The concept of wavefunction collapse in quantum mechanics is closely associated with the act of measurement or observation. When a measurement is made on a quantum system, such as the position or momentum of a particle, the wavefunction representing the system's state can "collapse" into one of the possible eigenstates corresponding to the measured value.
Now, when we consider two different observers, each making measurements on the same quantum system, there are a couple of possibilities:
If the two observers measure compatible observables, meaning the measurements commute with each other, they will obtain consistent results. In this case, the collapse of the wavefunction will lead to the same outcome for both observers, and they will agree on the state of the particle.
If the two observers measure non-compatible observables, such as position and momentum, the measurements do not commute. In this scenario, the wavefunctions describing these observables cannot have well-defined values simultaneously. Consequently, the outcome of one observer's measurement may affect the wavefunction's collapse and, therefore, the possibilities available to the second observer. As a result, the two observers may observe different outcomes and, consequently, perceive the particle's state differently.
It's important to note that the concept of wavefunction collapse and its implications for different observers are still subjects of ongoing debates and interpretations in quantum mechanics. Different interpretations, such as the Copenhagen interpretation or the many-worlds interpretation, provide different perspectives on how to understand the nature of wavefunction collapse and its consequences for observers.
In summary, if two observers measure compatible observables, they will agree on the state of the particle after wavefunction collapse. However, if they measure non-compatible observables, they may observe different outcomes and perceive the particle's state differently.