Is the world made of loops?

In discussions of the Aharonov-Bohm effect, Healey and Lyre have attributed reality to loops $\sigma_0$ (or hoops $[\sigma_0]$), since the electromagnetic potential $A$ is currently unmeasurable and can therefore be transformed. I argue that $[A]=[A+d\lambda]_{\lambda}$ and the hoop $[\sigma_0]$ are related by a meaningful duality, so that however one feels about $[A]$ (or any potential $A\in[A]$), it is no worse than $[\sigma_0]$ (or any loop $\sigma_0\in[\sigma_0]$): no ontological firmness is gained by retreating to the loops, which are just as flimsy as the potentials. And one wonders how the unmeasurability of one entity can invest another with physical reality; would an eventual observation of $A$ dissolve $\sigma_0$, consigning it to a realm of incorporeal mathematical abstractions? The reification of loops rests on the potential's ''gauge dependence''; which in turn rests on its unmeasurability; which is too shaky and arbitrary a notion to carry so much weight.

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Source https://hal.science/hal-00769689
Author Afriat, Alexander
Maintainer CCSD
Last Updated May 7, 2026, 16:00 (UTC)
Created May 7, 2026, 16:00 (UTC)
Identifier hal-00769689
Language en
Rights https://about.hal.science/hal-authorisation-v1/
contributor Sciences, Philosophie, Histoire (SPHERE (UMR_7219)) ; Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)
creator Afriat, Alexander
date 2013-01-03T00:00:00
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harvest_source_id 3374d638-d20b-4672-ba96-a23232d55657
harvest_source_title test moissonnage SELUNE
metadata_modified 2023-03-24T00:00:00
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