Dot Physics

[In part I of this post](, I struggled to show that a particle in an infinite well can only exist at certain energies. If you try to put a particle with more than one energy, the probability oscillates at a frequency (E2 – E1)/h. So, what is next? Well I think I am ready to attack the photon.

According to the ultimate source of truthiness (wikipedia), [the photon is the elementary particle responsible for the electromagnetic interaction]( In general, the photon is view as the particle manifestation of light where light can exhibit both particle and wave properties.

Before I go too far, I would like to mention a good summary paper of this problem from David Norwood.
- ["The Use and Abuse of the "Photon" in Nanomechanics" (pdf)](

I have said it before, and I will say it again. Science is all about models. In this case, there is a model for light that says it can be particle or wave. This model is not needed. Almost all of the stuff you think is an example of the particle property of light can be explained with the quantum nature of matter. I think the following sums this up well. The photon model for light uses the following relationship:

![Screenshot 97](

Where E is the energy of the “photon”, h is Planck’s constant and the greek letter nu (looks like a v) stands for the frequency of the light. There is a relationship like this, but it would be better to write it as:

![Screenshot 98](

Where nu is the frequency of the light (or the frequency of the changes in potential for a particle – it actually doesn’t have to be light). Delta E is the change in energy between two energy levels in a quantized system. h is still Planck’s constant.

The fundamental aspect of the problem is to explain the interaction between light and matter. [Here is a great site that has java applets which show the transitions between energy levels for matter.](

I took the liberty of making a movie of one of the applets from this site. I strongly encourage you to run the applet yourself (there are many fine applets on that site).

So, from this you can see what happens when you have an electromagnetic wave incident on the system. If the frequency of the wave (or disturbance) is (E2 – E1)/h, the particle will move from level 1 to level 2 OR from 2 to 1. It will change (either way). This is what happens during absorption and during stimulated emission. It turns out that spontaneous emission is quite a bit more complicated.

What about non-infinite square wells? Well, the same thing holds true. A system will transition from an energy level to another if it is stimulated with a frequency of Delta E/h. Light is not a particle.

**Complaint Section**

But what about….

  • Photon momentum: Most introductory texts show how an electromagnetic wave can give momentum to a charged particle.
  • The photoelectric effect: This is what people usually claim as evidence for the particle nature of light. Details about how this can be explained with the wave model for light can be found in [Norwood's paper](
  • Photo-multiplier tube: Any device that uses the interaction between light and matter will have this Delta E/h = frequency relation. It’s not a photon.
  • Shooting light particles: Even people that like the particle nature of light know that they are not actually little balls of light. Too bad you can still find this visual representation in some texts.

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.

I know that writing stuff like this might induce many people to think I am wacked out. This may be true, but don’t blame me. I would blame Norwood. I am sure he can give you some names of other people to blame.

**What to do from here?**

Norwood gave a talk to our faculty about this no-photon thing. One of the instructors afterwards was asking about what to do about photons when it comes up in the book. My answer is “why not just call it light?”

**PS** There is a great page [on the history of the development of the photon]( It is quite interesting story. It is also strange that the idea that light can be both a wave and a particle is what prompted people to think about the wave nature of matter.


  1. #1 bcooper
    November 12, 2008

    There are certainly lots of places where you can get very serviceable results using semiclassical models where you treat light classically while treating matter quantum mechanically. This is maybe a good argument that concerns about photons are perhaps overemphasized. But I don’t find it very convincing as an argument that photons don’t exist.

    The “antiphoton” paper that you link to doesn’t really go into very much detail, but at some point it does talk about the quantization of the electromagnetic field, and this is ultimately where the photons are coming from; they are excitations of a particular EM mode. (Note that this conception of them doesn’t offer any sort of spatial localization as we normally think of particles; for that you’d probably want a wave packet spread over a range of frequencies, much like you need if you want to talk about particles of matter as being spatially localized.) My understanding is that there is a pretty hefty amount of physics that demonstrates that this is a good way of looking at things, though this isn’t really my specialty.

    I know there have been recent papers in the so-called field of “circuit QED” where they look at the behavior of a superconducting qubit coupled to a microwave cavity and study it using the Jaynes-Cummings model, which accounts for quantization of the field energy in the cavity. Depending on the number of photons in the cavity, the resonant behavior changes, and there have been experiments done that allow you to in essence count the number of photons in the cavity as a result of this. I think these particular results would be difficult if not impossible to obtain semiclassically, though I am not certain.

  2. #2 Dan Riley
    November 12, 2008

    You seem to be going well beyond what Norwood says. Norwood says, in 1.2 and 4 of the “antiphoton” paper, that there are physical effects that require a quantum theory of radiation, while you seem to be denying that entirely. If so, what is the result when an electron and positron annihilate at rest in your universe?

    wrt the photoelectric effect, the photon model prediction is that the distribution of emission delay times will have a tail at shorter times than allowed by the semiclassical account. The experimental evidence agrees quantitatively with the photon model, while Norwood can only say that the results can be “described at least qualitatively” with a semiclassical model.

    Norwood has a point that semiclassical models have broader applicability than they generally get credit for, but I don’t think that point is very well served by his paper or your post. If, as you say, physics is all about models, shouldn’t you be arguing how the semiclassical model is better, rather than arguing that the photon is not needed? There seems to be an implicit assumption there…

  3. #3 rhett
    November 12, 2008


    Good point. Really, I am saying that the photon model of light is not needed for photoelectric effect and things like that. These are the phenomena that most people use to say light is both a wave and a particle. There is some other stuff – maybe the fields are quantized, but still not a particle. I am pretty sure Norwood would agree with this statement. Maybe he will reply.

  4. #4 agm
    November 13, 2008

    The first quantization, maybe you can approximate semi-classically, but the second quantization not so much.

    If I recall, a lot of the carbon nanotubes emitting light stuff can’t really be done semi-classically (but maybe I’m remembering wrong?).

  5. #5 Peter Morgan
    November 13, 2008

    Things are more complicated. The Fock space of quantum optics is graded, which is a discrete structure, but that’s too little to give quantum optics a robust particle interpretation, it’s more a field theory than a particle theory. Wigner’s idea of what particles are in a quantum field theory anyway makes photons pure wave-number modes of the quantum field that are spread evenly over all space, so that’s not so much your point particle (these photon modes are infinite norm in the Fock space, but ways to be routinely careful how we do the mathematics have been developed).

    Going farther, this month’s Studies in the History and Philosophy of Modern Physics has an article (available as a preprint at by a Philosopher of Physics at Waterloo, Doreen Fraser, that aims to show that a particle interpretation for interacting quantum fields is not possible, even if a particle interpretation might be possible for a non-interacting quantum field (which doesn’t help much for real stuff). Try also two (more elementary) papers by Art Hobson, in AmJPhys and PhysTeacher, that suggest that ideas about field theory should be used when teaching QM to undergraduates ( and 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. There’s also Stochastic Electrodynamics to consider, which can reproduce quite a bit that conventional SC cannot reproduce by introducing a Lorentz invariant fluctuating vacuum state of the classical electromagnetic field. If you dare to go through my name link, my own approach …

    Remember, however, that QM as engineering using Hilbert spaces and operators works quite nicely, so there’s no need to worry about any of this. If you do, you’ll cause yourself some trouble, so good luck with it, and it’s a dangerous subject, so Kudos for putting your feet deep in it already.

  6. #6 Anonymous
    November 13, 2008

    My apologies, but your dotphysics posting is preposterous. If you are uncertain about something, make your uncertainty clear. Don’t baldly state something with certainty that is apt to confuse lots of physics students who stumble upon your blog.

    The problem seems to be that you 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 particles, 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 your 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 you 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. Please stick to what you know.

  7. #7 rhett
    November 14, 2008

    I appeal to authority (where authority is someone who knows more than I do)
    W.E. Lamb, Jr. “Anti-photon”. Appl. Phys. B 60, 77-84 (1995)

    My point is the following: a photon is not a particle of light. The photoelectric effect and other phenomena commonly used to promote the photon can be explained with classical description of light and a quantum description of matter. Yes, there are some weird things dealing with quantized fields – but that still is not a particle of light.

    The problems is that the photon is used in introductory texts (almost all of them have this). I don’t think intro students are at a level to understand or not understand the interaction between light and matter.

  8. #8 Jamahl A. Peavey
    November 14, 2008

    The quantum model of physics is experimentally strong but weak conceptually and mathematically. It also removed what was the foundation of physics. It replaced visual models with mathematical models and the mathematical structures are difficult to explain physically. The mathematics is not strong because the numbers do not add up when it comes to light. Two Nobel Prizes are based on something unseen. Electroweak unification and the 2008 Award are based on the Higgs Field and Boson. I predict unification will occur without the conceptual or mathematical ideas of quantum mechanics and will prove quantum mechanics is a special case of classical physics

  9. #9 Matt Springer
    November 14, 2008

    Don’t worry, I’m not a bit riled up. In fact you make very good points! The photon is a slippery concept that’s a lot more subtle than the popular idea of little particulate bits of light. You’re right that it’s neither strictly required for many quantum phenomena nor it is a “light particle” in anything remotely approaching the standard sense of the word.

  10. #10 Jamahl A. Peavey
    November 15, 2008

    Einstein coin the term photon and during the last days of his life he said he did not know what this photon really was. Not knowing is a good thing because it keeps the door open for discovering the truth quantum physicist are certain about everything and if they are wrong then they would have certainly mislead and generations of physicist.

  11. #11 rhett
    November 15, 2008


    I am no historian, but according to what I have read Lewis coined the term “photon”. Einstein said something like localized light. This paper has a good account of the historical development:

  12. #12 Jamahl A. Peavey
    November 17, 2008

    Thanks for the correction. Question, why is there any doubt about photons being waves? Waves can exist in the same state and particles cannot. To my knowledge, if photons were particles you would not be able to produce a Bose-Einstein Condensate. Big question, do you think the person who explains what dark matter is should receive the Nobel Prize or the person who finds some kind of particle. Frankly I am tired of physicist finding particles and not advancing our understanding and If the particle is not found what does that say about the electoweak unification and the 2008 Nobel Prize.

  13. #13 Dan Riley
    November 19, 2008


    It looks like the central argument of the Lamb paper is essentially the same point that bcooper made in the very first comment, that the “single photon” state doesn’t correspond to a classical particle, and the thing that phenomenologically looks like a particle isn’t anything close to a single photon state. Lamb seems very unhappy about this ambiguity, but most of us don’t seem to mind it.

    Lamb also takes on the “phonon”, which I think is an instructive example. Lamb writes that he “was able to give a theory of the Mossbauer effect without use of the word ‘phonon’”, and leaves it at that. Intuitively, it seems reasonable that every result that uses phonons could be derived without them, given how the effective field theory for phonons is produced. However, in physics we tend to prefer models that give us greater physical insight, suggest new research directions, and so on, with minimalism pretty far down the list. By these metrics, I think it is clear that the phonon model has been an resounding success, and we would be much poorer (in wealth as well as physical insight) if we had rejected the phonon as unnecessary. Chad makes a similar point over at “Uncertain Principles”,

    wrt energy, and implicitly the various formulations of classical mechanics.

    My understanding is that there are (lots and lots of) high energy phenoma (starting with e+ e- to two photons) that require a second-quantized EM theory, and are phenomenologically described well by a photon particle model. Also, there are low energy/low rate phenomena (low intensity photoelectric effect, Chad cites anti-bunching) that are somewhere between awkward and impossible to get right with a semiclassical model. And, pedagogically, it seems to me that the photon model, once grasped, gives better physical insight, while the semiclassical models involve some pretty obscure subtleties. I suspect you disagree, but I don’t see where you or Norwood have made that argument–you leap from “not needed” to “not useful”. I’d like to see you make that step explicit.

  14. #14 turningnewton
    December 9, 2008

    I have no problem with the use of photon to describe a quantum of light energy.
    However it is not a particle, even of a Poincare group. I can think of no so called particle property that cannot be explained by conversion of photon energy at a single (quantum definition)point.

  15. #15 Chad
    May 15, 2009

    Dr. Allain,

    Sorry to be digging up old topics but:

    The photoelectric effect: This is what people usually claim as evidence for the particle nature of light. Details about how this can be explained with the wave model for light can be found in Norwood’s paper

    Seems to be a dead link. Could you update this? I’d like to check it out. . .or at least attempt to.