The process of an electron emitting photons is not a case of something coming from nothing. It is governed by the fundamental principles of quantum electrodynamics (QED), which describes the interaction between electrons (and other charged particles) and photons (particles of light).
In quantum mechanics, particles such as electrons do not have definite positions or momenta. Instead, they exist in a state described by a wavefunction that represents the probability distribution of finding the particle in different states. When an electron is in an excited state, it can transition to a lower energy state by emitting a photon.
According to QED, particles and their interactions are described by fields. The electron is associated with an electron field, and the photon is associated with an electromagnetic field. When the electron transitions to a lower energy state, its field changes, and this change propagates through space as a disturbance in the electromagnetic field. This disturbance is what we perceive as a photon being emitted.
The emission of a photon by an electron is a quantum process, meaning it involves probabilities and uncertainties. The exact timing and direction of the emitted photon cannot be predicted with certainty. However, on average, the emission of photons follows certain statistical patterns described by the laws of quantum mechanics.
It's important to note that the concept of "nothing" is not well-defined in physics. Even in seemingly empty space, there are quantum fields and fluctuations happening at the microscopic level. The emission of a photon by an electron is a manifestation of the underlying quantum nature of particles and fields.