Electromagnetism as a Purely Geometric Theory

(iopscience.iop.org)

84 points | by andyjohnson0 9 hours ago

8 comments

  • mikhailfranco 1 hour ago
    Reminds me of Feynman Checkerboard:

    https://en.wikipedia.org/wiki/Feynman_checkerboard

    and the work of David Hestenes:

    Zitterbewegung in Quantum Mechanics

    https://davidhestenes.net/geocalc/pdf/ZBWinQM15**.pdf

    Zitterbewegung structure in electrons and photons

    https://arxiv.org/abs/1910.11085

    Zitterbewegung Modeling

    https://davidhestenes.net/geocalc/pdf/ZBW_mod.pdf

  • nimish 5 hours 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 4 hours 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.

  • molticrystal 5 hours ago
    >The Dirac equation can be therefore interpreted as a purely geometric equation, where the mc2 term directly relates to spacetime metric. There is no need to involve any hypothetical Higgs field to explain the particle mass term.

    What happens to the Higgs field excitation and the Higgs boson, given the experiments confirming their existence? If this paper explains phenomena more effectively, does it require us to reinterpret these findings?

  • phkahler 6 hours ago
    "As the electrodynamic force, i.e. the Lorentz force can be related directly to the metrical structure of spacetime, it directly leads to the explanation of the Zitterbewegung phenomenon and quantum mechanical waves as well."

    Cool because traditional QM wave function waves are not electromagnetic waves even though they seem to be the same thing in a double slit experiment.

    • koolala 2 hours ago
      What makes them different when they perform the same way in a double slit? They act differently at different scales or something else?
  • nsoonhui 6 hours ago
    Forgive my ignorance but isn't this proven to be a dead end? There is this Kaluza Klein theory that proposes EM as the fifth dimension that has been ruled out, and Einstein spent large part of his later years trying to integrate EM into the GR geometric framework, with no success, mainly because he didn't know about strong and weak nuclear force as the other two fundamental force besides EM and gravity.
    • XorNot 6 hours ago
      Coming up with some "good enough" theoretical approximations could be extremely useful though.
  • ogogmad 8 hours ago
    For people wondering what "geometric" means here, they say: "the electromagnetic field should be derived purely and solely from the properties of the metric tensor".

    I'm not sure if that's exactly it.

    Question: Is there any relationship between this and Axiomatic Thermodynamics? I recall that also uses differential geometry.

    • nine_k 6 hours ago
      AFAICT the idea is that there are no "fields" or "forces" acting "in space", but the space itself bends just so that the normal mechanical motion through it looks the way the electromagnetic phenomena look.

      That is, the same deal as with gravity in GR.

      • pdonis 4 hours ago
        > the same deal as with gravity in GR.

        But it can't be quite "the same deal", because gravity obeys the equivalence principle, and electromagnetism does not. (Nor do the other known fundamental interactions.) The paper does not appear to address this at all.

      • soulofmischief 4 hours ago
        What bends the space?
        • klank 3 hours ago
          The stress-energy tensor.
          • soulofmischief 3 hours ago
            What is affecting the stress-energy tensor?
            • klank 3 hours ago
              The classic GR line is "the stress-energy tensor tells spacetime (i.e. the metric tensor) how to bend and spacetime tells the stress-energy tensor how to move".
    • philipov 7 hours ago
      Okay, so this is another attempt to unify quantum field theory and gravity. By using gravity to get quantum fields, rather than by trying to quantize gravity.
      • pdonis 4 hours ago
        I don't think so. The paper doesn't talk about gravity at all. It talks about electromagnetism.
        • philipov 4 hours ago
          If the paper is attempting to express electromagnetism in terms of the metric tensor, then it is putting it into a form that makes it potentially compatible with gravity, which is also a metric tensor. Quantum theories use a completely different type of math, and trying to express gravity in that way (quantizing gravity) results in a bunch of broken equations. If both systems can be described using differential geometry, that is a step in the direction of unifying the theories, even if it's not a hole-in-one.
  • mkoubaa 4 hours ago
    The most irritating kind of junior devs to work with are the ones who refactor code into abstraction oblivion that nobody can decipher in the name of code deduplication or some other contrived metric.

    That phenotype is well-represented in mathematical physics.

    • bawolff 30 minutes ago
      Mathematicians and computer programmers use abstraction to opposite ends
    • im3w1l 3 hours ago
      I think sometimes you have to build the abstraction hell to completion and live with it for a while to truly realize it is in fact inferior. And even then, in science sometimes it never dies fully but lives on in some niche where it has desirable qualities.
  • rkagerer 8 hours ago
    [flagged]