Size of a photon's electromagnetic field

  1. I have some specific, related questions, for which I haven't been able to find answers:

    1. At any instant in time, is the physical size or extent (e.g., length, width, diameter) of the electromagnetic field of a single photon (of a given wavelength) traveling through a vacuum determinate and invariable?

    2. Is there an equation which relates the physical size of the field to the photon's wavelength?

    3. What shape is the field at an instant in time, e.g. is it spherical? Is the length of the field (longitudinal in the line of travel) the same as in the dimensions transverse to the line of travel (colloquially, the width and height)?

    4. At any instant in time, does the field physically encompass one, less than one, or more than one full wave phase cycle?

    5. Does the maximum amplitude of the field vary depending on location within its boundaries, for example is the maximum amplitude greater near the physical "center" of the field than at the extreme outer edge? I wouldn't think so.

    I understand that one cannot pin down the specific "point" location of a photon at any instant in time without observing the photon (thereby causing the wave to collapse). But that is a separate issue from the question of the physical size of the wave's field at any instant in time.

    In the double-slit experiment each single photon interferes only with itself, not with other photons. Since the experiment implies that a single photon's electromagnetic field passes through both slots simultaneously, it seems to me that the physical width of the field (at least in the dimensions transverse to the photon's line of travel) must be at least as large as the distance between the two slots. As I understand it, in order for interference to occur there is a maximum limit to the distance between the slots, which is related to the photon's wavelength. I would appreciate if anyone knows the equation for the maximum slot distance. And whether it equals the physical width of the photon's field.

    I'm primarily interested in understanding the instantaneous physical length of the field along the photon's line of travel. It seems to me that the double-slit experiment doesn't shed light directly on that point (so to speak).

    I'm not asking about the concept of polarization, unless it directly relates to the physical size of the field in one or more dimensions.
    Last edited: Jan 4, 2009
  2. jcsd
  3. Light,an electromagnetic wave has only wavelength and frequency. It does not have length,width etc.

    There is no "size of electromagnetic field". It has no size. Electromagnetic and gravitational fields have infinite range. It has no finite range or size.

    About double slit experiment, there is no such thing as "physical width of the field". There is also no maximum limit to the distance between the slots. Even if the slots are separated to infinite distance,light enters in both slots but the interference pattern will not be clear. I think, my answer to DS experiment is correct.
  4. jtbell

    Staff: Mentor

    Don't think of a photon as a tiny localized bundle of electromagnetic fields, such that if you "add up" a lot of photons (and their fields) you get the classical electromagnetic radiation field.

    To put it another way, you can't get photons simply by "dividing up" the classical electromagnetic radiation field into little pieces. Think of classical electrodynamics and quantum electrodynamics as alternative (and very different) models which correspond to each other in such a way that their predictions agree more and more closely as you "move" from a microscopic to a macroscopic scale.

    Someone who knows quantum electrodynamics better than I do can probably answer this better, but the picture I have is of a quantum "photon field" which fills the space where you're doing the experiment, with photons being energy-quantized states of that field. I think I remember someone here using an analogy with vibrational modes of a bowl of Jell-O.
  5. Spidey and jtbell,

    I appreciate your description of the semantics. Perhaps it is incorrect to refer to the wave structure of an individual photon as an "electromagnetic field". Maybe the technical term is "quantum field" and it acts like a bowl of Jell-O. However, I note that Wikipedia among other sources consistently refers to the concept of an individual photon possessing its its own "electromagnetic field" which embodies the wave-like characteristics of the photon. I do understand that Wikipedia can't always be taken as gospel.

    Whether it is a "quantum field" or an "electromagnetic field", I'll just refer to it here as the photon's "wave field". I distinguish this term from the term "wavelength" because I don't know how many wave cycles (and therefore wavelengths) are physically embodied within a photon's wave field at any instant in time.

    It seems to me that the concept of physical size (measured instantaneously) MUST apply to the wave field. I see only three choices:

    1. The wave field is a "point" field with ZERO physical size. This choice doesn't seem valid because the wave field needs to have at least a finite physical size in the transverse dimension as large as the distance between the slits, in order to pass through both slits simultaneously.

    2. The wave field has an INFINITE physical size at any instant in time. Spidey, in this respect I disagree with your statement that electromagnetic and gravitational fields have infinite size. I agree that they have infinite POTENTIAL size given infinite travel time, but their measured ACTUAL extent at any given time will be finite if they have been traveling for only a finite time. For the purpose of this discussion I'm going to assume that the photon has been traveling for only a finite time.

    Even so, it seems unlikely to me that a single photon's wave field will expand indefinitely away from the photon at the speed of light. This would suggest that a single photon (or a tight beam comprised of many photons) could induce electromagnetic activity in matter located at a large distance ORTHOGONAL to the line of the photon's travel. This does not occur in reality (assuming that the photon beam and the distant matter are not entangled).

    It would also suggest that the strength (peak amplitude or intensity?) of the wave field diminishes with the square of the distance from the photon in accordance with Gauss' Law. I am not aware of any basis for such locational variation inside a photon's wave field.

    However, this choice may have to be adopted if, as you say, there is no maximum distance that the slits can be apart. I don't think that is correct. For example, the Wikipedia article on the double split experiment says there is a maximum slit distance which is related to the wavelength.

    3. The wave field has a FINITE extent (measured instantaneously) which is perhaps related to the wavelength. This seems entirely consistent with Wikipedia's description of the double slit experiment. I would picture this as a small bubble of "wiggling Jell-O" around the photon which travels with the photon. The precise location of the photon "particle" inside the Jell-O bubble is indeterminate at any instant in time. This suggests to me that the wave field bubble has a discrete outer boundary surface, i.e. the field strength is 100% all the way out to the distance where it becomes 0%.

    There are many authoritative sources which describe cosmological redshift as a physical "stretching" of each photon, thereby causing each photon's wavelength to increase. Perhaps this is just loose language. But if a photon's wave field does have a finite physical length which is related to its wavelength, then it does seem plausible that an individual photon's wave field could literally be stretched longitudinally (e.g. by gravity) causing its wavelength to lengthen.

    It makes the most sense to me that the wave field bubble is spherical and its size is related to the wavelength. So if an individual photon's wave field becomes "stretched" longitudinally, this causes the bubble to expand isotropically in all 3 spatial dimensions.
    Last edited: Jan 4, 2009
  6. jtbell

    Staff: Mentor

  7. Cthugha

    Cthugha 1,679
    Science Advisor

    Wikipedia sucks sometimes.
    The idea of photons having an em-field is a bit flawed. In principle the fields are the more fundamental quantities. The QED description is a bit more complicated, but the basics can be understood pretty well in a semiclassical model. Imagine an ensemble of emtters. Each of them produces an em-field. Now photons - a bit similar to intensity in the classical picture - are second order in terms of these fields. This means that you need a field and a complex conjugate field to describe them. But now the total field is a superposition of all the fields of the emitters, so photons can be the "result" of the field of one emitter alone (and its complex conjugate) or it can be the "result" of a field from one emitter and a complex conjugate from another. The second case makes it pretty much impossible to attribute one field to a certain photon, so the only meaningful scenario, where you can relate a photon directly to some em field is when you have just one field present, which gives an unambiguous situation. So you need single atoms, single molecules, single quantum dots or whatever.

    So in this case it makes at least a bit sense to talk about spatial extents of a photon and its em-field. The field itself has of course infinite size, but you can define some measure of the spatial distribution like the distance after which the amplitude falls to 1/2 of the maximum amplitude or something like that. In this case this special distance will be more depend on the coherence properties of the em-field. There is some uncertainty in the exact emission time of a photon. Generally speaking, the greater this uncertainty is, the longer will the coherence time be. The product of coherence time and c gives a rough estimate of what one could call some spatial extent. It is nevertheless not that useful. Switching to usual emitters again, the coherence time is also the timescale on which emitted photons are indistinguishable, so as said before attributing a field to a single photon is pretty pointless.

    Well, consider a photon, which is randomly emitted in any direction. The probability to detect it per unit area will of course diminish with the square of the distance due to the geometry.

    Could you point me to where they say that? Usually the maximum distance also depends on the coherence properties of the light.

    The wavelength is not really connected to the spatial dimension of the em field. However the wavelength gives a lower border for the localizability of a photon. You can define a superposition of single photon Fock states to describe a photon localized in some volume, but you will find out that this definition is only meaningful if the spatial extents are much larger than the wavelength of the photon. If you intend to localize a photon further, you will find out, that the detection probability and the energy density will depend nonlocally on the spatial photon probability density (which means that the maximum detection probability will be localized at a different position than the photon probability function...and the energy density will be at maximum at another position) and some other problematic stuff. If you are interested in details, see: Optical coherence and quantum optics by Mandel and Wolf, especially chapter 12.11 (the problem of localizing photons).

    This depends completely on the emission process. For example light, which is emitted in a certain direction, will certainly not have an isotropic field.
  8. jtbell, thanks for the references, which I read through. The authors often seem to be talking past each other. In addition to the difficulty of the technical jargon, I think the communication problem is mostly due to the questions not distinguishing clearly between the size of a photon particle itself (which is undefined and generally irrelevant to observables) vs. the size of the photon's EM field, which perhaps could be defined by reference to observables. For example, the size of a photon's field might meaningfully be related to the maximum distance between two slits that permits interference at a given frequency, or the smallest mesh size that a microwave of a given frequency can pass through. I'd like to know if there is a direct mathematical correlation between those two examples.

    Cthugha, thanks for your explanation, but I'm not sure we're addressing exactly the same question.

    Again, to be clear, my question does NOT relate to what the size of a photon particle itself is. I also am NOT asking about anything to do with nailing down, or calculating the probabilities of, a photon's precise position or momentum within phase space or Hilbert space. This latter topic seems to be the subject of the majority of the dialogue about QM.

    I'm not sure that I'm asking about events at the quantum scale at all. I'd like to pose my question starting "tops-down" at the macroscopic scale. Imagine a tight (nondivergent) pulsed beam of photons traveling along a specific one-dimensional line through a vacuum. (We will intentionally ignore any potential interaction with other photons emitted from the same source which diverge away from that line.) There will be a wavefront located at or near the lead photon in the pulse, which will travel forward along the line with the lead photon. Each individual photon in line behind the lead photon will generate its own individual wavefront. Unless the lightbeam is highly coherent, the spacing of these wavefronts will not be exactly equal to the wavelengths of the photons (which are assumed to be identical). The photons in this pulse are emitted far enough apart such that we can try to consider the contribution of each photon separately. Eventually the photon beam pulse will run into a double slit apparatus, and we will record, in sequential order, the locations at which each photon strikes the target.

    While the photon beam pulse is still travelling through space, what is the shape of the leading wavefront generated by the lead photon? It seems that the wavefront can't be spherical, because the photon moves forward at c so the wavefront can never extend ahead of the photon's position. Perhaps the leading wave front is hyperbolic, with the open ends of the hyperbola trailing behind the photon. Each following wavefront is then just another hyperbola nested inside the preceding hyperbola.

    However, I think that picture is wrong. I think the ONLY thing that causes the wavefront to propagate through space is the motion of the photon (or photon packet if you like) itself along its path. The leading wavefront exists only at or near the photon's then-current location. There is no part of the wavefront that radiates orthogonally away from the photon's travel line. A photon traveling through space radiates exactly ZERO energy in the directions orthogonal to its path. No inverse square law applies to orthogonal energy.

    I picture each photon cycling its EM amplitude repeatedly "on" then "off", through smooth wave increase and decay cycles, like a lightbulb repeatedly turned and off. Each time the photon's cycle hits the "off" minimimum (zero) amplitude, its EM wave's amplitude degenerates to zero. In other words, the wavefront must be continually renewed at each peak amplitude cycle. Wavefronts generated in earlier cycles do not "linger on" and trail behind the photon -- how could they, since both the photon and the wavefront travel forward at the same speed? Thus when a photon strikes a target and is absorbed, there is no residual EM field previously generated by that photon which remains (or radiates outwards) behind or orthogonal to the photon.

    [Edit: Or alternatively, maybe the photon doesn't blink on and off, maybe it's always "on". In that case the wave peaks are represented by the individual photons following along in line, and the troughs by the empty intervals between them. In this scenario maybe the smooth increase and decay in the wave shape tells us something about the size and configuration of an individual EM photon's EM field as the photon progresses forward toward and into the target absorber...}

    In any event, it seems to me that the only reason why EM fields radiate spherically and isotropically is because the field is comprised of a multitude of photons which themselves are moving isotropically in all directions. The lead wavefront then is the aggregation of the individual wave packets, subject to whatever interference occurs as between them. The inverse square law applies because the radiation flux (the photon density) decreases in proportion to the surface area of the expanding sphere, which is proportional to the square of the radius -- Gauss' Law. But this tells us nothing about whether or how EM energy propogates away from an individual photon.

    As I said, it seems to me that an individual photon's EM energy must be contained entirely within a wave envelope or "bubble" which accompanies the photon along its one-dimensional path and is tightly bound to it. Energy isn't constantly "leaking" away from the photon along its journey.

    In theory the lead photon's wavefront could be a "point" charge, or instead it could be characterized by a nonzero but finite extent and volume. I continue to feel that the wavefront must have a finite size which is related to its wavelength, at least in the transverse directions so that it can pass through both slits simultaneously, up to some maximum slit separation.

    But as I said my primary interest is in understanding whether the lead photon's wavefront or bubble has a nonzero longitudinal size related to its wavelength. We need to know this as a step toward figuring out whether EM radiation can be redshifted by the mechanical act of physically stretching its EM bubble.
    Last edited: Jan 5, 2009
  9. Cthugha

    Cthugha 1,679
    Science Advisor

    There usually is no thing like the photon being a point particle and going some special direction before it is detected. What travels with c are changes in the em field and these will always be spherical. Now a photon will of course always be detected at a distance to the source, which shows that "it has traveled" with speed c, but this only shows that the energy transfer is quantized. It does not show, that there has been a point particle following some explicit path. If the source emits radiation isotropically, the field will look spherical, too. If you prepare the em field in a state with defined k - for example due to some constraints due to conservation of momentum - you get a bit closer to your picture. But this is not the way light usual light sources behave.

    Again, this is not the way it works. There is no photon taking some well defined way prior to a measurement.

    Let me stress it again. The fields are more fundamental than photons are. The fields give rise to photons, not the other way round.

    Well, you will have to discard the idea of a clear 1D path. If the photon traveled just on a 1D line the double slit experiment would not work as the slits can be very far apart compared to the photon wavelength.
  10. I agree with your point, which I thought I had made myself, sorry if my wording wasn't clear. Instead of saying that the photon "particle" follows a straight 1D path, let's just say that the "photon packet" or "photon EM bubble" follows a straight 1D path. Please do not interpret anything I say to imply that the exact location, momentum, or path of an in-flight photon "particle" itself can be nailed down.
    I'm glad to hear that a single photon's travelling EM field "bubble" is known to be spherical in shape. That means the bubble must have a specific spatial volume, presumably related to the wavelength. Can you please cite or quote a specific reference for the spherical shape of the bubble?
    OK, what is the exact maximum distance that the slits can be apart, relative to the wavelength? This is one thing I'm trying to get a specific answer to.
    Interesting statement. The following quote from the Wikipedia article "Photon" seems to disagree. I'd appreciate your thoughts on how to bridge the contradiction:

    "However, experiments confirm that the photon is not a short pulse of electromagnetic radiation; it does not spread out as it propagates, nor does it divide when it encounters a beam splitter. Rather, the photon seems like a point-like particle, since it is absorbed or emitted as a whole by arbitrarily small systems, systems much smaller than its wavelength, such as an atomic nucleus (≈10E–15 m across) or even the point-like electron. Nevertheless, the photon is not a point-like particle whose trajectory is shaped probabilistically by the electromagnetic field, as conceived by Einstein and others; that hypothesis was also refuted by the photon-correlation experiments cited above. According to our present understanding, the electromagnetic field itself is produced by photons, which in turn result from a local gauge symmetry and the laws of quantum field theory."

    The "photon-correlation experiments" are cited as follows:

    "These experiments produce results that cannot be explained by any classical theory of light, since they involve anticorrelations that result from the quantum measurement process. In 1974, the first such experiment was carried out by Clauser, who reported a violation of a classical Cauchy–Schwarz inequality. In 1977, Kimble et al. demonstrated an analogous anti-bunching effect of photons interacting with a beam splitter; this approach was simplified and sources of error eliminated in the photon-anticorrelation experiment of Grangier et al. (1986). This work is reviewed and simplified further in Thorn et al. (2004).

    See also the "Quantum Interpretation" section of the Wikipedia article on the Hanbury Brown and Twiss effect.
  11. I have been following this thread with interest and curiosity. As a mathematician and engineer, I have no presumption of knowledge here - only an iota of understanding.

    Would my understanding be somewhat correct in the travel of the photon? ...

    When a photon is emitted from a source, one might be better to recognize that an EM field alone has been generated from that source. The path of radiance of that field is rather directional but with some uncertainty; the stochastic divergence of it's path is a function of its wavelength (lambda).

    I presume the EM field does expand with time (double slit principle). However, the centroid of the field is propagating at the speed c, and in the direction of the presumed photon's path. The total energy of the field over space is equal to E=h*v

    Now consider when an observing/interacting particle (say an electron) is in the path of eventual interception. The electron, by its nature, is able to interact with the photonic EM field, but the nature of interaction is constrained. The electron will only "experience" the photon (rather the EM field) when energy in the quantum of E=h*c/lambda is collected (boldly speaking). At this moment, the EM field collapses to a localization of its energy. Likewise, its position collapses to being at the position of the electron. This allows the electron to absorb (and do with it as it will) the full quantum of the EM field's energy, and the field then ceases to further propagate.
    Last edited: Jan 5, 2009
  12. Cthugha

    Cthugha 1,679
    Science Advisor

    Oh, that was not what I intended to say. I just wanted to say that - under usual conditions - there even is no well defined 1D path. In the statistical limit of high photon numbers this picture is ok and easy to visualize. Going to low photon numbers this picture breaks down unless you prepare some very specific states of the em field.

    Oh, I suppose we were talking past each other here. I just intended to say that changes in a field will spread out from a source of the field isotropically in all directions with speed c. I did not intend to say, that there is a bubble "around" a photon. It is just the surface of this bubble around the source, which is the analogon to the classical wavefront.

    the maximum distance does not depend on wavelength. It depends on the difference in distance between the source and the two slits. If the time you get by dividing this distance by the speed of light is much larger than the coherence time of the light, you will not see an interference pattern.

    The electromagnetic fields of Einstein were completely classical fields. The contradiction stated above comes from the fact that photons are always absorbed or emitted as a whole as was shown by antibunching in resonance fluorescence and other experimental settings. Classical fields do not predict this antibunching. The em fields of QED and CQED however are in this case not comparable to classic fields. In QED you have field operators(which - similar to the classical field - also contain the photon creation and annihilation operators) and a quantized field, which predicts antibunching correctly. So the energy contained in the em field is quantized. The quanta of these field are the photons. To give a simplified analogy: Using classical fields, you can calculate some intensity corresponding to the fields. In the case of low intensity, you would expect this intensity and the corresponding energy density to get smeared out all over the place, which leads to unphysical results. Using quantum fields, you just have a detection probabilty distribution, which is smeared out just like the intensity in the classical case. The actual detection however will only happen at one place and in a quantized way. But (for an isotropic emitter) prior to a measurement this one place where the detection will happen is by no means special. The probability to detect it here is as large as it is on the other side of the emitter or anywhere else on a sphere with the same distance to the source.

    Let me address the wikipedia quote, too. The second bold sentence is ok, although a bit misleading. In QED one considers the em field to be a set of harmonical oscillators, the modes of the field. Each photon is now one of these excited modes, corresponding to a harmonic oscillator. Now you can just use Fourier synthesis and superpose a lot of these modes and shape any field you like. Note that in this case the photons are modeled as Fock states: an infinitely long wave train with constant frequency. In this understanding it is completely impossible to attribute some physical size to a single photon. It really spreads out infinitely. However, this is not the idea, most laymen have of photons. They are not particle-like at all except for the fact, that their energy is quantized. This is all fine and well and it works great for free electromagnetic fields. But it is extremely messy as soon as you consider an interacting field. It is not very intuitive to describe a photon, which is created by some atom at some point by an infinite wave train. In this case I think it is more intuitive to use a more field-based model. However this is a bit like choosing between Schrödinger, Heisenberg and interaction picture. You shift some factors around and suddenly it makes more sense.

    Oh, I know this stuff. Been measuring stuff like this now for.....too long. ;)
    Note that this Wikipedia article also uses fields to explain the HBT effect. If you want to calculate the concrete probability amplitudes used in such an explanation you will need to replace a>, b>, A> and B> by a combination of quantum states of the em field and the necessary operators to define your interaction.

    From a given state of the em field, you can predict, how your photons will behave. Just from having information about some photons, you can usually not reconstruct the state of the field. If you could, all of the people doing quantum state tomography would need to find a new topic to work on.
    It was Roy Glaubers great insight that to really reconstruct the field by just looking at the photons, you would need to have detection locations and times of all photons and then calculate correlation functions up to arbitrary order to get the maximal possible information available about the field, which is why I consider the field more fundamental. It seems a bit more systematic to me to use 1 field for defining instead of n particles.

    If you are extremely enduring, you might also look here: or here: This topic arises here quite regularly.
  13. skeleton, I'm no expert either. I agree with you that it is easier to picture a photon as comprising a finite field whose total energy is a fixed quantum (fields by the teaspoonful). EM seems more field-like than particle-like, except for the added twist of the "full field point-emission" and "full field point-capture" phenomena. It is not clear to me that analogizing a photon to a point particle (e.g., to a massive particle such as a fermion) is ever required by a photon's behavior or is even helpful in picturing it.
    Last edited: Jan 5, 2009
  14. So Cthuga, what's your opinion on whether, from a QED perspective, the redshifting of an individual photon's frequency can be properly attributed to the application of a mechanical "force" such as gravity (or semantically spacetime warping if you prefer) physically stretching the spatial size (and spatial volume) of the individual photon's EM field (as viewed in an observer's rest frame)? (I note that relativistic time dilation of an EM field results in, and is equivalent to, spatial stretching).

    Or alternatively, is one limited to saying only that the photon's "energy has been diminished" by gravitational deceleration, without attributing spatial stretching as the cause?
  15. I'm still looking for information on:

    1. Over how large an area, in theory (practical measurement limitations aside), can the instantaneous size of a single photon's EM wave be detected;

    2. Does the intensity of that EM wave vary at different locations within its total envelope (bubble), or is it invariant?
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