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  1. The classical picture of EM radiation is the picture of a wave with electric and magnetic field oscillating perpendicularly to each other and to the direction of propagation. Let us neglect the magnetic field part. The energy carried per unit time by such a wave is proportional to the intensity of the wave which is defined as E^2. Here E is the electric field. Away from the source, E of the EM wave falls off by (1/r) where r is the distance from the source. So the energy carried by the EM radiation falls off by (1/r^2).

  2. The quantum picture of EM radiation is the picture of a Photon. The energy of a photon is defined as (h*f) where h is Plank's constant and f is the frequency of the radiation. So the energy of Photon is fixed.

Correspondence If in in classical description, one says that an EM wave has high amplitude or high intensity or high energy then the quantum mechanical way of interpreting is to say that the EM wave has high number of photons. So amplitude/intensity/energy of EM wave corresponds to number of photons.

Question: It is possible that at a point far away from the source, the electric field which falls of as (1/r) will attain a value such that k*(E^2)=h*f. where k is the proportionality constant between energy and intensity of the EM radiation. i.e. the energy of EM radiation will correspond to single photon. What will happen beyond this particular distance r? Beyond this distance E will fall off as (1/r) and energy will fall off as (1/r^2) in the classical picture. But the energy of the photon which only depends on frequency should remain constant (there can be no division or waning of the photon). How then is it possible to have the classical and quantum pictures consistent to each other beyond the distance r ?.

user103515
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    First at all one has to different between electromagnetic radiation, radio wave and photon, see http://physics.stackexchange.com/questions/90646/what-is-the-relation-between-electromagnetic-wave-and-photon/253957#253957 – HolgerFiedler Aug 18 '16 at 13:37
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    this blog post explains how classical fields emerge from the quantum electrodynamics fields which describe photons: http://motls.blogspot.com/2011/11/how-classical-fields-particles-emerge.html – anna v Aug 18 '16 at 14:22
  • Observations of star light provides a clue. Dim stars twinkle partly because the fluctuations in photon numbers become noticeable to our eyes. – Lewis Miller Aug 18 '16 at 14:26
  • The energy will still be absorbed in quanta, but the average absorbed energy per unit time will correspond to the classical power. – Andrea Aug 18 '16 at 17:35

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