Formalism of Generalized Contexts and Quantum Measurement
DOI:
https://doi.org/10.48160/18532330me9.234Keywords:
quantum foundations, quantum histories, quantum measurementAbstract
In this paper, the measurement process of a quantum system is described as an interaction of two physical systems: the system to be measured and the measuring instrument. Both systems form a composite system and its temporal evolution is determined solely by the Schrödinger equation, i.e., there is no collapse postulate. The description of the measurement process is performed using a formalism of quantum histories called formalism of Generalized Contexts. This formalism allows to express, using the conditional probability, the correlation between the properties corresponding to the measured observable, before the measurement, and the properties corresponding to the pointer variable of the measurement instrument, after the measurement. Using this formalism, two central problems of quantum measurement are discussed: the problem of definite outcome and the problem of preferred basis.
References
Ballentine, L. (1998), Quantum Mechanics. A Modern Development, Singapur: World Scientific.
Cohen, D. (1989), An Introduction to Hilbert Space and Quantum Logic, Nueva York: Springer-Verlag.
Gell-Mann, M. y J. B. Hartle (1990), “Quantum Mechanics in the Light of Quantum Cosmology”, en Zurek, W. (ed.), Complexity, Entropy and the Physics of Information, Reading: Addison-Wesley, vol. VIII.
Griffiths, R. (1984), “Consistent Histories and the Interpretation of Quantum Mechanics”, Journal of Statistical Physics36: 219-272.
Griffiths, R. (2002), Consistent Quantum Theory, Cambridge: Cambridge University Press.
Griffiths, R. (2013), “A Consistent Quantum Ontology”, Studies in History and Philosophy of Modern Physics44: 93-114.
Laura, R. y L. Vanni (2008), “Conditional Probabilities and Collapse in Quantum Measurements”, International Journal of Theoretical Physics47: 2382-2392.
Laura, R. y L. Vanni (2008), “Contexto de historias en la teoría de cuántica”, Epistemología e Historia de la Ciencia14: 519-528.
Laura, R. y L. Vanni (2009), “Time Translation of Quantum Properties”, Foundations of Physics39: 160-173.
Lombardi, O. y M. Castagnino (2008), “A Modal-Hamiltonian Interpretation of Quantum Mechanics”, Studies in History and Philosophy of Modern Physics39: 380-443.
Losada, M., Vanni, L. y R. Laura (2013), “Probabilities for Time Dependent Properties in Classical and Quantum Mechanics”, Physical Review A87: # 052128.
Mittelstaedt, P. (1998), The Interpretation of Quantum Mechanics and the Measurement Process, Cambridge: Cambridge University Press.
Omnès, R. (1988), “Logical Reformulation of Quantum Mechanics. I. Foundations”, Journal of Statistical Physics53: 893-932.
Omnés, R. (1994), The Interpretation of Quantum Mechanics, Princeton: Princeton University Press.
Omnès, R. (1999), Understanding Quantum Mechanics, Princeton: Princeton University Press.
Vanni, L. y R. Laura (2013), “The Logic of Quantum Measurements”, International Journal of Theoretical Physics52: 2386-2394.
Zurek, W. H. (1981), “Pointer Basis of Quantum Apparatus: Into What Mixture does the Wave Packet Collapse?”, Physical Review D24: 1516-1525.
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