Abstract
Different attempts to solve the measurement problem of the quantum me-chanics (QM) by denying the collapse principle, and replacing it with changes in the quantum formalism, failed because the changes in the formalism lead to contradictions with QM predictions. To the difference, Ghirardi, Rimini and Weber took the collapse as a real phenomenon, and proposed a calculus by which the wave-function should undergo a sudden localization. Later on, Ghirardi, Pearle and Rimini came with a change of this calculus into the CSL (continuous spontaneous localization) model of collapse. Both these proposals rely on the experimental fact that the reduction of the wave-function occurs when the microscopic system encounters a macroscopic object and involves a big amount of its particles. Both these proposals also change the quantum formalism by introducing in the Schr?dinger equation additional terms with noisy behavior. However, these terms have practically no influence as long as the studied system contains only one or a few components. Only when the amount of components is very big, these terms become significant and lead to the reduction of the wave-function to one of its components. The present work has two purposes: 1) proving that the collapse postulate is unavoidable; 2) ap-plying the CSL model to the process in a detector and showing step by step the modification of the wave-function, until reduction. As a side detail, it is argued here that the noise cannot originate in some classical field, contrary to the thought/hope of some physicists, because no classical field is tailored by the wave-functions of entanglements.
Highlights
In a profound analysis of tests of quantum systems, [1], J. von Neumann concluded that once a quantum system in the initial state ψ is tested and produces the result λk, the system remains in a state φk with the property that any subsequent measurement of the system for the same observable, would produce the same result, λk
Different attempts to solve the measurement problem of the quantum mechanics (QM) by denying the collapse principle, and replacing it with changes in the quantum formalism, failed because the changes in the formalism lead to contradictions with QM predictions
Adler proposed as a solution to the above problem, a proof in [37] by which the continuous spontaneous localization” (CSL) model predicts that the square variance of the measured operator, tends to regain its initial value if the measurement takes a very long time, and if the square of the measured operator commutes with the Hamiltonian or the Hamiltonian is negligible in comparison with the other terms in the stochastic Schrödinger equation (SSE)
Summary
In a profound analysis of tests of quantum systems, [1], J. von Neumann concluded that once a quantum system in the initial state ψ is tested (non-destructively) and produces the result λk , the system remains in a state φk with the property that any subsequent measurement of the system for the same observable, would produce the same result, λk (see for instance page 138 in [1]). Other evolutions of the noise begin, at a certain time, to reduce the number of involved particles, and in the end the detector remains unperturbed and does not click; the wave-packet which did not trigger the detector, is erased. Another purpose of this work is to prove that, in partial disagreement with Lüders, the disappearance of a wave-packet that didn’t trigger a detector placed on its path, is demanded by the QM formalism.
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