Historically this dates back to Weyl and Kaluza-Klein, a century ago. But those theories were flawed, so a lot of physicists think that the geometry did not work.
Here is a new video that explains it well: Electromagnetism Derived From Geometry!.
In short, you add a circle to each point of spacetime, connect the circles infinitesimally to nearby circles, and then the electric and magnetic fields become the curvature.
The video tries to relate this idea to string theory, but that is speculation that did not pan out. The idea is completely essential to the Standard Model of physics, and our best explanation of the fundamental forces.
Electromagnetism and Gravity "from Geometry": The Gauge-and-Kaluza–Klein Account versus the McGucken dx₄/dt = ic Framework https://elliotmcguckenphysics.com/
ReplyDeleteMarquardt-Demen's notes and companion video, "Electromagnetism Derived From Geometry!" (2026), present the standard geometric account of electromagnetism in two layers. The first is the gauge-principle derivation: begin with the Dirac Lagrangian, postulate local U(1) phase symmetry of the electron field, promote the partial derivative to a covariant derivative, and read the field strength F_μν = ∂_μA_ν − ∂_νA_μ as the curvature of a U(1) connection — a phase circle attached at every point of spacetime, with the electromagnetic field measured as the failure of the phase to close around a small loop (its holonomy). The second layer is Kaluza–Klein: the phase circle is taken to be a real fifth dimension, compactified to a tiny fixed radius near the Planck length, and electromagnetism is the geometry of that curled-up dimension. The video extends this toward extra dimensions and string theory, an extrapolation the accompanying review already identifies as speculation that did not pan out.
The title overstates what the video does
The title's operative word is derived. A derivation of electromagnetism from geometry would produce the electromagnetic field from geometry with nothing electromagnetic assumed at the outset. The video does not do this; it postulates the electromagnetic structure and then re-describes it geometrically. Local U(1) phase symmetry is assumed at the start — "I then postulate that the Dirac bispinor field is gauge symmetric," in the notes — and that gauge symmetry is electromagnetism itself, introduced with the postulate rather than obtained from geometry. The Dirac field, the spacetime, the Minkowski metric, and the imaginary unit i are likewise inputs, not results. The U(1) circle, the connection A_μ, and the covariant derivative are constructed because the electromagnetic structure is already known; the curvature F_μν is identified with the known field, not predicted from geometry alone. The accurate description is that the video reformulates electromagnetism as geometry, given the assumed U(1) symmetry — a correct and useful reformulation — while the word "derived" claims more than the construction delivers.
The Kaluza–Klein layer underscores this. Kaluza–Klein does not obtain electromagnetism from pure geometry either; it posits a fifth dimension specifically to house the electromagnetic phase, and the video concedes it cannot fix the radius of that dimension or detect it: "it's not clear what the radius of this curled-up dimension should be; and we certainly haven't been able to detect it." An added dimension of unfixed radius introduced to carry a field that is already known is an accommodation, not a derivation. The video also declines to state the reasons the program stalled — the unfixed and unstabilized radius, the extra scalar and the tower of unobserved massive modes, the difficulty of recovering the Standard Model's chiral matter — and redirects the non-detection into string-theory motivation rather than treating it as a defect.
Where dx₄/dt = ic is more foundational: the gauge layer
The McGucken Principle dx₄/dt = ic — the physical statement that the fourth dimension expands at the rate c from every event — derives what the geometric derivation assumes. The Lorentzian metric follows from the pullback (ic)² = −c² (Lemma 2.5 [29]); the Dirac equation and U(1) gauge invariance follow from the quantum chain [38]; the gauge groups follow from the McGucken Symmetry paper [41]; and i is the perpendicularity marker of the x₄ = ict advance. The phase circle the derivation attaches by hand is the Compton cycle of x
Oh, that's precious. Let's use a math model where nothing moves to model something else that does. Makes sense they would use a timeless model to act as a psuedo causation for the pseudo riemannian bullshit (which it isn't, and can't) which pretends the non-linear is just a suggestion, a minor inconvenience to be hand waved away.
ReplyDeleteAlso, Math (much less geometry) isn't causation, never was, never will be, even when you really really really want it to be.
Screwing around with the failed language of the LHC Scientist Employment McWork project (invoking fake dimensions, pretending fake curled up dimensions exist, fake concerns about the fake dimensions) isn't going to produce anything except a colossal waste of the very time their system can't even model.
``the non-linear is just a suggestion, a minor inconvenience to be hand waved away.''
ReplyDeleteThere, you nailed it.
``Also, Math (much less geometry) isn't causation, never was, never will be, even when you really really really want it to be.''
An unexpectedly good, fitting finish, to the same piece.
In a way, expected.
--Ajit