Indistinguishability through exchangeability in quantum mechanics?

Keano De Vos, Gert de Cooman, Jasper De Bock
Proceedings of the Thirteenth International Symposium on Imprecise Probability: Theories and Applications, PMLR 215:177-188, 2023.

Abstract

Arguments in quantum mechanics often involve systems of indistinguishable particles, such as electrons or photons. On the standard approach, the symmetrisation postulate is needed to model indistinguishable particles, and results in a theory of fermions and bosons. We investigate how indistinguishability can be implemented by incorporating structural assessments of symmetry in the sets of desirable measurements approach to uncertainty modelling in quantum mechanics, which is based on the theory of imprecise probabilities, and in particular on sets of desirable gambles. We show that an exchangeability assessment allows us to partially retrieve the concepts of fermions and bosons, but that in order to recover the complete fermion and boson framework, we need to rely on stronger symmetry assessments. We also lay bare the relationship between these stronger assessments and the count vector representation for sets of desirable measurements, which we argue corresponds to the commonly used second quantisation in quantum mechanics.

Cite this Paper

BibTeX
@InProceedings{pmlr-v215-de-vos23a, title = {Indistinguishability through exchangeability in quantum mechanics?}, author = {De Vos, Keano and de Cooman, Gert and De Bock, Jasper}, booktitle = {Proceedings of the Thirteenth International Symposium on Imprecise Probability: Theories and Applications}, pages = {177--188}, year = {2023}, editor = {Miranda, Enrique and Montes, Ignacio and Quaeghebeur, Erik and Vantaggi, Barbara}, volume = {215}, series = {Proceedings of Machine Learning Research}, month = {11--14 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v215/de-vos23a/de-vos23a.pdf}, url = {https://proceedings.mlr.press/v215/de-vos23a.html}, abstract = {Arguments in quantum mechanics often involve systems of indistinguishable particles, such as electrons or photons. On the standard approach, the symmetrisation postulate is needed to model indistinguishable particles, and results in a theory of fermions and bosons. We investigate how indistinguishability can be implemented by incorporating structural assessments of symmetry in the sets of desirable measurements approach to uncertainty modelling in quantum mechanics, which is based on the theory of imprecise probabilities, and in particular on sets of desirable gambles. We show that an exchangeability assessment allows us to partially retrieve the concepts of fermions and bosons, but that in order to recover the complete fermion and boson framework, we need to rely on stronger symmetry assessments. We also lay bare the relationship between these stronger assessments and the count vector representation for sets of desirable measurements, which we argue corresponds to the commonly used second quantisation in quantum mechanics.} }
Endnote
%0 Conference Paper %T Indistinguishability through exchangeability in quantum mechanics? %A Keano De Vos %A Gert de Cooman %A Jasper De Bock %B Proceedings of the Thirteenth International Symposium on Imprecise Probability: Theories and Applications %C Proceedings of Machine Learning Research %D 2023 %E Enrique Miranda %E Ignacio Montes %E Erik Quaeghebeur %E Barbara Vantaggi %F pmlr-v215-de-vos23a %I PMLR %P 177--188 %U https://proceedings.mlr.press/v215/de-vos23a.html %V 215 %X Arguments in quantum mechanics often involve systems of indistinguishable particles, such as electrons or photons. On the standard approach, the symmetrisation postulate is needed to model indistinguishable particles, and results in a theory of fermions and bosons. We investigate how indistinguishability can be implemented by incorporating structural assessments of symmetry in the sets of desirable measurements approach to uncertainty modelling in quantum mechanics, which is based on the theory of imprecise probabilities, and in particular on sets of desirable gambles. We show that an exchangeability assessment allows us to partially retrieve the concepts of fermions and bosons, but that in order to recover the complete fermion and boson framework, we need to rely on stronger symmetry assessments. We also lay bare the relationship between these stronger assessments and the count vector representation for sets of desirable measurements, which we argue corresponds to the commonly used second quantisation in quantum mechanics.
APA
De Vos, K., de Cooman, G. & De Bock, J.. (2023). Indistinguishability through exchangeability in quantum mechanics?. Proceedings of the Thirteenth International Symposium on Imprecise Probability: Theories and Applications, in Proceedings of Machine Learning Research 215:177-188 Available from https://proceedings.mlr.press/v215/de-vos23a.html.

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