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Wavefunction collapse amounts to the apparent reduction of a wavefunction consisting of a superposition of several eigenstates to a single eigenstate (by "observation"). It underlies measurement in quantum mechanics and connects the wave function with classical observables, in a thermodynamically irreversible interaction with a classical environment, normally disfavoring future QM interference.

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Have objective collapse theories been ruled out by recent experiments?

Have objective collapse theories been ruled out by recent experiments, such as the entanglement of macroscopic objects? (vibrating drumheads)
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