Photon size and classical fields

[phyzguy]

<<Moderator note: Split from thread Photon the smallest particle>>

@Orodruin - Let me ask a question. This is an aspect of QFT that has always puzzled me. Suppose we have an RF cavity or a laser cavity with a standing E-M wave. I understand that we can view the field in the cavity as a macroscopic number photons in the same quantum state. In this case, why do we say that the photons making up the field have zero spatial extent? How can a macroscopic number of photons with zero spatial extent add up to a measurable E-M field which fills the cavity? Is there a way of thinking of this that I am missing?

 

[Orodruin]

@Orodruin - Let me ask a question. This is an aspect of QFT that has always puzzled me. Suppose we have an RF cavity or a laser cavity with a standing E-M wave. I understand that we can view the field in the cavity as a macroscopic number photons in the same quantum state. In this case, why do we say that the photons making up the field have zero spatial extent? How can a macroscopic number of photons with zero spatial extent add up to a measurable E-M field which fills the cavity? Is there a way of thinking of this that I am missing?

First, a coherent state is not made out of a macroscopic number of photons. It is made out of an indefinite number of photons, but for a classical field the expectation value is rather high.

That you have a classical field does not mean that you spread your photons out over some region of space. That a particle has zero size does not mean it is localized. If you look at an electron, its wave function is not completely localized. In the coherent state, nothing is saying that there are places where "there are no photons".

 

[phyzguy]

Sorry, but this didn't help much. Let me ask some specific questions:

(1) Are you saying that it is not true that a classical E-M field in a laser cavity is not made up of a macroscopic number of photons in the same quantum state?

(2) If a photon is an excitation of the E-M field, and the E-M field has a definite spatial extent, what does it mean to say that the photon has zero spatial extent?

(3) Along the same lines, you say, "That a particle has zero size does not mean it is localized." What does that statement mean? If it doesn't mean that the particle is localized, what does it mean?

I'm not arguing, I'm just trying to understand what these statements mean.

 

[f95toli]

(1) Are you saying that it is not true that a classical E-M field in a laser cavity is not made up of a macroscopic number of photons in the same quantum state?

All it means it that a coherent state (which is the only state that re-assembles a "classical" field) does not have a fixed number of photons. Only number (Fock) states have a fixed number of photons

(2) If a photon is an excitation of the E-M field, and the E-M field has a definite spatial extent, what does it mean to say that the photon has zero spatial extent?

Photons do not have a "size" in the usual meaning of the word, but they certainly have an extent. It is often meaningful to talk about the shape of a photon, just as we we talk about different modes in classical E-M. You can even encode information by using photons of different shapes (as long as the modes are orthogonal)

(3) Along the same lines, you say, "That a particle has zero size does not mean it is localized." What does that statement mean? If it doesn't mean that the particle is localized, what does it mean?

This is really no different than electrons. They also have zero size (they are point particles) but we can still move them around one at a time or even trap them in well defined locations OR they can be de-localized as is frequently the case in solids. The physical size (or lack thereof) is not really relevant here.

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[Paul Colby]

Photons are simply integral energy increments in the classical field modes however they happen to be chosen. If you write the field in terms of cavity modes each mode will have a frequency $\omega_n$ and the corresponding photons energy, $\hbar \omega_n$ when quantized. The "particle" nature of photons is a useful picture when the classical modes used are taken as plane waves. Plane waves are useful (but not required) for boundary free problems which is the often case in the analysis of scattering problems.