[HN Gopher] Electromagnetism as a Purely Geometric Theory
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Electromagnetism as a Purely Geometric Theory
Author : andyjohnson0
Score : 143 points
Date : 2025-04-19 21:14 UTC (1 days ago)
(HTM) web link (iopscience.iop.org)
(TXT) w3m dump (iopscience.iop.org)
| rkagerer wrote:
| Couldn't get past the robot wall.
| xeonmc wrote:
| I recommend https://www.youtube.com/watch?v=Sj_GSBaUE1o instead
| sitkack wrote:
| 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.
| oriel wrote:
| At this point, should failing the test be an indicator of being
| human, rather than success?
| andyjohnson0 wrote:
| > 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/...
| 0hijinks wrote:
| Links to the article and the PDF both are behind this human
| test. Guess today is the day I learned I'm a robot.
| ogogmad wrote:
| 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.
| philipov wrote:
| 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 wrote:
| I don't think so. The paper doesn't talk about gravity at
| all. It talks about electromagnetism.
| philipov wrote:
| 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.
| pdonis wrote:
| _> 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._
|
| But the metric tensor of spacetime, in General
| Relativity, which is our best current classical theory of
| gravity, _only_ explains gravity. Gravity, by itself,
| uses up all of the degrees of freedom in the metric
| tensor. There aren 't any left for electromagnetism or
| anything else.
|
| To get classical electromagnetism, you need to add
| another, _different_ tensor to your model--a stress-
| energy tensor with the appropriate properties to describe
| an electromagnetic field. Of course doing this in
| standard GR is straightforward and is discussed in GR
| textbooks; but it does _not_ involve somehow extracting
| electromagnetism from the metric tensor. It involves
| describing electromagnetism with the stress-energy
| tensor, i.e., with _different_ degrees of freedom from
| the ones that describe gravity.(And if you want to
| describe the sources of the field, you need to add even
| more degrees of freedom to the stress-energy tensor to
| describe charged matter.)
|
| The paper does not, as far as I can see, address this
| issue; the authors don't even appear to be aware that it
| _is_ an issue. Which makes me extremely skeptical of the
| paper 's entire approach.
| nine_k wrote:
| 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.
| soulofmischief wrote:
| What bends the space?
| klank wrote:
| The stress-energy tensor.
| soulofmischief wrote:
| What is affecting the stress-energy tensor?
| klank wrote:
| 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".
| pdonis wrote:
| _> 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.
| jungturk wrote:
| Not "same" as in unifying EM and GR, but rather "same" both
| can be described as geometric regimes in spacetime (though
| GR be metric compatible and EM in this formulation
| requiring a relaxation to semi-metricity.
|
| From the conclusion: >Charge is therefore to be understood
| as a local compression of the metric in the spacetime,
| which relates to longitudinal waves as described in [12].
| This provides some aesthetical features into the model, as
| electromagnetism seems to be orthogonal to gravity in the
| sense that current theory of gravity is a theory based on
| metric compatible connections.
| phkahler wrote:
| "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 wrote:
| What makes them different when they perform the same way in a
| double slit? They act differently at different scales or
| something else?
| Devilspawn6666 wrote:
| I think they're referring to quantum wavesfunctions being in
| configuration space rather than real spacetime.
| nsoonhui wrote:
| 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 wrote:
| Coming up with some "good enough" theoretical approximations
| could be extremely useful though.
| molticrystal wrote:
| >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?
| kanddle wrote:
| Any good theory probably needs to explain or reinterpret past
| phenomenon that has already been proven by experiments under
| the previous paradigm.
|
| Part of what made Einstein's theories so good is that they
| reinterpreted past theories while providing new explanations
| that fixed major unknowns in the science of the time. Both for
| GR and QFT.
| nimish wrote:
| 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 wrote:
| 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 wrote:
| 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.
| leumassuehtam wrote:
| 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
| mkoubaa wrote:
| 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.
| im3w1l wrote:
| 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.
| aeonik wrote:
| It's not my fault the universe is built on a hell of
| abstractions, I just model it.
|
| You ignore the reality of nature at your own peril.
|
| Besides, you can just use computers automate the wrangling of
| this hell. It's what they are good at, after all.
| bawolff wrote:
| Mathematicians and computer programmers use abstraction to
| opposite ends
| aleph_minus_one wrote:
| > Mathematicians and computer programmers use abstraction to
| opposite ends
|
| I claim to be qualified in both disciplines. With this
| background, I disagree.
|
| If you are very certain what you want to model, abstractions
| are often very useful to shed light on "what really happens
| in the system" (both in mathematics and computer science, but
| also in physics).
|
| The problem with applying abstractions in computer programs
| (in this way) lies somewhere else: in business,
| users/customers are often very "volatile" what they want from
| the computer program, instead of pondering deeply about this
| question (even though this would be a _very_ good idea). Thus
| (certain kinds of) abstractions in computer code make it much
| harder to adjust the program if new, very different
| requirements come up.
| bawolff wrote:
| Perhaps i should say why i think this.
|
| In math (i am not a mathematician), abstractions are a base
| to build on. You define some concept (e.g. a group, a set,
| whatever) then you prove things about it, building ever
| more complexity around your abstraction.
|
| This works great because in math your abstractions don't
| change. You are never going to redefine what a group is. If
| you need something different,maybe you define some related
| concept, a ring, a semigroup, or whatever, but you never
| change your original abstraction. It is the base you build
| on.
|
| As a result you can pack a lot of complexity. E.g. if
| something is a group, what are all the logical consequences
| of that? Probably so many you can't list them all, and
| that's ok. The whole point of math is to pick out some
| pattern and figure out what that entails.
|
| In contrast in computer programming, the goal of
| abstraction is largely isolation. You want to be able to
| change something in the abstraction, and it not affect the
| system very much. The things the abstraction entails should
| be as limited as reasonably possible as everything it
| entails is a potential depedency that will get messed up if
| anything changes. Ideally you should be able to understand
| what the abstraction does by only looking at the
| abstraction's code and not the whole system.
|
| Just think about the traditional SOLID principle in OOP
| design. Its all about ensuring abstractions are as isolated
| as possible from each other.
|
| To summarize, i think in math abstractions are the base of
| the complexity pyramid. All the complexity is built on top
| of them. In computers its the opposite. They should be the
| tip of the complexity pyramid.
|
| P.S. my controversial opinion is that this is the flaw in a
| lot of reasoning haskell fans use.
| aleph_minus_one wrote:
| I have a feeling that our arguments are not that
| different (though not identical), but just phrased in
| very different words:
|
| > This works great because in math your abstractions
| don't change.
|
| This is just a different formulation about the
| "volatility" of a lot of requirements of software by the
| users/customers.
|
| > In contrast in computer programming, the goal of
| abstraction is largely isolation. You want to be able to
| change something in the abstraction, and it not affect
| the system very much.
|
| Here my opinion differs: isolation is at best just one
| aspect of abstraction (and I would even claim that these
| concepts are even only tangentially related). I claim
| that the better isolation is rather a (very useful) side
| effect of some abstractions that are very commonly used
| in software development. But on the other hand, I don't
| think that it is really hard to come up with abstractions
| for software development that would be very useful, but
| don't lead to better isolation.
|
| The central purpose of abstraction in computer programs
| is to make is easier to reason about the the code, and
| being able to avoid having to write "related" code
| multiple times. Similar to mathematics: you want to prove
| a general theorem (e.g. about groups) instead of having
| to prove one theorem about S_n, one theorem about Z_n
| etc.
|
| You actually partly write about the aspect of reasoning
| about the code by yourself:
|
| > Ideally you should be able to understand what the
| abstraction does by only looking at the abstraction's
| code and not the whole system.
|
| In this sense using more abstractions is a particular
| optimization for the goals:
|
| - you want to make it easier to reason about the code
| abstractly
|
| - you want to avoid having to duplicate code (i.e. save
| money since less lines have to be written)
|
| But this is not a panacea:
|
| - If the abstraction turns out to be bad, you either have
| to re-engineer a lot, or you will have a maintenance
| nightmare (my "volatility of customer requirements"
| argument). Indeed, I claim that the question of "do we
| really use the best possible abstractions in our code for
| the problem that we want to solve" is nearly always
| neglected in software projects, because the answer is
| nearly always very inconvenient, necessitating lots of
| re-engineering of the code.
|
| - low-level optimizations become harder, so making the
| code really fast gets much more complicated
|
| - since abstractions are more "abstract", (depending on
| the abstraction) you might need "smarter" programmers
| (who can be more expensive). For an example consider some
| complicated metaprogramming libraries of Boost (C++): in
| the hands of really good programmers such abstractions
| can become "magic", but worse programmers will likely be
| overwhelmed by them.
|
| - fighting about the "right" abstraction can become very
| political (for low-level code there is often less of such
| a fight, because here "what is more performant is
| typically right").
|
| ---
|
| Concerning
|
| > To summarize, i think in math abstractions are the base
| of the complexity pyramid. All the complexity is built on
| top of them.
|
| This is actually not a bad idea to organize code (under
| my stated specific edge conditions! When these specific
| edge conditions are violated, my judgment might change).
| :-)
|
| ---
|
| > P.S. my controversial opinion is that this is the flaw
| in a lot of reasoning haskell fans use.
|
| I am not a particular fan of Haskell, but I think the
| Haskell fans' flaw lies in a very different point: they
| emphasize very particular aspects of computer
| programming, and, admittedly, often come up with clever
| solutions for these.
|
| The problem is: in my opinion there exist aspects of
| software development that are in my opinion far more
| important, but don't fit into the kind of structures that
| Haskell fans appreciate. The difficulty is thus in my
| experience convincing Haskell fans that such aspects
| actually matter a lot instead of being unimportant side
| aspects of software development.
| bawolff wrote:
| I think we do largely agree in a lot of ways.
|
| > This is just a different formulation about the
| "volatility" of a lot of requirements of software by the
| users/customers.
|
| Yes. I would say that this is a defining feature of
| computer programming - change. The complexity of change
| is what computer programmers primarily want to use
| abstractions to deal with (where such a concern is really
| absent to a mathematician. Everything is immutable to
| them).
|
| And yes, reasoning about the code is part of that too,
| but in computer programming often its in the form of
| being able to reason about a code base that is slowly
| shifting under you as other programmers make changes in
| other parts (in the context of a large project with many
| devs. I suppose its a different story for a solo project)
|
| To bring it back to the original start of the thread, i
| guess what i'm saying is that what makes an abstraction
| good for math is different then what makes it good for a
| computer program, so naturally they are going to look a
| little different.
| mkoubaa wrote:
| And my original point is related to the idea that the
| kind of abstractions that are useful for math are
| sometimes harmful when applied to code, especially in the
| hands of unseasoned developers.
| vacuity wrote:
| I disagree with the idea that computer science has an
| inverted use of abstractions. Unfortunate naming aside,
| computer science is basically mathematics applied to
| computation and data (still theoretical!) and software
| engineering (a good name, if only more people followed
| it) is applied computer science. Abstractions (models)
| must be the basis of the codebase. The JVM is an
| abstraction. Assembly is an abstraction. Threads are an
| abstraction. And so on. Of course, software engineering
| adds the complication of changing specifications and
| hence changing abstractions. Don't confuse poor
| abstractions for a reason to not have abstractions.
| Indeed, we have abstractions everywhere.
| bawolff wrote:
| To be clear, when i mean abstractions in computer
| programming, i mean things like classes and polymorphism;
| abstractions that are used to structure code bases.
|
| I think abstractions in CS (Turing machines, etc) or
| other building blocks in computer systems (OS
| interfaces,computer languages, etc) are a different story
| and much more similar to how abstractions are used in
| math.
| mikhailfranco wrote:
| 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
| hasley wrote:
| 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?
| bsder wrote:
| I'm pretty sure this is what you want:
|
| "Collective Electrodynamics: Quantum Foundations of
| Electromagnetism" https://www.amazon.com/Collective-
| Electrodynamics-Quantum-Fo...
| hasley wrote:
| Thanks!
| inatreecrown2 wrote:
| Atom by Asimov?
| amelius wrote:
| 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
| jahnu wrote:
| That's a great explanation. Thanks!
| ajkjk wrote:
| This is upstream of that: geometric in the sense that it
| doesn't involve gluing an additional a U(1) field to spacetime
| at every point (from which coulomb's law etc. emerge).
| oh_my_goodness wrote:
| "charge density is a field, which propagates at the speed of
| light."
|
| Uh ...
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