the only description that fits everything we have verified, not just the most simplistic scenario.

Zz.

 

[vanesch]

I don't know. If we are using the classical picture of light, then an unpolarized light should have... what... the superposition of E field in all directions?

An E-vector which is a random variable with a certain distribution ?

If you use that, then you really don't have a simple, 1D SHO potential anymore. Then what do you put the "bound electrons" in?

Well, as a particle physicist, if I want to know what happens when I put some unpolarized electron beam on a target, I calculate what it does if I have a +1/2 polarized electron beam, then I calculate what it does when I have a -1/2 polarized beam, and then I take the average, which should be the response for an unpolarized beam (as long as the processes at hand are single-electron processes ; otherwise I have to make more sophisticated averages, like (++), (+-) and (--) or so).

A spherically symmetry 3D SHO? Would this be something Mendel and Wolf used? Would such a thing produce the same effect? Or does one consider only a 2D SHO considering that only the in-plane E-field would be the one most responsible for the energy transfer? I don't know and that's why I'm asking.

I don't have the book handy right here. I'll try to look it up.

I mean, even the old caloric theory of heat had SOME agreement with observations, but you don't see anyone still insisting that we must mention such a thing in thermodynamics textbooks just because it had some successes. This is why I am not that concerned when textbooks cite the photoelectric effect as "evidence" for the validity of the photon picture. While it isn't 100% correct, it is accurate in the sense that it is the only description that fits everything we have verified, not just the most simplistic scenario.

Well, we differ here in opinion. I would object to a thermodynamics text which would claim that the caloric theory has been rejected by an experiment where warm water was mixed with cold water and one measured the end temperature... because this is one of the things that was explained by the caloric theory ! So the argument would be all wrong (even though the conclusion would be right). As an old professor of me used to say: "in summer, the days are longer than in winter, and most objects expand when they are warm. But it is not because objects are longer when they are warm, that the days are longer in summer !"

Personally, I don't think one has to argue any *proof* for quantum theory in a quantum text - I think this is the wrong approach. One should study quantum theory simply because it works. So for me there's no need to introduce any "proof". But a wrong proof is definitely a bad idea.

 

[tehno]

Are you sure about that ? I thought is was in beta-emission that Bohr was ready to give up on energy conservation (because of the undetected neutrino). I didn't know he also was ready to do so for the photo-electric effect.

Yep,I'm positive (and I was also surprised to get known of it).
He was thinking of a EM field Einstein hypotesis in relation to photo-electric effect for many years and couldn't find another solution.
Well,at least I know to read and who Niels Bohr was.
And if he couldn't find solution I don't think the anonymous guys (to me) you mentioned succeded in doing so...

 

[QuantStart]

A reader pointed out to me this discussion and that it was left unresolved.

I agree with tehno and Max Born that the key point is the energy conservation
since in the photo-effect the electron is emitted at instant, as shown by the lack
of a time lag between incident light beam arrival and emitted photoelectron.

I haven't managed to get Mandl and Wolf, but I certainly agree with that part
quoted by vanesch (from p. 439). Many successes and usefulness of the semiclassical approach are well known. There is no doubt that also most
of the features of the photoelectric effect can be explained semiclassically.

Nevertheless, quanta of the electromagnetic field (photons), and not just
quanta of energy, are required to explain it COMPLETELY, including the
simple feature of the "immediate" emission.
(It is my impression the quoted text from p. 439 of Mandl and Wolf also
may hint at that, albeit vaguely.)

Consider the following:

Let electromagnetic radiation start impinging on the area A of a metal of
the work function W.

It is indeed true that the probability of transition, given Fermi's golden
rule, is immediately non-zero, as pointed out by vanesch.

However, the amount of energy the classical electromagnetic field has brought
on the area A after the time T is given by

A T c epsilon_0 [E^2]

where [E^2] denotes the average value of the electric field E squared,
c is the velocity of light, and epsilon_0 is the vacuum permittivity.

Therefore, for a very weak light source, i.e., very small [E2], a RELATIVELY
long time (say, T > 10^-8 seconds), given by

T > W /( A c epsilon_0 [E^2] ) ,

is needed for the absorption of the quantum of energy (h nu) which would exceed
the work function W and thus enable the start of the emission of electrons. But,
this is NOT found experimentally. I do not know what the experimental limit is
at present, but the lack of time lags between incident light beam arrival and
emitted photoelectron has long been an established experimental fact.

Therefore, if one insists on the classical EM field, the photoelectric
effect would imply the non-conservation of energy. On the other hand,
the quantized EM field, i.e., the photon concept, does not have the above
problem, as the absorption of the quantum of energy happens "at once",
when the electron and the EM field quantum interact.

 

[tehno]

Thank you for the elaboration of these points Quantstart.

 

[monish]

A reader pointed out to me this discussion and that it was left unresolved.

Interesting. Your discussion took place exactly one year ago, and last week I participated in a very similar discussion which was positively resolved two days ago when ZapperZ used his authority as a monitor to lock down the thread.

I haven't managed to get Mandl and Wolf, but I certainly agree with that...most
of the features of the photoelectric effect can be explained semiclassically.

Yes, this was also brought up in the recent discussion.

Nevertheless, quanta of the electromagnetic field (photons), and not just
quanta of energy, are required to explain it COMPLETELY, including the
simple feature of the "immediate" emission.

Yes indeed! I kept hoping someone would bring up this point because I wanted to respond to it. But we never got past the discussion of the frequency threshold.

Consider the following:

Let electromagnetic radiation start impinging on the area A of a metal of
the work function W...the amount of energy the classical electromagnetic field has brought on the area A after the time T is given by

A T c epsilon_0 [E^2]

where [E^2] denotes the average value of the electric field E squared,
c is the velocity of light, and epsilon_0 is the vacuum permittivity.

You haven't specified what value you're using for the area.

Therefore, for a very weak light source, i.e., very small [E2], a RELATIVELY
long time (say, T > 10^-8 seconds), given by

T > W /( A c epsilon_0 [E^2] ) ,

is needed for the absorption of the quantum of energy (h nu) which would exceed
the work function W and thus enable the start of the emission of electrons. But,
this is NOT found experimentally...I do not know what the experimental limit is
at present, but the lack of time lags between incident light beam arrival and
emitted photoelectron has long been an established experimental fact.
Therefore, if one insists on the classical EM field...

OK, we know where this argument leads. The spread-out wave energy is much too diffuse to be able to concentrate itself in the tiny cross-sectional area of an electron in such a short time as is observed experimentally. Usually people use the cross-sectional area of an atom to justify this claim.

People who do this kind of thing don't know how to calculate CLASSICAL absorption cross-sections. The absorption cross-section of a classical antenna is sometimes but not always close to the physical size of the antenna. A notable exception is the small lossless dipole. In the limit, the absorption cross-section is on the order of the square of the wavelength, no matter how small the physical antenna.

An isolated hydrogen atom in the superposition of s and p states, according to the Schroedinger equation, is an oscillating dipole antenna. If analyzed classically, its absorption crossection is on the order of 10,000,000 angstroms squared. This is much much greater than the size of the atom. That's why it can absorb enough energy to drive the transition between the two states.

What about the classical photo-electric effect?. I believe that the electron wave functions as calculated by band theory can be as big as the whole piece of metal. So there is no justification for trying to limit the absorption cross-section to a tiny area.
A correct analysis of a classical wave interacting with a real (quantum-mechanical) metal plate should show that the time for photo-emission is limited only be the time it takes for energy to build up over the entire surface of the metal. The cross-sectional area of the atom is irrelevant.

The only reason Einstein and others couldn't see how to explain the PE effect with waves was because they didn't know the Schroedinger equation for the electron.

Marty

 

[reilly]

If Einstein's photoelectric work was bogus, then so was Bohr's work on hydrogen. And, of course their work was not and is not bogus.Quite the contrary, their work is part of the foundations of today's physics.

Bogus indeed. The plain fact is that both of these brilliant gentlemen gave plausible, intuitive explanations for two of the most vexing problems of the day -- think dark matter, and quantized gravity as equivalent problems. In fact, discrete spectra and the photoelectric effect, as observed, simply could not happen, as in impossible -- by current theory. The explanations made by Einstein and Bohr were among the most gutsy and extraordinary creative leaps of physics, ever. Their impact is, as we say today, huge. Think about it, they started the breakdown of the 19th century view of physics, a breakdown still being fought today.

They were as right with their explanations as anybody could be at that time. And, in many respects their work was the practical beginning of modern quantum theory. The posts in this thread are testament to the importance and durability of their work.
Regards,
Reilly Atkinson

 

[Hans de Vries]

People who do this kind of thing don't know how to calculate CLASSICAL absorption cross-sections. The absorption cross-section of a classical antenna is sometimes but not always close to the physical size of the antenna. A notable exception is the small lossless dipole. In the limit, the absorption cross-section is on the order of the square of the wavelength, no matter how small the physical antenna.

An isolated hydrogen atom in the superposition of s and p states, according to the Schroedinger equation, is an oscillating dipole antenna. If analyzed classically, its absorption crossection is on the order of 10,000,000 angstroms squared. This is much much greater than the size of the atom. That's why it can absorb enough energy to drive the transition between the two states.

So, the claims of instantaneous emission would be the result of
calculating with the wrong cross-section... According to this:

http://www.iap.uni-bonn.de/lehre/ss05_laserspectroscopy/Uebungen/Warm%20up.pdf

The classical absorption cross-section is

$$\sigma=\frac{3\lambda^2}{2\pi}$$

Which seems to agree with your numbers. Do you have any other links?


Regards, Hans

 

[monish]

So, the claims for instantaneous emission would be the result of
calculating with the wrong cross-section... According to this:

http://www.iap.uni-bonn.de/lehre/ss05_laserspectroscopy/Uebungen/Warm%20up.pdf

The classical absorption cross-section is

$$\sigma=\frac{3\lambda^2}{2\pi}$$

Which seems to agree with your numbers. Do you have any other links?


Regards, Hans

I'm not sure I have any more authoritative links than what you've found. Of course there are two formulas, one is for maximum absorption and the other one is for lossless reflection. The second case is four times the area. I'm not sure which of those two formulas you've quoted.

What I can offer is an intuitive explanation. It goes something like this:

1. Any power you receive with an antenna must come from the incident wave.

2. Therefore, the existence of an absorbing antenna can be detected by sensitive field measurements far from the actual antenna.

3. But the far-field radiation pattern of a tiny antenna oscillating at, say, 100 amps, is not very different from a much larger antenna (100x) oscillating at 1 amp.

4. So the interaction of the fields, incident and absorbing, is not strongly dependent on the actual size of the absorbing antenna.

People call this result counter-intuitive, but its all a matter of looking at it the right way.
There is, however, a drastic effect on bandwidth as you get smaller. I don't have a reference handy, but I'm pretty sure if you take the classical bandwidth formulas and apply them to the hydrogen atom at its various frequencies, you get pretty much the correct spectral linewidths. I think those are called the Einstein alpha coeffecients in qm.
But they come right out of the classical antenna formulas.

Marty

 

[Hans de Vries]

1. Any power you receive with an antenna must come from the incident wave.

2. Therefore, the existence of an absorbing antenna can be detected by sensitive field measurements far from the actual antenna.

3. But the far-field radiation pattern of a tiny antenna oscillating at, say, 100 amps, is not very different from a much larger antenna (100x) oscillating at 1 amp.

4. So the interaction of the fields, incident and absorbing, is not strongly dependent on the actual size of the absorbing antenna.

People call this result counter-intuitive, but its all a matter of looking at it the right way.
There is, however, a drastic effect on bandwidth as you get smaller. I don't have a reference handy, but I'm pretty sure if you take the classical bandwidth formulas and apply them to the hydrogen atom at its various frequencies, you get pretty much the correct spectral linewidths. I think those are called the Einstein alpha coeffecients in qm.
But they come right out of the classical antenna formulas.

Marty

This goes back to the birth of quantum mechanics.

The cross-section is so large because it is a resonant absorber. Absorption is
classically the result of emitting radiation opposite to the incoming radiation.
An ideal, non-damped, resonant absorber has in fact an infinite cross-section.

What limits the cross-section is the radiation damping $\gamma$ which is not so easy
to specify. Resonant absorber:

$$\ddot{\textbf{x}}+\gamma\dot{\textbf{x}}+\omega_o^2 \textbf{x}\ =\ \frac{e}{m}E_o\ e^{i\omega t}$$

(see for instance (2.178) in Sakurai, advanced QM, or see I, §5 (7) of Heitler's
classic, The Quantum Theory of Radiation)

The radiation damping solves the infinite cross-section in the Kramers-Heisenberg
cross-section when the incoming radiation is equal to the resonance frequency.

$$\sigma_{tot}\ =\ \frac{8\pi_o^2}{3}\frac{\omega^4}{(w_o^2-\omega^2)^2+\gamma^2/4}$$

So the cross-section and thus the response time for photon emission varies over
a wide range depending on the situation as a result of the dependence on the
radiation damping. Regards, Hans

 

[monish]

The cross-section is so large because it is a resonant absorber. Absorption is classically the result of emitting radiation opposite to the incoming radiation. An ideal, non-damped, resonant absorber has in fact an infinite cross-section.

What limits the cross-section is the radiation damping which is not so easyto specify. ...So the cross-section and thus the response time for photon emission varies over a wide range depending on the situation as a result of the dependence on the radiation damping.


Regards, Hans

But we should be able to verify this by looking at the data. What I am claiming is that if you apply the classical antenna formulas to the hydrogen atom, you get the correct value for things like the Einstein alpha (and beta?) coefficients. Do you think this is correct?

My main point is that it's wrong to make simple arguments based on the cross-section of the atom to supposedly prove that the wave theory doesn't work.

Marty

 

[Hans de Vries]

My main point is that it's wrong to make simple arguments based on the cross-section of the atom to supposedly prove that the wave theory doesn't work.

Marty

Yes, but note that the mathematics describes gases, isolated atoms, which is much
simpler as the solid state physics involved in practical photon emission experiments.

Nevertheless it seems indeed a valid argument against "instantaneous emission" which
is by itself important enough.


Regards, Hans.

 

[malawi_glenn]

monish: You did not answer Zappers question, nor proving that your view was the correct one.

 

[Parlyne]

If Einstein's photoelectric work was bogus, then so was Bohr's work on hydrogen. And, of course their work was not and is not bogus.Quite the contrary, their work is part of the foundations of today's physics.

Bogus indeed. The plain fact is that both of these brilliant gentlemen gave plausible, intuitive explanations for two of the most vexing problems of the day -- think dark matter, and quantized gravity as equivalent problems. In fact, discrete spectra and the photoelectric effect, as observed, simply could not happen, as in impossible -- by current theory. The explanations made by Einstein and Bohr were among the most gutsy and extraordinary creative leaps of physics, ever. Their impact is, as we say today, huge. Think about it, they started the breakdown of the 19th century view of physics, a breakdown still being fought today.

They were as right with their explanations as anybody could be at that time. And, in many respects their work was the practical beginning of modern quantum theory. The posts in this thread are testament to the importance and durability of their work.
Regards,
Reilly Atkinson

Reilly, no one here is claiming that Einstein's work (or Bohr's, for that matter) is bogus. In both cases, the work was brilliant and led to huge advances in physics. The question at hand is a subtler one. I doubt that anyone here has a problem with the idea that Bohr model of the atom is taught as leading to fundamentally new ideas about atoms and having new explanatory power but, ultimately, being wrong. So, the fact that we teach that it doesn't correctly explain atomic phenomena is uncontroversial.

In the case of the photoelectric effect, however, Einstein's major idea has turned out to be correct; but, it is not the only structure in currently accepted physics that can correctly explain the effects he was discussing. In other words, the conclusion is correct but the argument is flawed. Of course, Einstein couldn't have known that then; so, this is not an indictment of him or his work. Really, the only important feature of the discussion is the idea that we should stop teaching that the elementary features of the photoelectric effect prove that light is quantized. They don't. The only prove that something is quantized.