What’s the Matter With Photons?

Over at Dot Physics, Rhett has just completed a two-part post (Part I, Part II) on quantum physics arguing against the use of photons in teaching quantum physics. Part I gives a very nice introduction to quantum physics, which is why I linked it, but Part II goes a little off the rails. There’s not as much physics content, and it ends with a list of phenomena that are able to be described by semi-classical models of light, leading up to a question:

So, if there are no photons, why are they in all the textbooks? That is a great question. I am glad I asked it. I really don’t have a great answer here. Maybe someone wrote a book about photons and a student read it. This student eventually wrote his/her own book and included the photon model of light. This new book was then read by a new student and so on.

The answer to the question is “Kimble, Dagenais, and Mandel.” Specifically, the 1977 experiment they did (Phys. Rev. Lett. 39, 691 (1977)) showing “anti-bunching” of the light emitted by single atoms. This result can only be explained in terms of quantized light, i.e. photons.

(Basically, they saw that when they detected light emitted by a single atom, there was some time delay before they could detect light emitted by that same atom again. In the photon model, this happens because after an excited atom emits a photon and drops down to a lower energy state it must be re-excited and decay again before you can get a second photon out. You can’t explain this with classical waves and quantized detectors, the way you can explain the experiments Rhett lists.)

The inspiration for this whole thing is a rather ranty PDF of a paper by David Norwood of Southeastern Louisiana University, who goes on at some length about the evils of the photon idea. I can’t for the life of me figure out what the problem is supposed to be, though.

Norwood’s argument is, basically, that you don’t need photons to explain most of the simple experiments usually held up as demonstrations of the existence of photons– the photoelectric effect, the Compton effect, and so on. This is perfectly true. All of the experiments we use to introduce photons in modern physics classes can be explained using semi-classical models, where light is treated as a continuous classical electromagnetic wave, and the energy states of atoms are quantized.

Of course, I could equally well say that you don’t need the concept of energy to explain classical mechanics. You can solve absolutely any problem in classical physics using nothing more than Newton’s Laws of Motion. So why do we teach students about energy in introductory physics classes?

Well, we teach them about energy because it’s a central concept in physics, and it’s really difficult to solve interesting problems without it. You can solve any problem in classical physics using nothing more than Newton’s Laws, but it won’t be a pleasant experience.

The same is true with photons. Yes, strictly speaking, you don’t need photons to explain the photoelectric effect, but the semi-classical explanation is hard. It’s basically a Fermi Golden Rule problem, which involves some subtle approximations, and a couple of integrals. This isn’t something you’re going to trot out in a sophomore modern physics class.

And since we know from the Kimble, Dagenais, and Mandel experiment (among others) that photons really do exist, why wouldn’t you use photons as the explanation? The photon explanation is clean, elegant, and can be explained to anyone in about half an hour.

Norwood’s answer seems to be “most students will never deal with a situation where photons are really essential,” to which I reply “So what?” Most students in introductory physics will never deal with a physics problem where energy is really essential, but we teach them about energy all the same, because it’s easier to solve problems using conservation of energy than it is to do numerical integration of Newton’s Second Law.

I might be convinced that photons have no place in the introductory curriculum if Norwood had some evidence of actual harm being done by introducing the comment. If he does, I’m not seeing it– the only thing he gives as an example of a problem is an infelicity of phrasing: the use of “stream of visible photons” instead of “light.” I’ve been known to get bent out of shape over some linguistic matters– ask my former students about my opinion of “utilize”– but this is weak tea.

Note that even Norwood is not arguing that photons don’t exist. You have to look carefully, but in his list of examples, he does grudgingly allow that there are situations that demand a quantum treatment of light. His only gripe is that they’re taught “too soon,” which gets him torqued off for some obscure reason.

So, to return to the original question: Why are photons in all the textbooks? Photons are in all the textbooks because photons are real. The electromagnetic field is quantized, and this description is crucial for certain experiments. It also turns out to be a convenient way to explain a lot of other experiments where it isn’t strictly necessary.

18 thoughts on “What’s the Matter With Photons?

  1. Glauber got the Nobel for really figuring out what a photon was, and that you had to look at correlations to see quantum effects. Mean values of things can often be described by some classical or semiclassical model.

    And for the photoelectric effect, how does the semiclassical verison explain that you can get a photon instantaneously??????

  2. Speaking as a non-professional physicist, I would also say that I think leaving out photons makes in difficult to segue into the electro-magnetic spectrum and high energy radiation such as gamma-rays.

  3. I remember when I first learned that you don’t “need” photons to explain the photoelectric effect. I was pretty surprised.

    But, in the end, you’re right, Chad: If photons really do exist, and they really are the mechanism for the photoelectric effect, then there is absolutely nothing wrong with teaching the actual mechanism. The criterion for whether we teach something in physics is not the mathematical necessity but rather the physical necessity: We may not need photons to make the math work, but we do need them to make the physics work.

  4. And for the photoelectric effect, how does the semiclassical verison explain that you can get a photon instantaneously??????

    It’s a Fermi Golden Rule process, and it gives you a constant transition rate. That means that, even if you look at a very short time interval, there’s some probability for getting an electron out.

    Now, the Fermi Golden Rule business assumes that the time is long in some sense, but the relevant scale is the oscillation frequency of the light. You can look for a long time relative to the light oscillation, and still be “instantaneous” within the sensitivity of realistic measurements.

  5. “This isn’t something you’re going to trot out in a sophomore modern physics class.”

    Then it would probably be an even worse idea to use it to explain fluorescence and absorption to biologists and chemists. 😉

  6. I’ve left a longer comment on dotphys, but for teaching purposes you might try two papers by Art Hobson, in AmJPhys and PhysTeacher, that suggest that ideas about field theory should be used when teaching QM to undergraduates (http://physics.uark.edu/hobson/pubs/05.03.AJP.pdf and http://physics.uark.edu/hobson/pubs/07.02.TPT.pdf). I also say there that most of quantum mechanics becomes more comprehensible if you think in terms of fields, because the distance between classical random fields and quantum fields is relatively less than the distance between classical particle physics and QM.

  7. The Fermi Golden rule thing doesn’t work well for 0. Perturbation theory gives you a transition rate proportional to t^2 that you integrate over frequencies, but for t=0 you are integrating 0, so truly instantaneous, no. But within realistic measurements, yes.

  8. photons make detectors go click. Get a bad sci fi movie with a Geiger counter in it.

    Of course the click is really a macroscopic current pulse of many many electrons…….

    Hobsons point about excitations of an oscillator is a good one.

  9. photons make detectors go click. Get a bad sci fi movie with a Geiger counter in it.

    Of course the click is really a macroscopic current pulse of many many electrons…….

    Photons can get you into trouble though. At the Rochester conference last year, many folks discussed whether the state |01>+|10> is entangled if its made by putting one photon on a 50/50 beam splitter. How can you have entanglement of one particle with itself? You can’t, for FIELDS, entanglement is between modes. Same as single photon interference as Mandel also showed in the lab and as Dirac said cryptically.

    Hobsons point about excitations of an oscillator is a good one.

  10. Dusting off old memories:

    Once upon a time, we spent a large proportion of the undergraduate physics curriculum unlearning what we’d spent much of the previous year learning. Comparing my transcript from the early 70s with my sons’ from thirty years later, the current curriculum gets a lot more done in the same time frame; there’s a good bit that they covered as sophomores that I never even got around to.

    So a key question is, “how much of the way we’re teaching physics is motion rather than progress?”

  11. And for the photoelectric effect, how does the semiclassical verison explain that you can get a photon instantaneously??????

    What Chad said, but also: A good detector has a dark rate of events; in more detail, the events also exhibit specific higher-order statistics that are characteristic of the detector in the vacuum state, which can be measured if we collect enough data in an ensemble. When we expose such a detector to different light or other sources, in general all the statistics of events change, reflecting the structure of both the source and the detector. However, this is a matter of a time-frequency analysis of discrete events, which does not allow us to say definitively at what time the statistics change from one to another. If an event happens just after a light source is exposed, is that a dark-rate event or an event that is caused by a photon? In detail, this way of thinking gets us in trouble, just as particle thinking gets us into trouble in Bell-EPR experiments etc.

    It’s better to think of the (quantum or random) field in which the detector is embedded changing over time, so the statistics of detector events also change over time. To gather an ensemble of data, therefore, requires that we repeatedly remove the barrier between source and detector, say, and carry out detailed time-series analysis of the data considered as multiple sequences over time. We can’t consider events in a single run to be independent of each other (and hence an ensemble of events) because the statistics are not invariant over time.

  12. I already get slightly annoyed when professors lie to us in order to simplify the math, but skipping photons would just be lying in order to complicate the math. It’s the worst of both worlds.

    But now I’m morbidly curious. How does the semi-classical version explain beam-splitters?

  13. The dotphysics posting is preposterous. The problem seems to be that they are using a classical definition of a particle, namely, that a particle is a pointlike object. But that definition went out the window with quantum mechanics.

    That’s not the definition that modern physicists use for photons, despite the sloppy language one often finds in textbooks. Modern physicists instead use the very clear definition of a particle that comes from Wigner’s classification of irreducible representations of the Poincare group (as one can easily read about, for example, in Ch. 2 of Weinberg’s treatise on quantum field theory).

    If one insists upon some other definition of a particle, then that may explain all the confusion. But if one uses the correct definition of a particle, then everything fits beautifully.

    It must also be kept in mind that photons only emerge when both quantum mechanics *and* relativity are taken into account. Indeed, both are crucial to Wigner’s classification! It is telling that the dotphysics posting only talks about the case of nonrelativistic physics, in which we already know that the quantized nature of electromagnetism does not appear. In the nonrelativistic limit, the photon blurs into a classical field, but when both relativity and quantum mechanics are taken into account, one cannot avoid treating the electromagnetic field quantum-mechanically, and its quantized definite-energy excitations are precisely photons having definite momentum. These states can then be superposed to get spatially localized photons, although never localized down to a sharp point.

    With the correct definition of a particle, the photon clearly exists and is a particle. After all, we all agree that we live in a quantum-mechanical universe. So the classical electromagnetic field must be the classical limit of a quantum field. According to the proper definition of a particle, the quantized electromagnetic field corresponds to a massless spin-1 particle that we call the photon. Indeed, the whole of electromagnetism, together with the Maxwell equations and gauge invariance, can be obtained by starting with a massless spin-1 particle and requiring Lorentz-invariance and locality. States describing classical electromagnetic fields then correspond to coherent superpositions of photon states. And the quantum electromagnetic field can only be excited in discrete amounts, which are precisely photons of definite momentum. Everything fits together perfectly.

    Indeed, we are all familiar with the Standard Model, in which the photon combines at high energies with the massive W and Z bosons (they’re massive, so are we allowed to say that they are particles?) to form an SU(2)xU(1) quantum theory of massless spin-1 bosons. Are we to say that the W and Z are real particles but that the photon is not? This makes no sense whatsoever.

    I’d also like to see how these people intend to compute photon loop effects without treating the electromagnetic field quantum mechanically. These loop calculations have been compared with experiment and agree perfectly. Read Peskin and Schroeder to see typical calculations.

    No, this “photons don’t exist” stuff is all bunk. Feynman was right when he said that light is made of particles.

  14. Thanks for the explanations and the reference to the anti-bunching!

    There was a similar discussion at backreactionfollowing a post on the photo effect, and I had been a bit clueless back then as to what is a good answer to “where are photons actually really needed”.

  15. I can’t remember the reference/s, but I read about some analyses saying that it was the quantization of the absorber (like, atoms) that was more crucial to light being effectively quantized than it was an “inherent” quantization. That gets into philosophy too, but I suppose one way to put it is: aside from absorbers, you can’t produce less energy that has “X-ray” properties than the U = h*nu relation allows. It’s sort of like saying, you can’t have less “gold” than one atom’s worth – ?

  16. (Some appropriate references are explicitly given by Stefan in the thread he links to, following upon my bringing them up.)

  17. If you want to mention photons, fine. But DO NOT tell students that light as classical E/M waves cannot explain the photoelectric effect. No lies – not even white ones!

  18. http://physics.fullerton.edu/~jimw/general/radreact/index.htm

    Radiation reaction is rarely a major part of a formal course of study in physics. In part this is because it’s only important in rather unusual circumstances. And in part it’s a consequence of the fact that radiation reaction has some peculiar features. The problems with radiation reaction have been known for almost a century. They were already old when Feynman put an outstanding summary of them into chapter 28 of volume two of his Lectures on Physics, now nearly forty years ago. A fair amount has been written on radiation reaction since then, but the difficulties he described remain. Chief among those difficulties are problems with “causality” (causes always preceding effects) and seeming transient violations of the conservation of energy and momentum. Much of what I’ll say here follows Feynman’s discussion, so you may want to take a look at what he has to say for yourself….

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