Artículo
Abstract:
The concept of individuality in quantum mechanics shows radical differences from the concept of individuality in classical physics, as E. Schrödinger pointed out in the early steps of the theory. Regarding this fact, some authors suggested that quantum mechanics does not possess its own language, and therefore, quantum indistinguishability is not incorporated in the theory from the beginning. Nevertheless, it is possible to represent the idea of quantum indistinguishability with a first-order language using quasiset theory (Q). In this work, we show that Q cannot capture one of the most important features of quantum non-individuality, which is the fact that there are quantum systems for which particle number is not well defined. An axiomatic variant of Q, in which quasicardinal is not a primitive concept (for a kind of quasisets called finite quasisets), is also given. This result encourages the searching of theories in which the quasicardinal, being a secondary concept, stands undefined for some quasisets, besides showing explicitly that in a set theory about collections of truly indistinguishable entities, the quasicardinal needs not necessarily be a primitive concept. © Springer Science+Business Media, LLC 2007.
Registro:
| Documento: | Artículo |
| Título: | A discussion on particle number and quantum indistinguishability |
| Autor: | Domenech, G.; Holik, F. |
| Filiación: | Instituto de Astronomía y Física del Espacio (IAFE), Casilla de Correo 67, Sucursal 28, 1428 Buenos Aires, Argentina Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Argentina |
| Palabras clave: | Particle number; Quantum indistinguishability; Quasicardinality; Quasisets |
| Año: | 2007 |
| Volumen: | 37 |
| Número: | 6 |
| Página de inicio: | 855 |
| Página de fin: | 878 |
| DOI: | http://dx.doi.org/10.1007/s10701-007-9129-5 |
| Título revista: | Foundations of Physics |
| Título revista abreviado: | Found. Phys. |
| ISSN: | 00159018 |
| Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00159018_v37_n6_p855_Domenech |
Referencias:
- Krause, D., (2003) Bol. Soc. Paranaen. Mat, 20, pp. 73-92
- French, S., Krause, D., (2006) Identity in Physics: A Historical, Philosophical, and Formal Analysis, , Oxford University Press
- Post, H., The Listener, 70, pp. 534-537
- reprinted in Vedanta for East and West 32, 14-22 (1963), cited in Ref. 2; Yu. I. Manin, A course in mathematical logic, Springer-Verlag (1977), p. 84, cited in Ref. 2; Yu. I. Manin, Mathematical Problems I: Foundations, in F. E. Browder, ed. (1976), p. 36, cited in Ref. 2; Santorelli, A., Krause, D., Sant'Anna, A., (2005) Logique Anal, 189-192, pp. 231-260
- Halmos, P., (1963) Naive Set Theory, , D. Van Nostrand Company
- Halvorson, H.P., Clifton, R., (2000) Br. J. Philos. Sci, p. 0008030
- Mittelstaedt, P., (1998) The Interpretation of Quantum Mechanics and the Measurement Process, , Cambridge University Press
- E. Schrödinger, What is an elementary particle?, reprinted in Interpreting Bodies: Classical and Quantum Objects in Modern Physics, E. Castellani, ed. (Princeton Un. Press, 1998), pp. 197-210; M. L. Dalla Chiara and G. Toraldo di Francia, in Physics, Philosophy and the Scientific Community, K. Gavroglu, et. al. eds. (Dordrecht, Kluwer Academic Publishers, 1995), pp. 39-46; Dalla Chiara, M.L., Giuntini, R., Krause, D., (1998) Interpreting Bodies: Classical and Quantum Objects in Modern Physics, , E. Castellani, ed, Princeton University Press, Princeton
- Sant'Anna, A., (2005) Found. Phys. Lett, 18, pp. 0894-9875
- da Costa, N.C.A., Krause, D., (2007) Logic J, , Interest Group Pure Appl. Logics to appear
Citas:
---------- APA ----------
Domenech, G. & Holik, F. (2007) . A discussion on particle number and quantum indistinguishability. Foundations of Physics, 37(6), 855-878.http://dx.doi.org/10.1007/s10701-007-9129-5
---------- CHICAGO ----------
Domenech, G., Holik, F. "A discussion on particle number and quantum indistinguishability" . Foundations of Physics 37, no. 6 (2007) : 855-878.http://dx.doi.org/10.1007/s10701-007-9129-5
---------- MLA ----------
Domenech, G., Holik, F. "A discussion on particle number and quantum indistinguishability" . Foundations of Physics, vol. 37, no. 6, 2007, pp. 855-878.http://dx.doi.org/10.1007/s10701-007-9129-5
---------- VANCOUVER ----------
Domenech, G., Holik, F. A discussion on particle number and quantum indistinguishability. Found. Phys. 2007;37(6):855-878.http://dx.doi.org/10.1007/s10701-007-9129-5
