It's usually said that "the direct observation of a process makes the wave function of the system to collapse".
How does really that process happen? What exactly means for a wave function to collapse?
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I am assuming the context is entanglement. In common language - The wave function does not collapse. Instead, the correlation of the wave function of the two entangled particles collapse. The wave function is such that the two particles are expected to give correlated outcome when measured. On the first measurement, the measured particle attains a different wave function and so, the correlation collapse.