Lamb and The Photoelectric Effect Without Photons

[Physics Monkey]

Lamb is specifically trying to address the question of whether this experiment probes the quantum or classical nature of the electromagnetic field.

I agree with you here, this does seem to be part of Lamb's point. My point is that the experiments Lamb is trying to explain are not of the type you describe. The body of experiments Lamb is referring to used, to my knowledge, semiclassical beams with many photons. So Lamb doesn't need to have a description of the low energy situation to discuss the experiments.

If he's saying that it can be explained with a classical EM field, then it's absolutely natural to ask whether the theory gives reasonable results in the limit of low-energy fields. A classical field is supposed to be okay when you take the low-energy limit, because it's not granular. If you get nonsense answers in the low-energy limit, that tells you that you're not succeeding with a description in terms of a classical field.

I disagree with you here. It's not necessarily natural to ask what happens in a certain limit if your model is assuming you aren't in that limit. Perhaps we can say Lamb's paper is unclear, since his assumptions are not clearly stated. However, the assumption that the beam is large and classical is visible. For example, supposing Lamb were trying to do everything classically even for small fields, he would at least have needed to include the classical dynamics of the field to have a chance of describing the extreme situation you are interested in. I think this makes it plausible that he was intentionally neglecting certain things, and hence he would agree that you can't push his theory too far. He's not saying light isn't quantized, or that some extreme version of the photoelectric effect wouldn't clearly show this, only that the experiments with large beams can be modeled without invoking the quantized field.

On the other hand, I think your statement is a good thought experiment which pushes us towards a more complete understanding. If one did these experiments and had Lamb's description in hand but with no knowledge of photons, then a natural direction for further experimental exploration would be decreasing the energy of the light beam. One might then discover photons.

I would distinguish between proving and disproving a theory. You can never really prove a theory with any finite number of experiments. But you can certainly disprove a theory with one experiment. E.g., the Rutherford alpha-scattering experiment conclusively disproved the raisin-cookie model of the atom.

I roughly agree here. With sufficient background information and context, the Rutherford experiment is clean enough to strongly disfavor certain ideas. My concern is that students often lack the relevant background and context to make such a determination. If you've never done the classical mechanics calculations for different types of scattering, if you've never thought hard about the assumptions and mechanism underlying scattering experiments, etc then just being told that Rutherford conclusively proved this or that isn't necessarily very convincing.

 

[Cthugha]

I'm going to speculate that any experiments involving thermal light can be explained equally well by the photon model or by the semi-classical approach, and that all the remaining sticking points ultimately boil down to some version of the anti-bunching phenomena as seen in so-called non-classical light.

I do not think it is that easy. I am not aware of any sensible classical or semiclassical explanation for single mode photon bunching.

 

[conway]

The normal explanation for bunching as in e.g Hanbury-Brown and Twiss is that a "photon" is more likely to be detected when there is a thermal fluctuation in the field, therefore the detection event also tends to be associated with higher fields hence more "photons". Once you get rid of thermal fluctuations, the bunching disappears e.g. laser light with pure Poisson detection statistics. These are all what you'd expect for classical light. I know the antibunching is problematic but I don't exactly know what you mean by single mode bunching.

 

[Cthugha]

Yes, this classical description works for most cases, but it gets nontrivial if you have a single thermal mode and not a superposition of modes and even worse if you consider complicated experimental situations like ghost imaging. I do not intend to turn the discussion around, but "Can Two-Photon Correlation of Chaotic Light Be Considered as Correlation of Intensity Fluctuations?" (PRL 96, 063602 (2006)) by G. Scarcelli, V. Berardi and Y. Shih (and the comments and replies) give a good overview of where it gets problematic, if you are interested in that topic.

 

[harrylin]

[..]
If you read the Lamb-Scully paper, the first thing you notice is that they explicitly state that photons are absolutely necessary in order to explain phenomena such as blackbody radiation, Compton scattering, spontaneous emission, and the Lamb shift. Any internet kooks who are trying to quote Lamb as an authority against quantization of light are way off base. [..]

That can be misleading, as you here refer to an old publication. Arnold Neumaier quotes Lamb as a Nobel prize winner who is against photons:

"the photoelectric effect does not
require the quantization of the radiation field,
a misconception perpetuated by the mills of textbooks".
Some people, such as the Nobel prize winner
Willis Lamb 1995 even take this as an indicator
that "there is no such thing as a photon"."
- http://arnold-neumaier.at/ms/lightslides.pdf

That quote is from a more recent paper:

W.E Lamb, Jr., Anti-Photon, Applied Physics B 60 (1995),
77{84. Reprinted in: W.E Lamb, Jr., The interpretation of
quantum mechanics, Rinton Press, Princeton 2001.

In that paper Lamb argues against the idea that radiation (I take him to mean EM radiation) consists of particles. As I understand it after a quick glance, he now argues against the use of the word "photon" (in contrast with the older paper that you cited) because it is often associated with the particle interpretation of "photon".

The Abstract:

"It should be apparent from the title of this article that the author does not like the use of the word "photon", which dates from 1926. In his view, there is no such thing as a photon. Only a comedy of errors and historical accidents led to its popularity among physicists and optical scientists. I admit that the word is short and convenient. Its use is also habit forming. Similarly, one might find it convenient to speak of the "aether" or "vacuum" to stand for empty space, even if no such thing existed. There are very good substitute words for "photon", (e.g., "radiation" or "light"), and for "photonics" (e.g., "optics" or "quantum optics"). Similar objections are possible to use of the word "phonon", which dates from 1932. Objects like electrons, neutrinos of finite rest mass, or helium atoms can, under suitable conditions, be considered to be particles, since their theories then have viable non-relativistic and non-quantum limits. This paper outlines the main features of the quantum theory of radiation and indicates how they can be used to treat problems in quantum optics."

Cheers,
Harald

 

[A. Neumaier]

Again, what is "quantized" for the conduction BAND?! This is a continuum energy states!

The rest of your post continues to perpetuate the faulty idea that the photoelectric effect is done on isolated atoms, which it is not! Photoionization is not the same as the photoelectric effect. If you truly think that it is the material that's responsible, then pay attention to the physics of the material!

There are free effective electrons in the conduction band and there are effective electrons that are loosely bound. Each of these is reasonably localized. It is the latter that behave as more or less independent qubits, since they can get excited to the energy of the conduction band. And only this counts for the photoeffect. The effect is not much different if one adds more complexity to the quantum mechanical model of the material - only the calculations become far more complex. In all applications of quantum mechanics, one simplifies the model to such an extent that, while the essential point is modeled precisely, everything else is neglected as far as possible.

If you think that this is not good enough, then please point to _any_ explanation of the photoeffect involving conduction electrons that satisfies you, so that I can see what you'd consider satisfactory.

There is also a recent related thread:
https://www.physicsforums.com/showthread.php?t=474537

 

[Iuval]

Classical EM field already quantized

Perhaps we can take the view that the classical electromagnetic field can already be cast in the form of a quantum wave function (PROGRESS IN OPTICS XXXVI, pp. 245-294
E. WOLF, Editor, Elsevier, Amsterdam, 1996, photon wave function, by Iwo Bialynicki-Birula). I have only recently become aware of this quite radical statement. Apparently Oppenheimer was already aware of it in 1931. There is no localization of photons in this view (can't define a postion operator for a highly relativistic particle of spin 1), but there is a possible localization of photon energies. The wave function is related to the positive frequencies of E+iB. I don't think this is quite correct because a macroscopic classical field is really a superposition of many body photon states. In this view, second quantization is a misnomer. You can't quantize what is already quantized, namely a wavefunction/EM field. You can however develop a sophisticated way of treating a many body system of bosons and/or fermions where the number of them is not necessarily conserved, and that is all second quantization is. There is no "wavefunctional" of the classical electromagnetic field.

So the main difference relevant here between photons and electrons is that the wave nature of electrons was not known until quantum mechanics, whereas the wave nature of photons was already known before quantum mechanics (which might at a deeper level be due to the statistical properties of fermions vs bosons). What was not known about photons before quantum mechanics is that under certain conditions they can be considered as having a well defined momentum and localized energy, which makes them particle-like. Also the fact that for a fixed frequency there is a minimum energy (hv) for the wave (consisting of one photon), and also the statistical description that a wavefunction provides for obtaining transition amplitudes, average values of measurables, etc. But this is obvious from the quantum theory. The particle description, without reference to the classical em field or equivalently the quantum wavefunction of the many photon system is less complete.

 

[Cthugha]

Welcome to these forums.

This thread has been dead for a while. If you are interested in ways to think about photon wavefunctions, you might find John Sipe's work on that of interest (Phys. Rev. A 52, 1875–1883 (1995), http://pra.aps.org/abstract/PRA/v52/i3/p1875_1).

However, I disagree with some of your claims. The photon is NOT perfectly localized in the standard particle picture (The Mandel/Wolf has a short chapter on why you cannot localize photons too far) and I do not see why the particle description is less complete. In the quantum optics picture, the meaning of the photon as a particle is that it is the excitation of a field, so if you want to discuss particles, you also discuss fields.

 

[Iuval]

If you are interested in ways to think about photon wavefunctions, you might find John Sipe's work on that of interest (Phys. Rev. A 52, 1875–1883 (1995), http://pra.aps.org/abstract/PRA/v52/i3/p1875_1).

That paper was referenced in the review article I referenced and read, so probably nothing new.

The photon is NOT perfectly localized in the standard particle picture (The Mandel/Wolf has a short chapter on why you cannot localize photons too far)

I did not say the photon can be perfectly localized, but that one can associate a localized energy with it. I haven't investigated the details of why the latter claim is so (I have however investigated a bit the details of what you thought I was saying), and this is one of the claims made in the review paper.

I do not see why the particle description is less complete.

Because a particle is a classical concept, and the world, at least as far as we know (some people, including myself are trying to recast quantum mechanics in a classical paradigm at a deeper level, but that is another story), is quantum mechanical, where there are no particles or waves, but particle/waves described by wave functions or equivalently operators.

in the quantum optics picture, the meaning of the photon as a particle is that it is the excitation of a field, so if you want to discuss particles, you also discuss fields.

I don't disagree with you, but I think this is an extremely strange thing that probably means something deeper that we have missed. Here is why: we can start with a quantum object, the photon particle/wave. It has a wave function which is roughly E+iB, which means everything we want from a wavefunction except localization in position space. Now because of the symmetry of many photon wavefunctions, a macroscopic classical field emerges when we have many photons. But this is sort of chimera. The real object is the wavefunction. However, if we forget that and "quantize" this classical chimera (which is nonsense since a wavefunction is already quantized), we get a bunch of independent harmonic oscillators in momentum space, with eigenenergies equal to the energies of a discrete number of photons. So based on the eigenenergies we (prematurely?) say that the photons are the excitations of the classical EM field. But the photons are not, as far as I know, Hermite polynomial wave functionals in the classical field (times a time dependent complex exponential), which are the solutions to the functional Schrodinger equation.

We don't get into this sort of trouble with fermions because there is no classical field emerging out of the many particle wavefunction (sorry, but Grassmanian fields have not been observed, not only because they are not Hermitian, but because they don't exist except in the minds of mathematicians).