In quantum mechanics, a measurement refers to the process of extracting information about a quantum system by interacting with it. When a measurement is performed on a quantum system, it causes the system to transition from a superposition of multiple possible states to a definite state corresponding to the measured value. This process is known as the collapse or reduction of the wavefunction.
The effect of performing a measurement in quantum mechanics is often described by the Born rule, which gives the probability of obtaining a particular measurement outcome. According to the Born rule, the probability of obtaining a specific measurement result is proportional to the square of the absolute value of the corresponding coefficient in the wavefunction.
The act of measurement disturbs the quantum system and introduces uncertainty into the measurement process. This disturbance arises from the interaction between the measuring apparatus and the quantum system being measured. The measurement process typically involves an observable quantity, such as position, momentum, energy, or spin, which corresponds to an operator in quantum mechanics.
After the measurement, the quantum system "collapses" into an eigenstate of the measured observable associated with the observed value. This collapse is non-deterministic, and the specific outcome of the measurement cannot be predicted with certainty. Instead, the theory provides probabilities for the different possible outcomes.
It's important to note that the measurement process in quantum mechanics is still an active area of debate and interpretation. Different interpretations, such as the Copenhagen interpretation, the many-worlds interpretation, and the pilot-wave theory, offer different explanations for the nature of measurement and the collapse of the wavefunction. These interpretations provide different perspectives on how to understand the effects of performing a measurement in quantum mechanics.