Electrons do not emit photons "from nothing." The emission of photons by electrons occurs through various physical processes, such as electron transitions between energy levels in an atom or electron interactions with other particles. Let's explore a couple of these processes:
Electromagnetic radiation: When an electron undergoes a transition from a higher energy state to a lower energy state within an atom, it can emit a photon. This process is governed by the laws of quantum mechanics. The energy difference between the two states corresponds to the energy of the emitted photon, as given by Planck's equation (E = hf), where E is the energy, h is Planck's constant, and f is the frequency of the photon.
Electron interactions: In certain situations, electrons can interact with other charged particles and exchange virtual photons. These virtual photons are not directly observable, but they play a role in mediating the electromagnetic force between charged particles. The exchange of virtual photons contributes to the overall behavior and interaction of charged particles.
It's important to note that the behavior of particles, such as electrons and photons, is described by quantum field theory, which accounts for the particle-wave duality and the probabilistic nature of quantum phenomena. In this framework, the emission and absorption of photons by electrons are described by mathematical equations and probabilistic amplitudes, which provide a theoretical framework to predict and understand their behavior.
So, electrons do not emit photons from nothing, but rather through specific physical processes governed by quantum mechanics and the laws of electromagnetism.