The concept of the "instantaneous collapse" of a wave function refers to a particular interpretation of quantum mechanics known as the Copenhagen interpretation. According to this interpretation, when a quantum system is measured or observed, its wave function, which describes the probabilities of different outcomes, undergoes an abrupt and discontinuous change called a collapse or a reduction.
In the Copenhagen interpretation, the wave function represents the state of a quantum system, and it evolves according to Schrödinger's equation, a mathematical equation that describes the time evolution of quantum systems. The wave function is a superposition of multiple possible states, each with a certain probability amplitude.
When a measurement is made on a quantum system, the Copenhagen interpretation states that the wave function of the system collapses or reduces to a single state corresponding to the measurement outcome. The collapse is instantaneous, meaning it happens in an indeterministic and non-deterministic manner at the moment of measurement.
For example, consider the famous thought experiment of Schrödinger's cat. In this experiment, a cat is placed in a closed box along with a radioactive substance that has a 50% chance of decaying within a certain time. According to the Copenhagen interpretation, until the box is opened and the cat is observed, the cat's state is described by a superposition of being both alive and dead. However, upon observation, the wave function collapses, and the cat is found to be either alive or dead.
It's important to note that the Copenhagen interpretation is just one of several interpretations of quantum mechanics. Other interpretations, such as the many-worlds interpretation or the pilot-wave theory, propose different explanations for the measurement process and the collapse of the wave function. These alternative interpretations do not involve instantaneous collapses but introduce different concepts to account for the observed phenomena in quantum mechanics.