Wave function collapse describes the conditional change of a quantum state associated with a measurement outcome. For an ideal projective measurement with projector , the outcome probability is and the conditional state is when , according to the Lüders rule.
If the outcome is ignored, the state becomes , which is generally a mixture rather than any one conditional state. These are different information conditions. General measurement instruments can produce other state changes with the same outcome probabilities, so the ideal projection rule is a specified measurement model. Its physical interpretation is part of the quantum measurement problem.
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Wave function collapse is a key concept in quantum mechanics that describes the process by which a quantum system transitions from a superposition of states to a single state when a measurement is made. In quantum mechanics, particles such as electrons exist in a superposition of multiple possible states, each with a certain probability. The wave function is a mathematical function that encodes all the information about the system and describes these probabilities.
The idea the the wave function of a small observed system collapses "obviously" cannot be the full physical truth, only a very useful approximation of reality.
Because then are are hard pressed to determine the boundary between what collapses and what doesn't, and there isn't such a boundary, as everything is interacting, including the observer.
The many-worlds interpretation is an elegant explanation for this. Though it does feel a bit sad and superfluous.