How Big Is a Photon?
John Clark
I recently realized I can't give a good answer to the seemingly simple question "how big is a photon?" so I did some reading on the subject and the short answer I can now come up with is "that depends". The slightly longer answer is it depends on how the photon is produced and what you mean by “size.” In one sense photons are elementary particles with no evidence of internal structure: scattering experiments show they have no parts. When a photon strikes a photographic plate it produces a localized point, not a smear, and there is no sign of matter interacting with one portion of a photon before another. Photons are also massless and electrically neutral, so they do not have a rigid physical boundary that could be measured like the surface of a ball.
But on the other hand red light has a wavelength of about 650 nanometers, so does that mean a red photon is 650 nanometers across? No, because Heisenberg's Uncertainty Principle must be taken into account. Wavelength tells us the spacing of the crests of the underlying electromagnetic wave, not how long a single photon is in space. The actual spatial extent of a photon depends on its coherence length, that is to say the distance over which its wave-like oscillations remain well defined. And coherence length = c × coherence time = c/(2πΔf).
So coherence length is tied to Heisenberg’s Uncertainty Principle: ΔE × Δt ≳ ℏ/2. A photon that is emitted over a short time interval (Δt is small) has a large uncertainty in energy (ΔE is large), which translates into a broad frequency spread and therefore a short coherence length. But if the emission lasts a long time then the frequency uncertainty is small and the photon can stretch out over a very long distance. The way the photon is produced can make a big difference.
A red photon from even a cheap laser diode has an extremely narrow frequency spread giving it a very long coherence length, several meters, and for high-quality lasers it can be several miles. By contrast, a red photon emitted from blackbody radiation, like the glow from an incandescent bulb, has a broad frequency spread, and therefore a very short coherence length, about the width of a human hair. In both cases the photons are indivisible quanta, but their wave packets have very different spatial extents.
So the “size” of a photon cannot be pinned down to a single number. In interactions, it behaves as if it has no size at all, striking at a point. But in terms of its wave-like character, it can extend over hundreds of nanometers in wavelength and, depending on how it is produced, anywhere from a fraction of a micrometer to many miles in coherence length. A photon is therefore not like a little ball of light with a fixed diameter, it's more useful to be thought of as a quantum excitation of the electromagnetic field that travels like a wave but interacts with matter like a particle, and whose spatial extent depends on both the uncertainty principle and the circumstances of its creation.
John K Clark See what's on my new list at Extropolis
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Brent Allsop
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