Question

Why does the system collapse into only one state? If we can formalize and model the system as a superposition of states when it isn't being measured, why can't we when it is? I understand that, of course, we can only measure one of the possible eigenvalues at a time, but why don't we think of that as the only eigenvalue/state we happened to measure instead of the only eigenvalue/state which exists at the moment of measurement? In other words, why do we interpret the probabilities as the probability of the system being exactly in a given state upon measurement rather than the probability that a given state just so happens to be the one we measure, even though the system is in a superposition of all possible states (at all times, not just when not being measured)?

Answer 1

The Copenhagen interpretation of quantum mechanics posits that a quantum system collapses into a single state upon observation, transitioning from a superposition. This collapse, associated with the wave function, is dictated by probabilities and is essential to technologies like quantum computing. The why behind wave function collapse is still a topic of debate and research in quantum theory.

Step-by-step explanation:

The question regards why a quantum system collapses into a single state upon measurement rather than remaining in a superposition. The core of this inquiry lies in the Copenhagen interpretation of quantum mechanics, which postulates that when a quantum system is not being observed, it exists in a superposition of all possible states. However, upon measurement, this superposition 'collapses', forcing the system to choose a single state with a definitive value, like the position of a particle or the alive/dead status of Schrödinger's cat.

In quantum mechanics, a system is described by a wave function, and the square of this function represents the probability density for finding the system in a particular state. This is expressed in Born's interpretation, which ensures that predictions are made based on probabilities. Yet the actual act of measurement affects the system, leading to what is known as state reduction or wave function collapse, which is not fully understood. Some interpretations of quantum mechanics suggest that other 'branches' of the superposition continue to exist even after we've observed one outcome, but these are not part of the Copenhagen interpretation.

Furthermore, this phenomenon is integral to how quantum computers operate, using qubits that store information in superpositions of states instead of the binary states (0 or 1) used in classical computing. This underlines the distinction between the probabilistic nature of quantum systems and the determinism of classical ones. Despite the counterintuitive nature of wave function collapse, it remains a cornerstone in our current understanding of quantum mechanics and the behavior of particles at the quantum level.