In quantum mechanics, the concept of a particle taking all possible paths simultaneously is described by the principle of superposition. This principle allows us to consider all possible paths that a particle, such as a photon, could take between two points. However, it does not imply that the particle is actually traveling along all these paths simultaneously or that it exceeds the speed of light.
In the context of the path integral formulation of quantum mechanics, the probability of finding a particle at a particular location is calculated by summing over all possible paths and their associated probability amplitudes. This includes paths that are classically forbidden or paths that would violate the speed of light limit. However, when we consider the actual motion of a particle, it follows a specific path corresponding to the most probable or dominant contribution to the sum of these amplitudes, known as the classical path.
For a photon, its behavior is governed by the laws of special relativity, which states that the speed of light in a vacuum is an absolute limit and cannot be exceeded. While the path integral approach in quantum mechanics allows us to consider all possible paths, the photon itself will always travel at the speed of light, c, and cannot go faster.
In summary, the idea of a particle taking all possible paths simultaneously is a mathematical construct in quantum mechanics, but it does not imply that the particle itself travels faster than light. The actual behavior of particles, such as photons, is consistent with the fundamental principles of relativity, which restrict their speed to the speed of light.