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?
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?
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.
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.
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.
>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?
"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.
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.
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.
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.
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.
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".
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.
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.
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.
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.
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?
I'm pretty sure this is what you want:
"Collective Electrodynamics: Quantum Foundations of Electromagnetism" https://www.amazon.com/Collective-Electrodynamics-Quantum-Fo...
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?
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.
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.
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
>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?
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
"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.
What makes them different when they perform the same way in a double slit? They act differently at different scales or something else?
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.
Coming up with some "good enough" theoretical approximations could be extremely useful though.
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.
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.
> 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.
What bends the space?
The stress-energy tensor.
What is affecting the stress-energy tensor?
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".
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.
I don't think so. The paper doesn't talk about gravity at all. It talks about electromagnetism.
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.
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.
Mathematicians and computer programmers use abstraction to opposite ends
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.
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At this point, should failing the test be an indicator of being human, rather than success?
> Couldn't get past the robot wall.
Nothing like that for me. I just clicked the big "article pdf" button at the bottom of the page.
Direct link to full pdf:
https://iopscience.iop.org/article/10.1088/1742-6596/2987/1/...
Links to the article and the PDF both are behind this human test. Guess today is the day I learned I'm a robot.
I recommend https://www.youtube.com/watch?v=Sj_GSBaUE1o instead
https://www.researchgate.net/publication/390640631_Electroma...
And then I got a bot check on researchgate, first time and I download a lot of papers from them.