Why does particle measurement cause quantum wavefunctions to collapse

It postulates III that says,

If the particle is in a state $|psirangle$, measurement of the variable (corresponding to ) $Omega$ will yield one of the eigenvalues $omega$ with probability $P(omega)propto |langleomega|psirangle|^2$. The state of the system will change from $|psirangle$ to $|omegarangle$ as a result of the measurement.

The postulates doesn't have proofs.

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Another aspect of this postulate says the measurement of the variable $Omega$ changes the state vector, which is, in general, some superposition of the form $$|psirangle=sum_{omega}|omegarangle langleomega|psirangle$$ into the eigenstate $|omegarangle$ corresponding to the eigenvalue $omega$ obtained in the measurement. Which is called the collapse or reduction of the state vector.

A simple way to look at it is to remember that the wavefunction describing a particle or a system of particles is a mathematical function, a solution of a specific quantum mechanical wave equation, with specific boundary conditions . When a measurement is made, an interaction with the system happens that changes the boundary conditions. This means that a new mathematical function will describe the particle or the system of particles after the measurement, and this is what is called "collapse", a misleading term. A wavefunction is not a balloon.

Not only is wave function “collapse” a misleading term, it is also not an intrinsic part of quantum mechanics. There are interpretations of quantum mechanics, such as the many-worlds interpretation, in which a wave function never collapses - it only appears to, due to our limited knowledge. If you loose one sock from a pair you do not describe this as “sock collapse” - the other sock is still out there somewhere, you just don’t know where.