The minimal interpretation of the double-slit experiment, often referred to as the wave-particle duality, implies that quantum particles such as electrons or photons can exhibit characteristics of both waves and particles. In this interpretation, the particle does not go through both slits simultaneously in a classical sense, nor can its trajectory be precisely determined.
When a quantum particle, such as an electron, is sent through the double-slit apparatus, it exhibits wave-like behavior. The particle's wave function, which describes its probability distribution, evolves and interferes with itself, leading to an interference pattern on a screen placed behind the slits. This pattern suggests that the particle has taken multiple paths and interfered with itself.
However, when one tries to determine which path the particle takes by introducing a measurement or a "which-slit" detector, the interference pattern disappears. This is known as the "collapse of the wave function," where the act of measurement disturbs the particle's wave-like behavior, forcing it into a definite state and eliminating the interference pattern.
The key point is that in the absence of measurement or interaction that determines the particle's path, it exists in a superposition of states, where it can be thought of as "going through both slits" simultaneously in a probabilistic sense. It is important to note that this does not mean the particle is physically present in two places at once, but rather that its behavior is described by a wave function that encompasses the possibility of being in different states.
In summary, the minimal interpretation of the double-slit experiment suggests that quantum particles exhibit wave-particle duality, where they can exhibit wave-like behavior and interfere with themselves. Without measurement or interaction to determine the particle's path, it exists in a superposition of states, which is described by the wave function.