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PreprintCC BY 4.0arXiv

On the Limits of a Space-Time Description and the Physical Meaning of Phase Space in a Nonlocal Continuum

  • E. J. Thompson
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Abstract

In a previous paper we derived an uncertainty relation for nonlocal fields by showing that the physical localization width in nonlocal quantum field theory is broadened by the response kernel generated from the entire-function regulator. In this follow up we will reinterpret that result as just the position-sector limit of a more symmetric statement as we did not take into account the inherent nonlocality of momentum. We find and we prove under normalized, centered response kernels for both position and momentum the variance laws and derive the corresponding nonlocal phase-space uncertainty relation. The result still preserves the conclusions of the original paper all while strengthening the interpretation as nonlocal quantum field theory implies not merely a minimal measurable length, but a finite phase-space cell. We also explore experimental routes to test the theory.

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Cite

BibTeXRIS
BibTeX
@misc{thompson2026limits,
  title = {{On the Limits of a Space-Time Description and the Physical Meaning of Phase Space in a Nonlocal Continuum}},
  author = {E. J. Thompson},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.26876},
  eprint = {2610.26876},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.26876},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - On the Limits of a Space-Time Description and the Physical Meaning of Phase Space in a Nonlocal Continuum
AU  - E. J. Thompson
PY  - 2026
DA  - 2026/10/07
PB  - arXiv
DO  - 10.48550/arxiv.2610.26876
UR  - https://arxiv.org/abs/2610.26876
AB  - In a previous paper we derived an uncertainty relation for nonlocal fields by showing that the physical localization width in nonlocal quantum field theory is broadened by the response kernel generated from the entire-function regulator. In this follow up we will reinterpret that result as just the position-sector limit of a more symmetric statement as we did not take into account the inherent nonlocality of momentum. We find and we prove under normalized, centered response kernels for both position and momentum the variance laws and derive the corresponding nonlocal phase-space uncertainty relation. The result still preserves the conclusions of the original paper all while strengthening the interpretation as nonlocal quantum field theory implies not merely a minimal measurable length, but a finite phase-space cell. We also explore experimental routes to test the theory.
ER  -