The extended Bloch representation of quantum mechanics and the hidden-measurement solution to the measurement problem
- Center Leo Apostel for Interdisciplinary Studies and Department of Mathematics, Brussels Free University, Brussels (Belgium)
A generalized Bloch sphere, in which the states of a quantum entity of arbitrary dimension are geometrically represented, is investigated and further extended, to also incorporate the measurements. This extended representation constitutes a general solution to the measurement problem, inasmuch it allows to derive the Born rule as an average over hidden-variables, describing not the state of the quantum entity, but its interaction with the measuring system. According to this modelization, a quantum measurement is to be understood, in general, as a tripartite process, formed by an initial deterministic decoherence-like process, a subsequent indeterministic collapse-like process, and a final deterministic purification-like process. We also show that quantum probabilities can be generally interpreted as the probabilities of a first-order non-classical theory, describing situations of maximal lack of knowledge regarding the process of actualization of potential interactions, during a measurement. - Highlights: • An extended Bloch representation of quantum measurements is given. • Quantum measurements are explained in terms of hidden-measurement interactions. • Quantum measurements are explained as tripartite processes. • The Born rule results from a universal average, over all possible measurement processes.
- OSTI ID:
- 22403512
- Journal Information:
- Annals of Physics (New York), Vol. 351; Other Information: Copyright (c) 2014 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA); ISSN 0003-4916
- Country of Publication:
- United States
- Language:
- English
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