In the context of quantum mechanics, coherent waves, such as those associated with particles, exhibit wave-particle duality. This means that particles can exhibit both wave-like and particle-like behavior. When considering the motion of particles, such as electrons or photons, they can be described by a wave function, which represents the probability distribution of finding the particle at different positions.
According to the principles of quantum mechanics, particles can take all possible paths simultaneously, including virtual paths. This is known as the principle of superposition. However, when we measure the particle's position, we only observe it at a specific location, not spread out over all possible positions. The act of measurement "collapses" the wave function to a single outcome, corresponding to the particle being detected at a particular position.
The probability associated with each possible outcome is determined by the squared magnitude of the particle's wave function at that position. In general, the most likely paths will have higher probabilities. However, it's important to note that probabilities are not the same as classical determinism. Quantum mechanics introduces inherent randomness into the behavior of particles, even when the probabilities are strongly peaked in certain regions.
The randomness in the chosen landing position of a particle arises from the inherent probabilistic nature of quantum mechanics. It is fundamentally impossible to predict with certainty where an individual particle will be detected. Instead, we can only calculate the probabilities associated with different outcomes. The specific outcome is determined when the measurement occurs, and it can be seen as a random event, governed by the probabilities dictated by the wave function. This randomness is an intrinsic feature of quantum mechanics and is not due to any external causes.
It's worth noting that the above discussion is a simplified explanation of quantum mechanics, and the underlying concepts can be quite complex. Quantum mechanics is a highly successful theory that accurately describes the behavior of particles at the microscopic scale, but it does introduce conceptual challenges and philosophical questions about the nature of reality and our ability to predict outcomes precisely.