Final answer:
The collapse of a wavefunction is specific to the particle being measured and only that wavefunction is affected during the measurement, not all wavefunctions in space. Quantum mechanics and the Copenhagen interpretation describe this process as a change from a superposition of states to a single definite state, with probability determining the outcome.
Step-by-step explanation:
The student's question touches on an important concept in quantum mechanics related to wavefunction and measurement. The wavefunction, denoted as Ψ(x, t), indeed suggests that particles have a wave-like distribution and exist in a superposition of all possible states until a measurement is made. According to the Copenhagen interpretation of quantum mechanics, when we perform a measurement, we observe the system in a definite state, and the wavefunction collapses to a single outcome with a certain probability, which is given by P(x, x + dx) = |Ψ(x, t)|² dx. This collapse of the wavefunction does not simultaneously affect all possible wavefunctions but only the one associated with the particle being measured due to the probabilistic nature of quantum mechanics.
The wave properties of particles such as electrons mean that they do not have specific locations until they are observed. Individual measurements yield precise results, but when repeated measurements are taken, they show a distribution that is consistent with wave behavior. This illustrates the concept of wave-particle duality. Finally, it's key to note that measurements affect the system being measured, confining our knowledge of a particle's properties, an idea firmly rooted in Heisenberg's uncertainty principle. Though every wavefunction can be thought to exist everywhere, only the probability of finding a particle at a particular location can be known, and this does not imply interference with other wavefunctions not involved in the measurement.