The phenomenon you are referring to is known as electron self-interference, which is a fundamental concept in quantum mechanics. It is important to note that electron self-interference is not due to the electron interacting with its own emitted photon. Instead, it arises from the wave-like nature of electrons.
In quantum mechanics, particles like electrons are described by wavefunctions, which are mathematical entities that represent the probability distribution of finding the particle in different states or locations. The wavefunction of an electron can be thought of as a probability wave that spreads out in space.
When an electron is sent through a double-slit experiment, for example, it passes through two slits and interferes with itself. The interference pattern that emerges on the screen behind the slits is the result of the overlap and interference of the electron's wavefunction from the two different paths.
The key point here is that the wave-like behavior of electrons is not dependent on the electron physically interacting with itself or with any other particle. Instead, it is a consequence of the mathematical description of the electron's wavefunction and the principles of quantum mechanics.
The speed at which the information about the electron's position propagates is limited by the speed of light (c). However, this does not restrict the interference of the electron's wavefunction. The wavefunction itself is not a physical object in space but rather a mathematical description of the electron's probabilistic behavior. It can propagate and interfere with itself without violating the speed limit imposed by the speed of light.
In summary, electron self-interference arises from the wave-like nature of electrons described by their wavefunctions, and it does not require physical interactions between the electron and itself or any other particles. The behavior of the wavefunction is governed by the principles of quantum mechanics, which allow for non-local interactions and interference patterns to occur.