from Hacker News

Electromagnetism as a Purely Geometric Theory

by andyjohnson0 on 4/19/25, 9:14 PM with 64 comments

  • by mikhailfranco on 4/20/25, 5:07 AM

    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

  • by molticrystal on 4/20/25, 12:57 AM

    >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?

  • by nimish on 4/20/25, 1:01 AM

    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?

  • by ogogmad on 4/19/25, 10:20 PM

    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.

  • by amelius on 4/20/25, 10:46 AM

    Purely geometric, except I suppose you still need Coulomb's law and relativity. Both of which can be easily put in a geometric framework.

    The rest is just how magnetism emerges from this, and Einstein already figured it out. This guy explains it pretty well in layman's terms: https://www.youtube.com/watch?v=sDlZ-aY9GN4

  • by mkoubaa on 4/20/25, 2:11 AM

    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.

  • by nsoonhui on 4/19/25, 11:51 PM

    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.

  • by phkahler on 4/19/25, 11:49 PM

    "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.

  • by hasley on 4/20/25, 7:40 AM

    Related question: What resources are there that might teach one about Maxwell‘s equations and the electromagnetic field tensor arisig from relativity? The magnetic field is a description of the electric field with relativistic effects. Is there a way of describing electromagnetism without the magnetic field?

  • by amai on 4/21/25, 9:18 AM

    These purely formal manipulations seem to skip over some important issues: If the equations of EM are the same as for gravity, then EM- charges should behave like mass. But like masses do attract each over, unlike EM-charges which do repel each other. I don't see how they resolve this basic difference between the behavior of masses and charges.

  • by mxmilkiib on 4/21/25, 12:55 PM

    reminds me of the end section of the "magnetic forces do no work" video by Angela Collier

    https://youtu.be/fHG7qVNvR7w?t=27m4s

    I love the entire rant/communication, but it ends with a classical view from a David Griffiths AIP interview, regarding a project by Jacob Barandes

    bit closer https://youtu.be/fHG7qVNvR7w?t=29m46s

  • by Iwan-Zotow on 4/21/25, 3:15 AM

    But this is non-linear EM

  • by oh_my_goodness on 4/20/25, 12:18 PM

    "charge density is a field, which propagates at the speed of light."

    Uh ...

  • by rkagerer on 4/19/25, 10:01 PM

    Couldn't get past the robot wall.