When physicists describe a particle as an "excitation in a field," they are referring to the fundamental concept of quantum field theory. According to this framework, particles are not considered as distinct, solid objects but rather as localized disturbances or fluctuations in their respective fields.
In quantum mechanics, particles are described by wave functions that evolve over time according to Schrödinger's equation, which is a deterministic equation. However, when a measurement is made on a particle, its wave function "collapses" to a particular eigenstate corresponding to the observed value. This collapse is a non-deterministic process, and the outcome of the measurement is probabilistic.
In the context of quantum field theory, the concept of a particle as an excitation in a field applies both before and after the wave-function collapse. Before a measurement, the particle is described as a superposition of different states, each associated with a certain probability amplitude. It exists as a quantum field excitation spread out in space and time.
When a measurement is made, the wave function collapses, and the particle is observed in a specific state. However, even after the collapse, the particle is still understood as an excitation in the field, but now localized to a particular position or momentum. The collapse of the wave function determines which specific state is observed, but it doesn't fundamentally change the particle's nature as an excitation in the field.
In summary, the description of a particle as an excitation in a field is a fundamental concept in quantum field theory and applies both before and after the wave-function collapse. The collapse of the wave function determines the specific state observed, but it doesn't alter the underlying nature of the particle as a field excitation.