The behavior of electrons (and other particles) in the double-slit experiment is governed by the principles of quantum mechanics, which can be quite different from our everyday experiences with classical physics.
In the double-slit experiment, when a stream of electrons is directed towards a barrier with two small slits, they exhibit wave-like behavior. This means that each electron can be described by a probability wave that spreads out and passes through both slits simultaneously. This is known as the wave-particle duality of quantum mechanics.
The probability wave associated with each electron interferes with itself as it passes through the slits. This interference leads to an interference pattern on a screen placed behind the slits, similar to the patterns observed when waves, such as water waves or light waves, interfere with each other.
The decision of which path the electron "chooses" is not a deterministic one. It is not that the electron decides or knows which path to take. Rather, the electron's behavior is described by the probability wave, which represents the likelihood of finding the electron at different positions on the screen. The interference pattern arises due to the interaction of these probability waves.
When the electron is observed or detected, its wave function collapses to a specific position on the screen. This collapse is probabilistic in nature and is determined by the probabilities described by the wave function. Each electron's position on the screen after passing through the double slits is essentially a random outcome based on the probabilities associated with the wave function.
It is worth noting that the act of observation or measurement disturbs the system and can affect the interference pattern. This is known as the observer effect or the measurement problem in quantum mechanics, and it is an active area of research and debate among physicists.