Hegerfeldt's theorem

Hegerfeldt's theorem is a no-go theorem that demonstrates the incompatibility of the existence of localized discrete particles with the combination of the principles of quantum mechanics and special relativity. It has been used to support the conclusion that reality must be described solely in terms of field-based formulations.[1][2]

Specifically, Hegerfeldt's theorem implies that an initially localized free particle whose time evolution is determined by a positive Hamiltonian must instaneously expand its wavefunction to infinity, thus violating Einstein causality by exceeding the speed of light.[3][4]

The theorem was developed by Gerhard C. Hegerfeldt and first published in 1998.[5][6]

References
  1. Halvorson, Hans; Clifton, Rob (November 2002). "No place for particles in relativistic quantum theories?". Ontological Aspects of Quantum Field Theory. pp. 181–213. arXiv:quant-ph/0103041. doi:10.1142/9789812776440_0010. ISBN 978-981-238-182-8. S2CID 8845639.
  2. 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.
  3. Barat, N.; Kimball, J. C. (February 2003). "Localization and Causality for a free particle". Physics Letters A. 308 (2–3): 110–115. arXiv:quant-ph/0111060. Bibcode:2003PhLA..308..110B. doi:10.1016/S0375-9601(02)01806-6. S2CID 119332240.
  4. Hobson, Art (2013-03-01). "There are no particles, there are only fields". American Journal of Physics. 81 (3): 211–223. arXiv:1204.4616. Bibcode:2013AmJPh..81..211H. doi:10.1119/1.4789885. S2CID 18254182.
  5. Hegerfeldt, Gerhard C. (1998). "Causality, particle localization and positivity of the energy". Irreversibility and Causality Semigroups and Rigged Hilbert Spaces. Lecture Notes in Physics. Vol. 504–504. pp. 238–245. arXiv:quant-ph/9806036. doi:10.1007/BFb0106784. ISBN 978-3-540-64305-0. S2CID 119463020.
  6. Hegerfeldt, G.C. (December 1998). "Instantaneous spreading and Einstein causality in quantum theory". Annalen der Physik. 510 (7–8): 716–725. arXiv:quant-ph/9809030. doi:10.1002/andp.199851007-817. S2CID 248267636.

See also


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