No, it is not possible for a photon and an electron to occupy the same space without interacting with each other. According to the principles of quantum mechanics, particles such as photons and electrons are described by their wave functions, which determine the probability distributions of their positions.
The Pauli exclusion principle, a fundamental principle in quantum mechanics, states that no two identical fermions (such as electrons) can occupy the exact same quantum state simultaneously. This principle prevents the electron and the photon from occupying the same quantum state or the same physical space without interacting.
If a photon were to interact with an electron, such as through the process of absorption or scattering, their wave functions would become entangled, and their behavior would be described by a combined wave function. This interaction would typically result in changes to the energies and momenta of both the electron and the photon.
It's worth noting that even if the photon and electron were to occupy overlapping regions of space, they would still influence each other through the electromagnetic interaction. This interaction is responsible for processes such as absorption, emission, and scattering of photons by electrons.
Therefore, due to the principles of quantum mechanics and the Pauli exclusion principle, it is not possible for a photon and an electron to occupy the same space without interacting in some way.