Particles, Localization and "Collapse"
Abstract
Hegerfeldt's theorem shows that the localization of a particle (or field) is not possible under very general assumptions of quantum mechanics and special relativity. This theorem, and further developments and associated theorems force penetrating questions on the proper understanding of the theory and its use. In particular, the use of the collapse postulate is called into question. The existence of particles and even localized fields are called into question. And, this in turn challenges local measurements. It generally forces one to consider the profound problems and even wrong results that arise from the collapse postulate. We give a qualitatively new example of such a wrong result. Researchers and students alike are bothered by these fundamental issues. Students' ability to learn the material, and even their interest in physics, can be compromised by such disturbing conundra that seem to make physics, or at least QFT and its QM limit, seem incomprehensible and even inconsistent. This article resolves these issues in a way accessible to undergraduates, by applying the natural (minimal) interpretation of quantum mechanics (QM) (the ensemble interpretation) and explicating and clarifying the basic principles and premises used in QM and the Hegerfeldt theorem and its application to measurements.
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BibTeX
@misc{rizzi2026particles,
title = {{Particles, Localization and "Collapse"}},
author = {Anthony Rizzi},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.32101},
eprint = {2609.32101},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.32101},
}
RIS
TY - UNPB
TI - Particles, Localization and "Collapse"
AU - Anthony Rizzi
PY - 2026
DA - 2026/09/26
PB - arXiv
DO - 10.48550/arxiv.2609.32101
UR - https://arxiv.org/abs/2609.32101
AB - Hegerfeldt's theorem shows that the localization of a particle (or field) is not possible under very general assumptions of quantum mechanics and special relativity. This theorem, and further developments and associated theorems force penetrating questions on the proper understanding of the theory and its use. In particular, the use of the collapse postulate is called into question. The existence of particles and even localized fields are called into question. And, this in turn challenges local measurements. It generally forces one to consider the profound problems and even wrong results that arise from the collapse postulate. We give a qualitatively new example of such a wrong result. Researchers and students alike are bothered by these fundamental issues. Students' ability to learn the material, and even their interest in physics, can be compromised by such disturbing conundra that seem to make physics, or at least QFT and its QM limit, seem incomprehensible and even inconsistent. This article resolves these issues in a way accessible to undergraduates, by applying the natural (minimal) interpretation of quantum mechanics (QM) (the ensemble interpretation) and explicating and clarifying the basic principles and premises used in QM and the Hegerfeldt theorem and its application to measurements.
ER -