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Do photons carry more than energy, momentum and angular momentum?

  1. Oct 15, 2013 #1
    Noether theorem says that with symmetries come conservation laws, and so because of time, translation and rotation symmetry, EM field itself guards energy, momentum and angular momentum conservation.
    While atom deexcitation there clearly appears energy and angular momentum difference, so there should be created EM field configuration/wave "carrying this difference".
    Photon's angular momentum is usually imagined as only some abstract quantum property, but in fact it is a very real "mechanical" torque.
    For example Richard Beth in 1936 has measured the tiny reaction torque due to the change in polarization of light on passage through a quartz wave plate: http://prola.aps.org/abstract/PR/v50/i2/p115_1
    Here is nice video of rotating macroscopic object using circularly polarized light - at about 20 second the polarization was switched to opposite one:

    Is optical photon something more than just EM wave carrying energy, momentum and angular momentum?
    If not - what more? Other than EM interactions? Some electric/magnetic moments?
    Is it just a "twist-like wave"? - like behind marine propeller, but this time in viscosity-free environment - and so does not dissipate: can travel undeformed for years (is soliton) from a concrete deexciting atom to be absorbed by anther one ...
    We say that because of spin conservation, it has also spin 1 - e.g. due to electron changing spin from -1/2 (down) to +1/2 (up) ... but isn't it just 180deg rotation - twist again? Especially that in opposite to other particles with spin, photon doesn't have magnetic dipole moment...
    Another question: why it has momentum? Is that just required for this kind of waves or maybe there is some momentum change required while atom deexcitation?
    Last edited by a moderator: Sep 25, 2014
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  3. Oct 15, 2013 #2


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    Classical electromagnetic field theory (Maxwell's equations) tell us that light has momentum; it follows from Poynting's theorem.

    There are two kinds of angular momentum: from light polarization (circular, elliptical) and beam structure (orbital angular momentum). You can read about the sources for angular momentum here:


    But a photon is not an electromagnetic wave, though we often think of it that way: little packets that make up the light. Instead it is the quantization of the electromagnetic field modes, and its state function gives the probability amplitude.
  4. Oct 15, 2013 #3
    Indeed photon's angular momentum can change both spin of electron in atom, or its angular momentum, like in this summary table for selection rules.

    If by "photon is not an electromagnetic wave" you have meant plane wave, I completely agree - given photon was produced by concrete atom in concrete moment and this energy doesn't dissipate while traveling through light years - photon is localized collective excitation of EM field (is soliton).
    It has time length of order of single period (lambda/c), what can be seen by introducing delay in one arm of Mach-Zehnder interferometer: we loose interference if delay is larger than about lambda/c.
  5. Oct 15, 2013 #4


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    Sorry, but this is incorrect. What you are describing is perhaps an ultrafast laser pulse.

    I'm not interested in discussing your private theory of how things work.
  6. Oct 15, 2013 #5
    What is incorrect? selection rules? photons being EM waves? please elaborate
    I cannot find it now, but I have read somewhere that if you introduce delay (glass plate) in one arm of M-Z interferometer for single optical photons, you loose interference if delay is larger than about lambda/c ... do you disagree?
  7. Oct 15, 2013 #6

    How does that follow?
  8. Oct 15, 2013 #7
    Indeed, Poynting theorem says only about energy transfer ... and you are using there that photons are EM waves (not necessarily plane waves).
  9. Oct 15, 2013 #8
    I'm not sure the Poynting theorem is even valid in non-plane cases. A standing wave won't transfer any energy but you wouldn't put your faith in ExH being zero everywhere.
  10. Oct 15, 2013 #9


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    None of this is correct. Whether you see interference or not depends solely on the coherence time of the photon, which may be short or long. A photon is not necessarily localized. It is just a quantized excitation. You cannot even localize it much better than half a wavelength, otherwise strange effects occur like the maximum of the energy density occuring at a different position than the maximum of the probability density for photon detection for polychromatic light fields (see e.g. the Mandel/Wolf, which has a short chapter on the problem of localizing photons).

    Also the emission event does not necessarily happen in some distinct moment. It has uncertainty associated with it. You can get the emission time with an accuracy roughly equal to the coherence time of the light. (lambda/c) amounts to roughly 1.5 fs for blue light. Due to time-energy uncertainty this would require a very broad spectral distribution. In most cases, the coherence time is rather given by the spectral width of the transition of the atom which is usually rather narrow. Even in semiconductor settings, where coherence times are usually pretty short, single photon coherence times of tens of nanoseconds have been realized.
  11. Oct 15, 2013 #10
    Cthugha, but if you have a single photon source which is in some distance from the detector - when photon is detected, with high precision (up to uncertainty) you can tell where this photon was in given moment before (between source and detector) - doesn't it mean that this photon was quite well localized?

    Problem appears when we add interference - e.g. Mach-Zehnder interferometer between them. Then you have two different positions this photon could be in given moment before detection.
    However it doesn't mean that it objectively hasn't been (localized) in just a single one of them - in dBB interpretation corpuscle travels through single trajectory, while its conjugated wave travels through all of them - "piloting" to interference, like in interference for Couder's walking droplets.

    ps. About interference depending only on the coherence time, so you say that no matter what delay you would put in one arm of M-Z interferometer for single optical photons, you can still get interference?
    If not, what is this maximal time such that, in orthodox language, "single photon can interact with itself" to get interference?
    Isn't this time time length of single photon?
    Last edited: Oct 15, 2013
  12. Oct 15, 2013 #11


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    You can tell that the detection event was localized. Thinking this tells you something about what happened in transit is jumping to conclusions. You took out one quantum of energy from the field locally. That does not mean that a bullet of energy traveled ballistically to this position or that the energy was localized in the field at the same position.

    Well, the delay still needs to be shorter than the coherence time is. People have done that. See for example Matthiesen et al., "Subnatural Linewidth Single Photons from a Quantum Dot", Phys. Rev. Lett. 108, 093602 (2012). Also available on the Arxiv: http://arxiv.org/abs/1109.3412. The delay where you still see interference corresponds to a distance of several meters.
    Last edited: Oct 15, 2013
  13. Oct 15, 2013 #12


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    See here for example (page 3 onwards):


    [Oops, that server doesn't allow access to that page from the link above, but you can access it through Google. Do a Google search for "electromagnetic momentum density." For me, it's the third hit, titled "Electromagnetic energy and momentum".]

    It doesn't use Poynting's theorem, but the development is similar to the one for electromagnetic energy density. You can probably find something similar in any decent E&M textbook: Griffiths, Jackson, etc.

    Added: I think the first sentence of the section on conservation of momentum has a typo. "Conservation of momentum has led us to energy flux." should surely read "Conservation of energy has led us to energy flux."
    Last edited: Oct 15, 2013
  14. Oct 15, 2013 #13
    Cthugha, If this energy did not traveled through trajectories, so how it has traveled for a single photon in just an empty space (vacuum)?

    Even for double-slit interference they can now (weakly) measure average trajectory of photons ( http://www.sciencemag.org/content/332/6034/1170.abstract ) - aren't they trajectories of energy transfer?
  15. Oct 15, 2013 #14
    Thanks for the help, but I'm getting access denied.

    Is this momentum definitely a classical feature, or is it due to the introduction of relativistic corrections? I know Griffiths and Jackson both go into this territory.
  16. Oct 15, 2013 #15


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    I just realized it myself. Do a Google search as described in my edit.

    It's definitely purely classical. As I recall, Griffiths does it before he starts on relativity.
    Last edited: Oct 15, 2013
  17. Oct 15, 2013 #16


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    Pick your favorite interpretation. Most of them (including de Broglie-Bohm variants) introduce some non-locality somewhere.

    Average trajectories of average energy transfer. Yes. But Steinberg's experiment does not say anything about what happens in a single run for a single detection event. They even make clear that this is not the case by saying " It is of course impossible to rigorously discuss the trajectory of an individual particle" near the end of the manuscript.
  18. Oct 15, 2013 #17
    Cthugha, the nonlocality in Wikipedia dBB interpretation article is described as: "The de Broglie–Bohm theory is explicitly nonlocal: The velocity of any one particle depends on the value of the guiding equation, which depends on the whole configuration of the universe."
    This is exactly like in explanation of tunneling for Couder's droplets - there is some additional field (of quantum phase in QM) - medium for wave propagation, which depends on the whole history of the system - making e.g. going through energy barrier practically unpredictable (we cannot exactly measure this field in QM).

    But in both Couder's experiments and dBB interpretation, this field evolves in deterministic, continuous way - energy had to travel through some trajectories.

    Having a single photon emitter and detector in vacuum, please explain how this photon could not came thorough a natural trajectory between them?

    ps. I have added it previously about delay in M-Z interferometer:
    About interference depending only on the coherence time, so you say that no matter what delay you would put in one arm of M-Z interferometer for single optical photons, you can still get interference?
    If not, what is this maximal time such that, in orthodox language, "single photon can interact with itself" to get interference?
    Isn't this time time length of single photon?
  19. Oct 15, 2013 #18


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    It follows from Maxwell's equations and the Lorentz force law, so it is valid in all cases where those are valid, not just plane waves. A standing wave is not a counter-example.

    My favorite pages on energy and momentum conservation on EM are here:
  20. Oct 15, 2013 #19


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    This is the same discussion as for entanglement stuff. We know that - in a nutshell - a good theory of quantum optics must either violate locality or realism (some other things like superdeterminism and scenarios without free will are also possible, but usually not considered that important in physics). Why should it come through a trajectory? Maybe it does, but there is no single experiment showing any evidence of what is happening in between emission and detection of a photon. Even the emission process is usually not really clear. The excitation may be delocalized over the whole field and taken from the field in a non-local manner, it may not have a defined value beforehand at all (by the way there is no generally agreed upon position operator for photons which complicates things a bit). We do not know. We just get to see an ensemble average over many repetitions and can speculate what happens in a single run. Pick your interpretation. There is no experimental evidence showing us what is happening.

    I already gave that answer: The maximal time delay is the coherence time of the photon. This is mostly determined by the line width of the emission process. The concept of a "time length of a single photon" does not exist. There are timescales associated with light like the duration of a cycle or its coherence time, but none of these really tell us much about what happens for single photons in a single emission and detection event.
  21. Oct 15, 2013 #20
    About the first answer, you have refereed to the free will ... so there was no quantum mechanics before the first organisms with free will have evolved? Why they even consider Big Bang?
    Sure we cannot measure the values of fields, but does it mean that they objectively have no values? And lots of physics work this way - assume some objective state we cannot directly measure (like starting inflation), and find some far predictions we can measure (like hydrogen energy levels).
    If there are two observers in light year distance and one of them kills a cat depending on nuclear decay, this information needs a year to propagate to the second observer - so accordingly to his QM, meantime the cat is in quantum superposition ... but does it mean that it objectively isn't dead or alive?

    Returning to the single photon in vacuum, if it didn't travel in a line, changing direction means momentum transfer - with what?

    About the second answer, so how long the deexcitation process lasts?
    Why not exactly this decohence time - delay making photon "misses itself" in interference?

    Or what happens while 21as delay in photoemission? ( http://www.sciencemag.org/content/328/5986/1658.abstract ).
  22. Oct 15, 2013 #21


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    What? I have not said anything like that. I said that there are experiments showing that either locality or realism are violated - unless you assume some loopholes like for example free will not existing. You cannot make up something and claim I said it.

    You can measure fields (within some limits). See e.g. E. Goulielmakis et al., Science 305, 1267 (2004). For single photons, though, you deal with probability amplitudes for detection events, not with fields.

    Yes, these are models. If your model does not make any testable predictions, it is rather an interpretation like de-Broglie Bohm vs. MWI vs. ensemble interpretation vs. many other things. Your initial proposal that single photons have a duration on the order of a single cycle is however ruled out by experiment. First, in that case single photons would always be spectrally very broad (broader than the whole visible spectrum) which does not agree with antibunching measurements. Second, you should not see interference in a Mach-Zehnder interferometer for delays larger than a single cycle. As experiments with single photons have shown interference for large delays, that hypothesis is ruled out.

    You have some misconceptions about qm and decoherence. This is not how Schroedinger's cat works. The second observer will get a mixed state, not a superposition. The "dead" and "alive" possibilities should not interfere.

    You still cling to the idea that something localized is necessarily physically traveling somewhere. This may be the case, but there is no experimental evidence for that. The energy might just as well be delocalized over the whole field.

    I do not get the meaning of your second question. The sentence seems to be off. The deexcitation process has no fixed duration. It depends on the line width of your transition. This can be very narrow for single atom spontaneous emission or very broad for short processes like the attosecond pulses used in the paper you cite. Think about the emitter being in a superposition of the excited and the ground state which gives rise to some dipole moment.

    If people knew that in detail, there would be no need to write papers about that, but how is that related to the discussion at hand? Ferencz Krausz and coworkers are pretty much pushing optics to the shortest possible pulses and do great work, but they are far away from the single photon level. To answer your question: What people guess is that there are some interesting electron correlations going on during that delay, but I am not sure whether they did some follow-up experiments to check that. Attosecond optics is a pretty complicated field. The spectral width of the pulses is so broad that it would span pretty much the whole visible regime from 400 to 800 nm if its center was in the visible. They work in the extreme UV, where the same width is less intimidating, but still challenging.
  23. Oct 15, 2013 #22
    I apology, I just really don't like the need for free will of some orthodox quantum mechanists.
    I also don't see the need for nonlocality or nonobjectivity - I am referring to concrete dBB intuitions, exactly like in Couder's experiments - you can literally see where quantum phenomenas come from, including interference.

    You are referring to violation of Bell inequalities - the "unability theorem".
    I didn't wanted this thread to go this direction - instead of focusing on what photon is.
    Ok, Bell inequalities say that correlations of entangled photons are against our "evolving 3D" intuition ...
    1) From one side, all physics we know is Lagrangian mechanics, which can be seen that the present moment is action optimizing equilibrium between past and future - we live in "full 4D" spacetime, what implies intuitions/correlations different from natural for us. And if we do thermodynamics in 4D - e.g. assume Boltzmann distribution among possible paths/trajectories: use euclidean path integrals/maximal entropy random walk, we get the squares connecting amplitudes and probabilities - leading to violation of Bell inequalities. Amplitudes correspond to probabilities on the end of half-paths toward past or future: to get randomly a given value, you have to get it twice: from past and future. Thermodynamics in 4D does not agree with Bell inequalities .
    2) These correlations in EPR is just angular momentum conservation - it is Noether theorem: the whole filed guards this conservation ... while in Bell inequalities you look only at well defined spins ("classical arrows") - completely neglecting the field around, guarding this conservation.

    I see both violating Bell inequalities and conservation of angular momentum in EPR as expected, but I don't want to spoil this thread with such discussion.
    So please let us stay in concrete models, like dBB/Couder's intuitions - please don't refer to general "unability theorems", but show concrete problems there.
    You can gain some information about the field, but as you disturb it by the way, this information will never be complete - what would be required to perform deterministic simulation.
    dBB interpretation is just Schrodinger equation after Madelung transformation: substituting psi=R*exp(iS). Then for density (R^2) you get just continuity equation, for action (S) you get Hamilton-Jacobi with h-order correction from quantum phase: the wave nature. Intuition is exactly like in Couder's experiments and it is just equivalent to Schrodinger.
    In contrast, MWI says that spacetime splits in every measurement - what disagrees with everything, like Lagrangian mechanics.
    I don't understand the spectrum counterargument: imagine you place something flat in water and rotate it 180 degrees - you create twist-like wave, which can then twist something else.
    Why optical photon isn't something like that - created from angular momentum of electron or twisting it 180 deg: from -1/2 to +1/2 spin?
    I think I have read somewhere something opposite - could you maybe refer to some source?
    It was supposed to be standard Schrodinger's cat experiment, but with perfect: spatial separation, but I agree that it is a bit different than superposition.
    However, still wouldn't the external observer's description be (|dead>+|alive>)/sqrt(2) ... while objectively it would be dead or alive?
    Still, don't you need momentum exchange to change its direction?
    The orthodox qm sees deexcitation as an instant process - and so the purpose of the next question was to show that it cannot be like that - there is at least some 21as process inside.
    Also from quantum point of view, wavefunction collapse can be seen as interaction with environment - as a continuous/unitary process - there is some concrete evolution behind deexcitation and optical photon is "Noether's shadow" (due to conservation laws) of this process: wave carrying energy, momentum and angular momentum difference of deexcitating atom.
    So time length of this deexcitation process, multiplied by c should be spatial length of single optical photon why it is not so simple?
  24. Oct 15, 2013 #23


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    dBB is non-local, too. You can follow any interpretation you like. I do not consider dBB to be too intuitive in my field. I am not for it or against it. It is just important to notice that it is does not explain anything more than other interpretations.

    Then let us skip that topic. Your comments on it let me think it is better that way.

    You can get pretty far using homodyning and tomography, but of course this is indirect. You cannot perform a single shot measurement of both quadratures of the field. That is obviously true.

    Intuition is a personal thing. Personally, I prefer neither dBB, nor MWI.

    If the photon was that short temporally, it must be very broad spectrally. This is simple time-energy uncertainty. People can demonstrate antibunching - the hallmark for proving that one created a single photon state - for light emission which is way narrower in the spectral regime. Therefore, the temporal duration cannot be that short.

    For example the paper I cited in my post #11 shows single photon coherence times in the nanosecond range. It is figure 3. Pretty much any paper on coherence in resonance fluorescence will show similar results.

    No. He should get a mixed state. A density matrix with dead and alive states on the diagonals occurring each with 50% probability. The difference lies in the fact that the cat state is a real superposition which can show interference, while the mixed state will not show interference and the 50/50 probability just describes a lack of knowledge.

    Depends on the model you consider. If you consider it as delocalized, it does not have a well defined position anyway and there is no need for momentum exchange.
    Note that I am not advocating one model over the other. All are plausible

    I cannot follow you. The 21 as delay happens between absorption of a photon and emission of an electron. Or do you talk about deexcitation of the em field? Do you mean the emission process?

    Besides that, photon emission is usually not seen as instantaneous. For emission processes, the excited state and the ground state are in a superposition state. If you have a look at e.g. the simple harmonic oscillator, you will find that a superposition of two modes results in a spatial oscillation of the probability distribution function. As we are talking about a spatial oscillation of the probability density for a charged particle here, this also means that oscillation will give rise to a dipole moment and dipole radiation. This superposition can break pretty quickly or it can take a pretty long time, but it is this superposition and oscillation which is the emission process.

    Well, that gives you the coherence time. One should be careful to identify it with a length of a photon, but if you know what you are talking about, the idea may be ok. However, this deexcitation is very far from instantaneous as I noted above.
  25. Oct 16, 2013 #24


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    Just a quick question about localization: is the crucial difference between the electron and the photon that the photon can't be prepared in a localized state because it is always absorbed in measurements or is it something else?
  26. Oct 16, 2013 #25
    See Couder's experiments (analogous to dBB) - without any nonlocality, they give clear intuition for:
    - interference in double-slit experiment (particle goes a single way, but "pilot" waves it creates go through all paths - leading to interference): http://prl.aps.org/abstract/PRL/v97/i15/e154101 ,
    - tunneling (the field depends on the whole history, making that getting through a barrier is practically random): http://prl.aps.org/abstract/PRL/v102/i24/e240401 ,
    - orbit quantization (to find a resonance with the field, the clock has to perform an integer number of periods while enclosing an orbit): http://www.pnas.org/content/107/41/17515 ,
    - "classical Zeeman effect" (Coriolis force instead of Lorentz): http://prl.aps.org/abstract/PRL/v108/i26/e264503.
    Do you disagree that they give proper intuition about quantum phenomenas?
    Please refer to a concrete quantum phenomena which indeed needs some nonlocality or nonobjectivity?
    Thanks. Violation of Bell inequalities shows only that our natural past->future "evolving 3D" intuition is wrong ... what is also obvious from other fields of physics: using Lagrangian mechanics and is broken e.g. in quantum retrocausality: Wheeler's or delayed choice quantum eraser experiments.
    This violation is not in disagreement with living in a field theory governed by Lagrangian mechanics (before or after quantization).
    Ok, http://prl.aps.org/pdf/PRL/v108/i9/e093602 [Broken] ... but it is about quantum dots: harmonic oscillators.
    I completely agree that waves produced by harmonic oscillators should be very different from standard optical photons: results of deexcitation of excited atom ... what are "time lengths" for them?
    Sure, but still does the mixed state in his quantum mechanics means that the cat is not objectively dead or alive?
    So when two paths in M-Z interferometer are indistinguishable, you get interference?
    But are they really indistinguishable?
    Reflecting photon by mirror means momentum transfer - doesn't final situation of photon going one or second path differ by final momentums of mirrors?
    You could measure it by placing these mirrors floating in vacuum and finally measuring their positions after some time.
    Quantum mechanics is h-order expansion of classical one by the wave nature ... in Feynman path integral you usually start with classical trajectory and make variation around it ...
    So you say that this expansion allows energy to travel through curved trajectories without momentum exchange?
    Like while reflecting by mirrors in M-Z interferometer?
    But what's wrong is about having broad spectrum?
    Take electron, twist it by 180deg, changing its spin by 1: e.g. from -1/2 to +1/2 ... Noether theorem says that the used angular momentum has to create twist-like wave.
    Exactly like behind a marine propeller, but this time the medium (EM field) has no viscosity - such twist-like wave can travel without dissipating ... e.g. finally getting to another electron and twisting it 180 deg.
    What's wrong with this picture?
    I meant only that everything in internal dynamics of a single atom takes time/evolution - and so we should be able to ask how much time deexcitation lasts - changing orbital angular momentum or twisting spin of electron.
    Accordingly to Noether theorem, this angular momentum changing process should produce wave carrying this angular momentum (optical photon) - of spatial length being time length multiplied by the propagation speed (c).
    Why it is not so simple?
    ... is photon something more than just a wave carrying energy, momentum and angular momentum - to compensate differences in deexciting atom?
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