Physics:Hegerfeldt's theorem
Hegerfeldt's theorem is a no-go theorem that demonstrates the incompatibility of the existence of spatially localized discrete particles with the combination of the principles of quantum mechanics and special relativity. A crucial requirement is that the states of single particle have positive energy. It has been used to support the conclusion that reality must be described solely in terms of field-based formulations.[1][2] However, it is possible to construct localization observables in terms of positive-operator valued measures that are compatible with the restrictions imposed by the Hegerfeldt theorem.[3]
Specifically, Hegerfeldt's theorem refers to a free particle whose time evolution is determined by a positive Hamiltonian. If the particle is initially confined in a bounded spatial region, then the spatial region where the probability to find the particle does not vanish, expands superluminarly, thus violating Einstein causality by exceeding the speed of light.[4][5] Boundedness of the initial localization region can be weakened to a suitably exponential decay of the localization probability at the initial time. The localization threshold is provided by twice the Compton length of the particle. As a matter of fact, the theorem rules out the Newton-Wigner localization.
The theorem was developed by Gerhard C. Hegerfeldt and first published in 1998.[6][7]
See also
- Wave–particle duality
- Local realism
References
- ↑ Halvorson, Hans; Clifton, Rob (November 2002). "No place for particles in relativistic quantum theories?". Ontological Aspects of Quantum Field Theory. pp. 181–213. doi:10.1142/9789812776440_0010. ISBN 978-981-238-182-8.
- ↑ Finster, Felix; Paganini, Claudio F. (2022-09-16). "Incompatibility of Frequency Splitting and Spatial Localization: A Quantitative Analysis of Hegerfeldt's Theorem". Annales Henri Poincaré 24 (2): 413–467. doi:10.1007/s00023-022-01215-8. PMID 36817968.
- ↑ Moretti, Valter (2023-06-07). "On the relativistic spatial localization for massive real scalar Klein–Gordon quantum particles". Letters in Mathematical Physics 66. doi:10.1007/s11005-023-01689-5.
- ↑ Barat, N.; Kimball, J. C. (February 2003). "Localization and Causality for a free particle". Physics Letters A 308 (2–3): 110–115. doi:10.1016/S0375-9601(02)01806-6. Bibcode: 2003PhLA..308..110B.
- ↑ Hobson, Art (2013-03-01). "There are no particles, there are only fields". American Journal of Physics 81 (3): 211–223. doi:10.1119/1.4789885. Bibcode: 2013AmJPh..81..211H.
- ↑ Hegerfeldt, Gerhard C. (1998). "Causality, particle localization and positivity of the energy". Irreversibility and Causality Semigroups and Rigged Hilbert Spaces. Lecture Notes in Physics. 504-504. pp. 238–245. doi:10.1007/BFb0106784. ISBN 978-3-540-64305-0.
- ↑ Hegerfeldt, G.C. (December 1998). "Instantaneous spreading and Einstein causality in quantum theory" (in en). Annalen der Physik 510 (7–8): 716–725. doi:10.1002/andp.199851007-817.
 |  |
