Gauge Matters More Than Curvature — Draconitic Research

Abstract

Recent orthodoxy, which we call Curvature Fundamentalism, posits that the field strength F on spacetime exhausts the physically significant content of electromagnetism, at least on prosaic (contractible) spacetimes. We argue that it is gauge invariance that constrains physical significance. As a result, there are physically significant quantities that F does not capture, even on contractible spacetimes. We show that this result is robust: in the presence of charged matter fields, there are interference experiments whose outcome cannot be predicted by F or any other point-local gauge invariant quantities on the basis of initial Cauchy data. We prove this using the example of relative phase of a Klein-Gordon-Maxwell field, and use it to identify a context in which the widely-claimed equivalence between the Maxwell-Faraday formulation EM₁ and the gauge formulation EM₂ of electromagnetism is untenable, and that new strategies may be needed for the reductionist project.

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BibTeX RIS

BibTeX

@misc{gomes2026gauge,
  title = {{Gauge Matters More Than Curvature}},
  author = {Henrique Gomes and Bryan W Roberts},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.13017},
  eprint = {2609.13017},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.13017},
  note = {CC BY-NC-SA 4.0},
}

RIS

TY  - UNPB
TI  - Gauge Matters More Than Curvature
AU  - Henrique Gomes
AU  - Bryan W Roberts
PY  - 2026
DA  - 2026/09/11
PB  - arXiv
DO  - 10.48550/arxiv.2609.13017
UR  - https://arxiv.org/abs/2609.13017
AB  - Recent orthodoxy, which we call Curvature Fundamentalism, posits that the field strength F on spacetime exhausts the physically significant content of electromagnetism, at least on prosaic (contractible) spacetimes. We argue that it is gauge invariance that constrains physical significance. As a result, there are physically significant quantities that F does not capture, even on contractible spacetimes. We show that this result is robust: in the presence of charged matter fields, there are interference experiments whose outcome cannot be predicted by F or any other point-local gauge invariant quantities on the basis of initial Cauchy data. We prove this using the example of relative phase of a Klein-Gordon-Maxwell field, and use it to identify a context in which the widely-claimed equivalence between the Maxwell-Faraday formulation EM_1 and the gauge formulation EM_2 of electromagnetism is untenable, and that new strategies may be needed for the reductionist project.
ER  -

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