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The question What are the dimensions, width and length, of a photon?, and similar posts, repeat the assertion that photons do not have a defined length.

Yet femto-photography appears to contradict this assertion by recording, presumably many billions of, photons in 5cm length pulse which continues to retain its shape to mm accuracy along a 30cm long path.

Imaging at a trillion frames per second (Ramesh Raskar, TED Talk, 2012).

Surely this places an upper bound on photon length or its statistical distribution?

Emilio Pisanty
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cumfy
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3 Answers3

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A single photon does not have a defined length (or width or duration). A pulse of many photons, on the other hand, can be a coherent superposition of waves, a “wave packet”, which does have a length. What you see in the video is the scattered remnants of a pulse of billions of coherent photons which all interfere in such a way as to have energy only within a defined area. This wave packet, as well-defined as it is, is not an intrinsic property of a single photon. It could be constructed to be arbitrarily large or small; it’s details rely on the details of the laser which emitted it.

Gilbert
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The notion of a photon as a scientifically established entity is only relevant when it is absorbed or emitted. Nobody can say anything about the existence of a photon when there is no observation.

having said that, nothing prevents one from using some picture in one's mind to make thing understandable. So therefore physicists often talk about photons as if they have an existence of their own even when they are not observed. The problem is that when it comes to questions about the properties of photon under such conditions one cannot give answers that are scientifically established.

So what can one say about the length of a photon? Perhaps, one needs to consider the physically relevant propeties of light that give rise to what is being oberved. In this case it would be the coherence length of the light. Perhaps one can take it that the length of a photon is the same as the coherence length. Then one merely need to compute the coherence length and then you have the answer.

For a femto second laser source the coherence length would be confined to the ;egth of the pulse (unless some special effort is made to make different pulses mutually coherent).

flippiefanus
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Surely this places an upper bound on photon length or its statistical distribution?

Basically, the latter. Photons don't have a "size", because of the issues identified in the answer you've linked to.

What you're seeing in the video is a wavepacket, i.e., a confined light wave moving in space; this consists of a large number of photons in the video shown but it is perfectly possible to have a wavepacket that contains a single photon. The length of this wavepacket is inversely proportional to the bandwidth of the wavepacket, i.e., the length of the interval of wavelengths that combine to make up the wavepacket.

In principle, it is possible to make wavepackets that are as short as you want, so long as you have a light source with enough bandwidth to sustain them. For light sources in the infrared, the titanium-sapphire laser used by Raskar has basically been taken to its bandwidth-limited form, as showcased here and in related questions. Shorter pulses have been achieved (though not with laser light - you need to start with a laser and then generate high-order harmonics from it) with bandwidth going in to the ultraviolet and extreme UV regimes. Raskar's camera is probably unable to resolve those, but it's conceivable that a modified version could keep up.

If you want to look those things up, though, the key metric to consider is to look for the temporal duration of the pulse as it passes a fixed location (so, femtosecond pulses for IR lasers, and attosecond pulses for the ones generated by their harmonics), and this will give you much richer search results. Since light moves at a constant speed, the two quantities are directly equivalent.

But, again, this is all a property of the classical wavepacket which contains the photon - it does not tell you anything at all about the "size" of the photon itself.

Emilio Pisanty
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