Are we sure photons are particles, given that a 1 Hz photon is bigger than our planet?

Question

A photon of 1 Hz has a wavelength of 300000 km, making it bigger than our planet. Are we sure photons are particles ???

lambda = c/f = 300000/1 = 300000 km

Answer 1

Photon is a problematic concept to explain (and use). It is sometimes called a particle, but it is not a classical particle, which have definite position and small size. Popularization descriptions often suggest it is such a particle, and even physicists often talk about it that way, but this works only in some situations (X-ray/gamma scattering on small things like atoms). In others, such as reception of radio waves, such picture is really misleading and inappropriate. It's the well-known particle/wave problem; in some experiments, radiation looks more like particles, in others, like waves .

In mathematics of quantum EM field theory, photon is an integer part of EM mode excitation in an EM field Hamiltonian eigenstate. Sometimes (often), the field is in such state that there aren't really any definite number of photons (coherent states, similar to classical EM field). Photon isn't really the primary object that is assumed to exist in theory; instead, the quantum EM field is the thing that exists, the quantum state describes it, and photon is a difference between two special kinds of such states. When the EM wave has wavelength 300000 km, one can't say the corresponding quantum field or difference between two such fields (photon) has size smaller than that. One can't even say there is definite number of photons in such EM wave, because it's more like a coherent state, where any mode is in superposition of different energy eigenstates.

One can have wave packets made of several components with different frequencies that are very small in space, but 1) the smaller the volume, the higher the frequencies of the components have to be 2) such wave packet is not single photon, because it involves different frequencies with different weights. photons So, you have a point, such low frequency photons can't be localized to a smaller size than their wavelength.

I can hear people coming to protest this, saying "but we see localized dots on detectors, or hear localized clicks, which are interpreted as due to localized photons of light". This is a misconception. What is localized are the detector pixels, or grains in photofilm, or times of detector firing, but this does not necessarily mean that quantum EM field just before that was so localized(see the radio example below). One can at best say that exchange of energy and change of matter state due to EM field (chemical reaction, photoelectric emission) got localized to such pixel/film grain; but this can only ever be observed when localized pixels/film grains are present.

The detector pixel/film grain example is not a a good one for my point, because visible light wavelength and grain size are comparable, so one could imagine the light to come in packets smaller than the pixels/grains, and in some cases, this may be true (if the source produces very short pulses of light).

A better example is detection of AM radio station emitting at carrier frequency 600 kHz, which has wavelength 500 m. Any photons one could try to imagine in this emission would be changes of EM field in a space region with size of that and greater length. But a pocket radio can detect the wave and convert energy from it in a space region many times smaller. This is not an evidence for radio photons localizing into a small volume of the radio receiver just before the energy exchange happened. Instead, it shows radiation-matter interaction can happen between large wavelength EM wave and much smaller matter system, without any localized wave packets of light being present.

Localized wave packets are a much better picture in case of X-ray or gamma radiation, with wavelengths on the scale of atom size. With such high frequencies allowed in the Fourier expansion, one can have a wave packet that is comparably small; but again, a wave packet is not a single photon, but a superposition of many different field states with different frequency.