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Am I missing something but the whole point of gauge theory (connections on a principal bundle) is that this is true, right? U(1) gauge theory gets you electroma

by nimish 1y ago

Am I missing something but the whole point of gauge theory (connections on a principal bundle) is that this is true, right? U(1) gauge theory gets you electromagnetism as a purely geometric result already?

pdonis 1y ago
Yes, but the "geometry" in question is not the geometry of spacetime, it's the geometry of spacetime plus an abstract space that's sort of "attached" to spacetime. (In the original Kaluza-Klein viewpoint, it was viewed as an extra 5th spacetime dimension, basically a circle at every point of spacetime.) What this paper appears to be doing (although I can't make complete sense of it) is to somehow derive Maxwell's Equations (or more precisely a nonlinear generalization of them--which seems to me to mean that they aren't actually deriving electromagnetism, but let that go) as a property of the geometry of spacetime alone, without any abstract spaces or extra dimensions or anything of that sort.
- guerrilla 1y ago
  Why would nonlinear generalizations be an issue? Wouldn't adding some constraints get us Maxwell's Equations? It seems significant that this can be done at all even if its not complete but maybe I'm missing something. It reminds me of Einstein's original geometrization, possibly even a breakthrough if it turns out to have uses in further development of theory.
  - Iwan-Zotow 1y ago
    Nonlinearity is not observed
- ajkjk 1y ago
  The fact that it's some generalization of Maxwell makes it more fun, though---should means it's testable.
leumassuehtam 1y ago
You're right that he is just rederiving electromagnetism through local U(1) gauge symmetry. He define his metric as g_{\mu\nu}=A_\mu A\nu, which is a gauge dependent metric that gives you Maxwell's equation in the covariant formulation when you identify the gauge field A_\mu with the vector potential. Sprinkling geometric algebra in gives a feel of novelty but these results is at least one hundred years old. *typo

by nimish 1y ago

pdonis 1y ago

Yes, but the "geometry" in question is not the geometry of spacetime, it's the geometry of spacetime plus an abstract space that's sort of "attached" to spacetime. (In the original Kaluza-Klein viewpoint, it was viewed as an extra 5th spacetime dimension, basically a circle at every point of spacetime.) What this paper appears to be doing (although I can't make complete sense of it) is to somehow derive Maxwell's Equations (or more precisely a nonlinear generalization of them--which seems to me to mean that they aren't actually deriving electromagnetism, but let that go) as a property of the geometry of spacetime alone, without any abstract spaces or extra dimensions or anything of that sort.

guerrilla 1y ago
Why would nonlinear generalizations be an issue? Wouldn't adding some constraints get us Maxwell's Equations? It seems significant that this can be done at all even if its not complete but maybe I'm missing something. It reminds me of Einstein's original geometrization, possibly even a breakthrough if it turns out to have uses in further development of theory.
- Iwan-Zotow 1y ago
  Nonlinearity is not observed
ajkjk 1y ago
The fact that it's some generalization of Maxwell makes it more fun, though---should means it's testable.

leumassuehtam 1y ago

You're right that he is just rederiving electromagnetism through local U(1) gauge symmetry. He define his metric as g_{\mu\nu}=A_\mu A\nu, which is a gauge dependent metric that gives you Maxwell's equation in the covariant formulation when you identify the gauge field A_\mu with the vector potential. Sprinkling geometric algebra in gives a feel of novelty but these results is at least one hundred years old. *typo