Measurements are described with diverse concepts in quantum physics such as; wave functions/probability amplitudes, evolving unitary and deterministic/preserving information, according to the linear Schrödinger equation, superposition of states, i.e., linear combinations of wave functions with complex coefficients that carry phase information and produce interference effects/the principle of superposition, quantum jumps between states accompanied by the "collapse" of the wave function that can destroy or create information, probabilities of collapses and jumps given by the square of the absolute value of the wave function for a given state, values for possible measurements given by the eigenvalues associated with the eigenstates of the combined measuring apparatus and measured system, the Heisenberg indeterminacy principle. The original problem, said to be a consequence of Niels Bohr's "Copenhagen interpretation" of quantum mechanics, was to explain how our measuring instruments, which are usually macroscopic objects and treatable with classical physics, can give us information about the microscopic world of atoms and subatomic particles like electrons and photons. Bohr's idea of "complementarity" insisted that a specific experiment could reveal only partial information, for example, a particle's position. "Exhaustive" information requires complementary experiments, for example to determine a particle's momentum. Some define the problem of measurement simply as the logical contradiction between two laws describing the motion of quantum systems; the unitary, continuous, and deterministic time evolution of the Schrödinger equation versus the non-unitary, discontinuous, and indeterministic collapse of the wave function. Von Neumann saw a problem with two distinct procedures. The mathematical formalism of quantum mechanics provides no way to predict when the wave function stops evolving in a unitary fashion and collapses. However, we can say this occurs when the microscopic system interacts with a measuring apparatus. Others define the measurement problem as the failure to observe macroscopic superpositions. Decoherence theorists, e.g., H. Dieter Zeh and Wojciech Zurek, who use various non-standard interpretations of quantum mechanics that deny the projection postulate - quantum jumps - and even the existence of particles, define the measurement problem as the failure to observe superpositions such as Schrödinger's Cat. Mario Mastriani
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