No, a wave does not always behave as a particle when it is measured. The behavior of a wave or particle depends on the nature of the system being observed and the specific experimental setup.
In quantum mechanics, the behavior of particles is described by wave functions, which can exhibit both wave-like and particle-like properties. The wave-particle duality suggests that particles can display characteristics of both waves and particles, depending on how they are observed or measured.
When a wave-like entity, such as an electron or photon, is measured, its wave function collapses, and the particle's properties, such as position or momentum, become definite. This collapse is often referred to as the wave function collapse or the measurement problem in quantum mechanics.
The specific outcome of a measurement depends on the experimental setup and the interaction between the measuring apparatus and the system being observed. In some cases, the wave-like behavior dominates, and in others, the particle-like behavior is more prominent.
For example, in the double-slit experiment, if the system is not observed or measured during its journey through the slits and onto the screen, the electrons or photons display wave-like interference patterns. However, if individual measurements are made to determine which slit the particle passes through, the interference pattern disappears, and the particle behaves more like a classical particle.
It's important to note that the behavior of quantum particles is probabilistic, and the outcome of a measurement can only be predicted in terms of probabilities. The exact reasons behind why and how a wave collapses into a particle-like state upon measurement are still areas of ongoing research and debate in quantum mechanics.