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How the instant collapse of a spatially-extended quantum state is consistent with the relativity of simultaneity

A thought experiment is considered on the observation of the instantaneous collapse of an extended wave packet. According to the relativity of simultaneity, such a collapse being instantaneous in some reference frame must be a lasting process in other frames. But according to quantum mechanics, collapse is instantaneous in any frame. The probabilistic nature of quantum-mechanical phenomena eliminates any contradictions between these two apparently conflicting statements. It is shown that the consistency of quantum collapse with relativity follows directly from the Born postulate without any use of mathematical properties of quantum operators, which allows us to discuss this topic in an introductory course of modern physics. The consistency of quantum mechanics with relativity is also shown for instant disentanglement of an extended composite system.