In the double-slit experiment, when particles such as electrons are sent through two slits and observed on a detector screen, the interference pattern that emerges suggests that the particles exhibit wave-like behavior. However, if one tries to determine which slit an electron passes through by measuring its momentum or velocity, the interference pattern disappears. This is known as the "which-path" information problem, and it arises due to the nature of quantum mechanics.
In quantum mechanics, particles can exhibit both wave-like and particle-like behavior, depending on how they are observed or measured. When a particle is not observed and its behavior is described in terms of probabilities, it can be thought of as existing in a superposition of all possible states or paths simultaneously. In the case of the double-slit experiment, the electron can take multiple paths and interfere with itself, resulting in an interference pattern on the detector screen.
However, when we try to determine which path the electron takes, we need to make an observation or measurement. In order to determine the momentum or velocity of the electron, we need to interact with it, for example, by bouncing photons off it or using some other method of measurement. This interaction disturbs the delicate quantum state of the electron and collapses it into a specific path, destroying the interference pattern. The act of measurement effectively localizes the particle-like behavior, removing the wave-like properties responsible for interference.
In summary, attempting to measure the momentum or velocity of the electron to determine which path it takes in the double-slit experiment disrupts the delicate quantum state and destroys the interference pattern. The act of measurement introduces uncertainty and collapses the wavefunction, preventing us from simultaneously obtaining information about the particle's path and observing the interference pattern.