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Is the world made of loops?

Abstract : 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.
keyword : loops gauge
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https://hal.archives-ouvertes.fr/hal-00769689
Contributor : Alexander Afriat <>
Submitted on : Friday, January 3, 2014 - 3:22:57 PM
Last modification on : Tuesday, April 14, 2020 - 2:38:35 PM
Long-term archiving on: : Saturday, April 8, 2017 - 10:42:14 AM

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  • HAL Id : hal-00769689, version 2

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Alexander Afriat. Is the world made of loops?. 2013. ⟨hal-00769689v2⟩

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