What are the dimensions, width and length, of a photon?

Question

Everyone is always talking about photon's wavelength. But what about its dimensions? What is length and width of it? And does it even have a point to think about such things? Or those dimensions are non-existent in such cases?

Answer 1

The fundamental particles we know today (of which the photon is one) are called fundamental exactly because they have no substructure, or indeed, spatial extent, we know of. They are point-like when localized.

Note that these "particles" are quantum objects, not classical particles, so you should not imagine them as points whizzing about in space - they possess delocalized states where they take no definite shape at all (for example, the "electron cloud" around atoms is such a delocalized state).

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The above is a short, non-relativistic view of "particles". When going to the relativistic description that is actually needed for the full description of fundamental particles, things get considerably more murky. For one, we lose the naive position operators, and the notion of "localization" becomes a bit ill-defined because the new "position operator", the Newton-Wigner operators, do not allow to speak of localization in an observer-independent way. The generic particle state that is scattered in QFT calculations is usually a sharp momentum state, and therefore strongly delocalized, so any notion of "point-like" can't really rely on the localization of a particle state.

In this picture, the proper notion of a "point-like" particle is one whose scattering behaviour indicates no substructure or spatial extent. For extended objects consisting of subobjects, their scattering behaviour will typically change when the energies/length scales of the scattering process reach their size, because then their internals get resolved and the individual subobjects start participating in the scattering. So then our notion of size becomes that the scattering behaviour is scale-independent. For more on this notion of size in QFT, see e.g. this answer by Bosoneando.

Answer 2

The photon can be experimentally shown to not be point-like. The Young's slits experiment involves the interference of a photon with itself (the photon behaves in some ways like a particle, in some ways like a wave and in some ways like a probability distribution. in reality these are convenient models that we apply to it - in reality it is none of these - it is a photon). The interference patterns shown in the Young's slit experiment remain even if the stream of photons is reduced to the extent that photons go through 1 at a time. The length difference in the 2 paths can be varied to determine the coherence length. I believe this turns out to be in the order of 1m. Further experimental proof that the photon must have a significant length is that the spread in its frequency is minimal. if it reduced to 0 amplitude over (e.g.) only 3 wavelengths then this would give it a significant spread in frequencies

Answer 3

For me I prefer an experimental definition of the size of a photon. If you pass light through an aperture you start to see interference effects when the aperture approaches the wavelength of the photon, as if you're clipping the edges. Why do we need to make it more complicated than this?

If the photon is point-like then the energy density would be infinite which seems unrealistic.

It must be localized in space as photons can be detected from the other end of the universe. If photons are spreading out then their energy density would tend to zero over these distances.

Answer 4

This is an excellent question. Following is an abbreviated version of the answer that I wrote in the physics textbook "Light and Waves: A Conceptual Exploration of Physics" (2023).

A photon is typically described as a point particle, with no size whatsoever. This makes sense when considering that there is no limit to the number of photons that can exist in a fixed volume of space, the fact that individual photons can interact with very tiny objects, and the fact that photons are absorbed in their entirety and all at once. In this point particle explanation, the photon is just a point but its position is some random location that has a probability that is given by the corresponding wave function.

On the other hand, it’s often helpful to think of photons as having larger sizes. For example, when a molecule absorbs a photon, the photon is not absorbed at a tiny spot within the molecule, but by the entire molecule at once. Likewise, when a radio antenna absorbs a radio wave photon, it gets absorbed over the entire length of the antenna. Thus, it’s reasonable to say that when individual photons interact with objects, then the size of the photon must be the same as the size of the object.

Yet larger sizes arise when considering diffraction and interference experiments. Light (like all types of waves) goes through holes that are bigger than a wavelength with low power loss and is essentially blocked by holes that are smaller than a wavelength, suggesting a photon size of about one light wavelength. In two-slit interference, single photons interfere with themselves, implying that each individual photon goes through both slits at once; this suggests a size of a millimeter or more. In an interferometer, a single photon gets split into two pieces that might be meters, or even kilometers, apart from each other, now suggesting that a single photon’s size could be reasonably considered to be multiple kilometers across.

As another answer, one can imagine measuring the electromagnetic field in the light beam, where one would see regular peaks and troughs over short distances, but different sets of waves over longer distances. The length scale over which the waves are reasonably regular is called the coherence length of the light source. Lasers, and light from point-sources such as distant stars, have large coherence lengths, often of meters or larger; however, light from large sources, such as the sun or light bulbs, have short coherence lengths that are in the micron range. Coherence lengths set the limit on the sizes of interference phenomena, such as the maximum separations of two-slit interference experiments. Thus, another useful measure for the size of a photon is the light’s coherence length.

Taking all of these arguments together, there is no good single answer for the size of a photon. Instead, there are situations where photons are best considered as point particles, and other situations where larger sizes, even up to kilometers or longer, are more meaningful.

Answer 5

Fundamental particles have no dimensions, they are point like. At times it is convenient to associate some finite, non-zero value though.

For example, the classical radius of the electron helps with some electromagnetic problems. $r_e=\frac{e^2}{4\pi \epsilon_0m_ec^2}$.

One can also associate the Reduced Compton Wavelength of the electron: $\lambda_e=\frac{\hbar}{m_ec}\implies r_e=\lambda_e\alpha = a_0\alpha^2$ where $\alpha_0$ is the Bohr Radius and $\alpha$ is the Fine Structure Constant, $\alpha \approx 1/137 $.

Something similar applies to photons. $\lambda_p=\frac{hc}{E}$ where E is the energy of the photon.

In general, the uncertainty is position has a minimum of half the Compton wavelength as mentioned here.

Answer 6

I suggest looking at this paper, and references therein. Such a simple question is not so simple to answer as, the authors point out, " ...the quantum state vectors that represent photons do not have position-space representations that are analogous to the familiar wave functions of nonrelativistic quantum mechanics. Thus there is no quantity analogous to ""psi squared"" giving a probability density for finding the photon in space."

The calculated photon: Visualization of a quantum field Martin Ligarea) and Ryan Oliveri Department of Physics, Bucknell University, Lewisburg, Pennsylvania 17837 ~Received 21 May 2001; accepted 7 September 2001! We calculate spatial localization and phase properties of spontaneously emitted photons. Our model is simple yet fully quantized: the emitting atom is a two-level atom located in a one-dimensional multimode optical cavity. Although the photon state vector does not have a position-space representation, the expectation value of the square of the electric field operator ~intensity! is spatially localized and this pattern shifts at the speed of light. The emitted photon exhibits classical-like phase properties in the intensity expectation value when it ‘‘interferes with itself’’ after reflection. The phase properties of the emitted radiation are also evident at times sufficiently long for the radiation to have returned to the emitting atom before the decay of excited atomic state is complete. © 2002 American Association of Physics Teachers. @DOI: 10.1119/1.1417531#

Answer 7

It’s a great question. In college, my professor was rather unclear on this topic.

Electrons are experimentally point sources. No matter how high an energy is used to smash them together no size is evident in the result.

Photons can’t collide so this experiment doesn’t help us.

It is interesting that in NSOM photons can pass through extremely tiny apertures, much, much smaller than a wavelength of light.

Experimentally photons seem to behave as objects that have a size on the order of a few wavelengths. On the other hand, photons of a wavelength of roughly $500$ - $1,000\ nm$ can be absorbed and emitted by atoms with dimensions of about $0.3\ nm$.

I guess if you think in terms of string theory you would say that the inherent size of a photon is on the order of the Planck length but it has a range of action on the order of a few wavelengths.

Answer 8

IF d is set as the distance light travels in one quantum of time, t; and c is set at exactly 3 d/t, then light will encircle its “diameter” exactly 3 times in the one time-unit (not pi times). One of those 3 revolutions can be thought to represent the x direction, with the other two revolutions corresponding to y and z… A “Planck’s constant” = 3^.5 then becomes applicable. This indicates a photon “sphere” with radius= 3^.5 (diameter=3) and volume = 4/3 * 3 * r^3 = 4r^3 = 4*3^(3/2)