In quantum mechanics, the concept of measurement is central to understanding and characterizing quantum states. The measurement process is influenced by the observer and can yield different outcomes depending on the measurement performed. This phenomenon is captured by the principle of superposition and the concept of quantum state collapse.
According to the principle of superposition, a quantum system can exist in a superposition of multiple states simultaneously. These states are described by a mathematical representation called a wavefunction. However, when a measurement is made on a quantum system, the wavefunction collapses into one of the possible eigenstates associated with the observable being measured.
The outcome of a measurement can vary depending on the observable being measured and the basis in which the measurement is made. Different observables have associated operators that act on the wavefunction, and the eigenvalues of these operators correspond to the possible measurement outcomes. For example, the observable of spin in quantum systems can yield either "spin up" or "spin down" as measurement outcomes.
The act of measurement selects a specific eigenstate from the superposition of states, and the observer obtains the corresponding measurement outcome. This selection process is probabilistic, and the probability of obtaining a particular outcome is determined by the squared magnitude of the probability amplitudes associated with the eigenstates.
It's important to note that different observers measuring the same quantum system can obtain different outcomes because they may choose to measure different observables or perform measurements in different bases. Each observer's choice of measurement affects the collapse of the wavefunction and determines the outcome they observe.
In summary, different observers measure different quantum states because the measurement process is inherently probabilistic, influenced by the choice of observable and basis made by the observer. The principle of superposition and the collapse of the wavefunction play crucial roles in understanding the variability of measurement outcomes in quantum mechanics.