# Length of a Photon

Posted on 2008-05-05 as a part of the Photonics Spotlight (available as e-mail newsletter!)

Permanent link: https://www.rp-photonics.com/spotlight_2008_05_05.html

Author: Dr. Rüdiger Paschotta, RP Photonics AG

Abstract: A frequently encountered question concerns the length of a photon. The article shows that this is not a sensible question, because there is no comprehensive model of a photon to which this question could be applied.

Ref.: encyclopedia article on photons

A question which is frequently brought up by lay persons, but sometimes also by journalists reporting about some scientific experiments, concerns the length (and possibly also the transverse extent) of a photon.

The trouble with that question is essentially that the photon is a theoretical construction which does not have any straightforward connection either with an entity of physical reality or with anything simple which we can imagine. Some people are so much disturbed by this problem that they even consider the notion of photons and the corresponding scientific theories as totally flawed. Others adhere to more or less mechanistic models of photons and feel free to equip those with some details which actually do not occur in any of the common scientific theories. The latter approach can lead to questions such as the one concerning the length of a photon. If a photon were known to be something like a hard particle, or alternatively perhaps a wave packet, some kind of length could easily be defined. According to quantum theory, however, a photon is neither simply a particle nor simply a wave; instead, it has properties both of particles and waves, or more precisely speaking, the phenomenon of light exhibits both features of particles and waves.

In this situation, it doesn't even make much sense to ask about the length of a photon, at least without defining what exactly such a length should mean. If answers are given anyway, confusion is the natural consequence. Some people argue that a photon cannot be larger than the area which is filled by light, and this limits e.g. the transverse extent of photons in laser beams. Others consider the transfer of one photon energy to an atom, and conclude that this energy must be much more concentrated. Another approach is setting a lower limit to the extent, essentially by considering the minimum pulse duration of light with a certain optical bandwidth, and multiplying this with the velocity of light in order to convert it into a length. One may also consider the length of a photon wavepacket; see e.g. the famous interferometric experiment of Hong et al. (C. K. Hong, Z. Y. Ou and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference”, Phys. Rev. Lett. 59, 2044 (1987), doi:10.1103/PhysRevLett.59.2044).

Obviously, all these thoughts are based on particular physical models of reality, not on observations, and often come without a clear definition of what the length of a photon should be (e.g. how it should be measured).
The manifold of mutually contradicting results just reflects the manifold of more or less suitable physical models and more or less appropriate interpretations of those.
In other words, I think there is no comprehensive model of a photon of a kind which makes that question sensible.
At most, it can make sense to ask about the length in one particular sense, but not about *the* length of a photon.

By the way, the encountered problem is not specific to photons. The same occurs e.g. with electrons. In some sense, an electron can be considered as a point-like particle, but we also know about the electron's wave properties and in fact use wave functions which can be as extended as a whole atom or even a whole crystal. This leads to another hint for those denying the existence of photons (or more precisely, the validity of any photon concept) based on such problems: if you decide for that path, then you should do the same with electrons, protons, neutrons, etc., which also have a wave nature.

This article is a posting of the Photonics Spotlight, authored by Dr. Rüdiger Paschotta. You may link to this page and cite it, because its location is permanent. See also the RP Photonics Encyclopedia.

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## Questions and Comments from Users

2021-02-11

The length of a photon could reasonably be measured as the maximum difference in the paths between the two paths in a 2 slit (Young's slits) experiment before there is no observed interference pattern. I believe that this results in a length of the order of 1 m.

Answer from the author:

Basically, you are just proposing a particular definition of the length of a photon: you would just take the coherence length of the radiation. A weakness of that definition would be that you can't apply it to single photons, since you need many photons to record an interference pattern.

In practice, the coherence length can be much longer are much shorter than 1 m.

2021-10-13

Interferometry experiments can be done with single photons (see for example https://www.osapublishing.org/DirectPDFAccess/ACDD3557-F93A-4AAF-9F0E68ED8051809E_336918/josk-19-6-555.pdf?da=1&id=336918&seq=0&mobile=no). In this experiment it appears that the coherence length is about what one would calculate classically.

A QFT calculation of an atom emitting a photon in a cavity has a length for the energy density (a finite region of non-zero energy). See http://www.eg.bucknell.edu/physics/ligare/ajp_visualization.pdf. It would be interesting to collect experimental results and put in one place to see what attributes a photon demonstrates.

Answer from the author:

Thank you for the comment!

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2020-08-24

This answer is nonsense. If wavelength is used to define the photon as a wave, the question is legitimate. But if you don't know how to answer, it's better not to answer, Dr. Paschotta.

Answer from the author:

I definitely agree with the latter statement, but don't think that it applies to this particular case. Besides, I did not say that the question on the length of the photon is not legitimate. It is only that the question is not clearly stated, and in fact people are often not aware that it is not even clear how to define the length or spatial extent of a photon.

The author of that comment has unfortunately not explained his own view on the subject, so that we can neither make progress nor admire his or her greater wisdom.