Spherical EM wave or one or more photons?

[gambit64]

My understanding is that the EM field at r.t generated by a radiating source can be described as the amplitude of the EM fields at r, at time t. Is there a corresponding photon associated with that wave? A unit surface area at large r from the source will have less energy passing through it per unit time, i.e. power. Is there a photon flux equivalent to this power, computed using the E=h x frequency of the radiating source?

 

[marcusl]

Hi gambit64, welcome to PF! You are on track, at least up to the last sentence. The photon flux is proportional to the field intensity as you surmise, so a more intense propagating EM field (higher power flux) is described in quantum mechanics by a higher photon flux. The photon energy E that you mention is given by the EM wave frequency, but is independent of the intensity or flux.

 

[gambit64]

Thank you marcusl. I guess I am groping for a picture of how conversion might take place from the energy in a (continuous) spherical wave to a localized photon somewhere in a unit volume per unit time. I suspect I am looking for too easy a bridge between classical EM theory and quantization trying to avoid such details as wave packets and integrating over all space and such.

 

[jtbell]

If there are few enough photons that they can be detected individually as they strike a hypothetical spherical-shell detector surrounding the source, I don't think it's meaningful to talk about the classical electromagnetic radiation fields. The classical field corresponds to the limit of a very large number of photons, so that you can ignore statistical fluctuations.

 

[gambit64]

Thank you jtbell. Does this mean that a detector far from the radiating source, since it "sees" a classical EM field sees a large number of photons and if it doesn't it is because the source is so far away that the field and the number of photons is below the detection threshold of the detector?

 

[Dale]

My understanding is that if you have an emitter which emits spherical waves then Maxwell's equations tell you the wave function. Since the wave function is spherical it is equally likely to detect a photon in any direction. If the source is relatively intense then you will get a large number of photons detected, corresponding to the classical fields. But if the source is a very low intensity, then you will get individual photons detected with a probability defined by the spherical wave function.

 

[gambit64]

Thank you DaleSpam (a too modest a pen name it seems to me but I get the idea I think). Your explanation supports my qualitative picture of the situation. So at large distances (or even space-time? if this is a valid generalization) from the source, at some point the signal will weaken sufficiently to show statistical (quantum mechanical) behavior. If this is correct, then there will be regions of space (and space-time?) where there is an absence of EM energy or photons coming from the radiating source. Presumable there will be a continuum of microwave background radiation. Can that background be reduced to an equivalent photon density or flux?

 

[Dale]

Can that background be reduced to an equivalent photon density or flux?

Certainly, but the cosmic microwave background radiation is such a low frequency that there are a lot of very low energy photons and they are hard to detect individually.

 

[gambit64]

Thank you DaleSpam. From the replies to my first post it seems that a given EM wave has many photons. So can we think of these photons as having a frequency distribution like a black body spectrum or are they all of the same frequency as the source (radio antenna) an in number such to have conservation of energy over a period of time? Thank you again?

 

[Dale]

Thank you DaleSpam. From the replies to my first post it seems that a given EM wave has many photons.

It depends on the intensity of the source, but generally if the intensity of an EM wave is so low that you detect individual photons then you stop talking about an "EM wave" and start talking about a "wavefunction". They follow the same laws, however, so the transition is somewhat arbitrary.

So can we think of these photons as having a frequency distribution like a black body spectrum or are they all of the same frequency as the source (radio antenna) an in number such to have conservation of energy over a period of time?

That depends on the type of source. A blackbody will have a black body spectrum, by definition. A coherent source like a laser will have a very narrow spectrum. A fluorescent source will also have a narrow spectrum. And so forth.

 

[gambit64]

Thanks DaleSpam and jtBell. Sorry to belabor the point beyond your explanations. It seems to me that if a radiating source like a radio antenna at say a fixed frequency is emitting spherical EM waves this energy flux over a spherical surface should correspond to a large but finite number of photons. So can one calculate that number by integrating over a spherical surface and is the photon energy given by the radiating frequency or do we get a frequency(energy) distribution in the photons such that when integrated (similar to black-body radiation) over the spherical shell, energy is conserved with respect to the radiating source. your indulgence and answers over this long text will be much appreciated. As you can see I am looking for a relatively simple conversion or unification of the classical and quantum mechanical perspective.Thank you.

 

[sophiecentaur]

Thank you DaleSpam. From the replies to my first post it seems that a given EM wave has many photons. So can we think of these photons as having a frequency distribution like a black body spectrum or are they all of the same frequency as the source (radio antenna) an in number such to have conservation of energy over a period of time? Thank you again?

From a CW radio transmission, the photons would all have more or less the same energy. Definitely not black body radiation.

 

[Dale]

There is always a distribution of frequencies, but sometimes it can be quite narrow even to the point where you can consider it to be a single frequency for all practical purposes. Energy is always conserved.

 

[vanhees71]

A radio wave is far from being a photon! In fact, it's pretty hard to produce a single photon. A radio wave is a coherent state, for which the photon number is not sharply defined. It's a pretty clever coherent superposition of a lot of many-photon states of different photon number.