The 1/r^2 law, also known as the inverse square law, is a fundamental law that describes the decrease in the intensity of a radiation field with distance. In the context of quantum electrodynamics (QED), which is the quantum field theory of electromagnetic interactions, the 1/r^2 law arises due to the behavior of photons and their interaction with charged particles.
In QED, electromagnetic interactions are mediated by the exchange of virtual photons between charged particles. When two charged particles interact, they exchange virtual photons that carry momentum and energy. These virtual photons create an electromagnetic field around the charged particles.
The intensity of the electromagnetic field decreases with distance according to the inverse square law because the virtual photons can be thought of as spreading out over an expanding sphere as they propagate away from their source. The surface area of a sphere increases as the square of its radius (4πr^2), so the number of virtual photons passing through a given surface area decreases as 1/r^2.
As a result, the intensity of the electromagnetic field, which is proportional to the number of photons, follows the same inverse square relationship. This behavior is consistent with classical electromagnetism and can be derived from the quantum mechanical calculations within QED.
It's worth noting that the 1/r^2 law is a macroscopic approximation that holds at large distances compared to the sizes of the interacting particles. At smaller distances, other effects, such as quantum corrections and higher-order interactions, become important and modify the behavior predicted by the inverse square law.