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Hermitian operators (or more correctly in the infinite dimensional case, self-adjoint operators) are not used because measurements must use real numbers, but rather because we almost always decide to use real numbers. As the OP mentions at one point, you might choose to use complex numbers to label a two-dimensional screen, and in that case you'll be able ...


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When in doubt go back to the masters. From Dirac's Principles of QM When we make an Observation we measure some dynamical variable. It is obvious physically that the result of such a measurement must always be a real number, so we should expect that any dynamical. variable that we can measure must be a real dynamical variable. One might think ...


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ANSWER: Mutually-exclusive events cannot exist before measurement, in the probabilistic formulation of quantum mechanics (Copenhagen interpretation-CIQM), because, maximally, CIQM is required to violate local realism and, minimally, it might break the principle of locality. And after measurement, the problem you mentioned does not exist because it is ...



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