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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

    UltrafastPED

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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:

    http://en.wikipedia.org/wiki/Angular_momentum_of_light


    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

    UltrafastPED

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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
    Really?

    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

    Cthugha

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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

    Cthugha

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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.

    edit:
    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

    jtbell

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    See here for example (page 3 onwards):

    http://www.physics.usu.edu/Wheeler/EM/EMenergy.pdf‎

    [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

    jtbell

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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

    Cthugha

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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

    Dale

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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:
    http://farside.ph.utexas.edu/teaching/em/lectures/node87.html
     
  20. Oct 15, 2013 #19

    Cthugha

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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 ).
     
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