Review of: "Fundamental Issues and Measurement Problem in Quantum Mechanics"

I read this article with great interest.I think that the author correctly partitions the fundamental objects in the currently existing model for quantum mechanics into those that carry de nite meaning like the set of eigenvalues of an observable and those that carry meaning only after the measurement has been performed, like the wave function, state/density matrix, and probability distribution of an observable in a given state.However, these two apparently distinct types of quantities are very closely related.Indeed, an observable is modeled as a Hermitian matrix/operator in a Hilbert space, and its eigenfunctions/eigenvectors do carry de nite meaning.An observable is not speci ed by just its set of eigenvalues; to specify it completely, one also requires the corresponding set of eigenvectors.Given a state/wave function, one can compute the probability distribution of the set of measurement outcomes on measuring an observable in this state completely in terms of the inner product between the given state/wave function and the set of eigenvectors of the observable.Moreover, two different observables may have the same set of eigenvalues but a different set of eigenvectors, which may force them even not to commute with each other.Thus, in this case, the two probability distributions of these two observables in a given state, although concentrated on the same set, will be distinct, and even worse, both of these two observables cannot be simultaneously measured.This is a form of the Heisenberg uncertainty principle.A mixed state is speci ed by two kinds of quantities: one, the set of eigenvalues of this mixed state density matrix, and two, the set of corresponding normalized eigenvectors.The former can be regarded as de ning a classical probability distribution over the set of eigenvectors, and the eigenvectors de ne pure states, and one can compute the probability distribution of an observable in each of these pure states and then, by the law of total probabilities, one can compute the probability distribution of the observable in the mixed state.Thus, if we admit mixed states into the Qeios qeios.com