4 ms·

Then stop playing with words and say what you mean. Point charges make sense without qualification in EM, that much is true. But that doesn't mean that there

Then stop playing with words and say what you mean. Point charges make sense without qualification in EM, that much is true. But that doesn't mean that there is something strange or fishy going on here. You can formulate Lorentz forces using mass distributions and you're fine (it's right there in the next subsection of the wiki). The pathologies don't appear. Of course the resulting equations are non-linear, and that is the origin of the failure of point sources to make sense. If you then try to recover point sources by taking a limit, the details of the assumptions you make matter a great deal [1]. For a very easy example, your point source might have a dipole. This problem is kind of well known and studied in the General Relativity literature where the non-linearity of the field equations forces you to confront similar type of problems already when trying to derive geodesic motion [2]. I suspect all this is familiar to you. I would phrase the conclusion as such: The Newtonian idea of focusing exclusively on the motion of the centre of mass, which reflects the influence of distributed forces on a rigid body, breaks down in any relativistic theory. This is simply because the notion of a rigid body breaks down. As such the point mass, which was a conceptual cornerstone of Newtonian mechanics, along with the notion of a force acting on it, are relegated to a technical tool useful only when non-linearities are neglected. [1] https://arxiv.org/abs/0905.2391 https://arxiv.org/abs/0905.2391 When googling for this paper I found a nice set of slides by Wald about this whole business: http://www.math.utk.edu/~fernando/barrett/bwald1.pdf http://www.math.utk.edu/~fernando/barrett/bwald1.pdf [2] https://arxiv.org/abs/gr-qc/0309074 https://arxiv.org/abs/gr-qc/0309074

jules 8y ago
I'm not trying to play with words...by EM I mean Maxwell's equations and the Lorentz force law. I think that's the conventional meaning. The point is that these two are taught in an EM class as if it's a single coherent theory that tells you what point charges do. Mass distributions don't solve the issue in a satisfactory way, in my opinion. If you replace a particle with a finite size sphere you've solved the infinity but lost relativistic invariance. You could perhaps come up with a way to hold the charge distribution together in a relativistically invariant way, but that can hardly be considered part of EM, and might involve arbitrary choices. That a dipole behaves differently than a monopole is clear. That's already the case even if you ignore the self interaction. The question "What happens if I put an electron in a uniform magnetic field?" or "What happens if I have two electrons?" seems like it should be answered by EM. One can hardly ask a simpler question. I'm pretty sure that most physics students who've had an EM course are under the impression that they should be able to answer this question. When I was in such a class it was never explained that this was even an issue, and when I asked about it the answer I got was "just wait for QED". If you don't like the word "schizophrenic" for this issue, that's cool. I think it's descriptive, but YMMV. Wald's slides say: > Classical Electrodynamics as Taught in Courses > At least 95% of what is taught in electrodynamics courses at all levels focuses on the following two separate problems: (i) Given a distribution of charges and/or currents, find the electric and magnetic fields (i.e., solve Maxwell’s equations with given source terms). (ii) Given the electric and magnetic fields, find the motion of a point charge (possibly with an electric and/or magnetic dipole moment) by solving the Lorentz force equation (possibly with additional dipole force terms). That's all I meant by it. Wald's slides are interesting, thanks :)
- DoctorOetker 8y ago
  I would like to respond to your reply at https://news.ycombinator.com/item?id=18846249 https://news.ycombinator.com/item?id=18846249 and I was going to use among other things the example of an electron in a uniform magnetic field. So I was totally surprised when I read this comment already mentioning > ... "What happens if I put an electron in a uniform magnetic field?" ... Either 1) this is pure coincidence (and you are contrasting the difficulty of the 2 electrons compared to the "simpler" electron in a magnetic field), or 2) you are referencing a certain 'issue' or puzzle about the electron in a uniform magnetiic field? Could you clarify if it is 1) or 2) or something else? and if 2) clarify the puzzling issue regarding the "electron in a unifoorm magnetic field"? Then I will feel more comfortable answering the other comment you made, so I can clarify my earlier reply to you :)
  - jules 8y ago
    It's fundamentally the same issue, and the same difficulty. The reason I mentioned 2 charges orbiting around each other is to avoid getting into a discussion about the uniform magnetic field, and that maybe the extra radiation energy is just coming from the uniform magnetic field, and that energy is still conserved because the total energy was infinite to begin with.
- Certhas 8y ago
  If you take a non-relativistic model of your matter content, then the theory becomes non-relativistic. That's trivial. So take a relativistic model for your matter and you have no problem [1]. EM gives you a theory of EM Fields and their interaction with matter. It shouldn't be surprising that EM doesn't give you a theory of matter. I maintain there is no conceptual problem with EM, the problem is with your electron model which is unphysical. It might seem reasonable to you, but that's because of your intuition to build up matter from point particles, which is only justified by QFT considerations that came almost a century after EM. [1] A simple matter model often used in GR is dust. I'm sure this would work for EM even better.
  - jules 8y ago

jules 8y ago

I'm not trying to play with words...by EM I mean Maxwell's equations and the Lorentz force law. I think that's the conventional meaning. The point is that these two are taught in an EM class as if it's a single coherent theory that tells you what point charges do. Mass distributions don't solve the issue in a satisfactory way, in my opinion. If you replace a particle with a finite size sphere you've solved the infinity but lost relativistic invariance. You could perhaps come up with a way to hold the charge distribution together in a relativistically invariant way, but that can hardly be considered part of EM, and might involve arbitrary choices. That a dipole behaves differently than a monopole is clear. That's already the case even if you ignore the self interaction. The question "What happens if I put an electron in a uniform magnetic field?" or "What happens if I have two electrons?" seems like it should be answered by EM. One can hardly ask a simpler question. I'm pretty sure that most physics students who've had an EM course are under the impression that they should be able to answer this question. When I was in such a class it was never explained that this was even an issue, and when I asked about it the answer I got was "just wait for QED". If you don't like the word "schizophrenic" for this issue, that's cool. I think it's descriptive, but YMMV. Wald's slides say: > Classical Electrodynamics as Taught in Courses > At least 95% of what is taught in electrodynamics courses at all levels focuses on the following two separate problems: (i) Given a distribution of charges and/or currents, find the electric and magnetic fields (i.e., solve Maxwell’s equations with given source terms). (ii) Given the electric and magnetic fields, find the motion of a point charge (possibly with an electric and/or magnetic dipole moment) by solving the Lorentz force equation (possibly with additional dipole force terms). That's all I meant by it. Wald's slides are interesting, thanks :)

DoctorOetker 8y ago
I would like to respond to your reply at https://news.ycombinator.com/item?id=18846249 https://news.ycombinator.com/item?id=18846249 and I was going to use among other things the example of an electron in a uniform magnetic field. So I was totally surprised when I read this comment already mentioning > ... "What happens if I put an electron in a uniform magnetic field?" ... Either 1) this is pure coincidence (and you are contrasting the difficulty of the 2 electrons compared to the "simpler" electron in a magnetic field), or 2) you are referencing a certain 'issue' or puzzle about the electron in a uniform magnetiic field? Could you clarify if it is 1) or 2) or something else? and if 2) clarify the puzzling issue regarding the "electron in a unifoorm magnetic field"? Then I will feel more comfortable answering the other comment you made, so I can clarify my earlier reply to you :)
- jules 8y ago
  It's fundamentally the same issue, and the same difficulty. The reason I mentioned 2 charges orbiting around each other is to avoid getting into a discussion about the uniform magnetic field, and that maybe the extra radiation energy is just coming from the uniform magnetic field, and that energy is still conserved because the total energy was infinite to begin with.
Certhas 8y ago
If you take a non-relativistic model of your matter content, then the theory becomes non-relativistic. That's trivial. So take a relativistic model for your matter and you have no problem [1]. EM gives you a theory of EM Fields and their interaction with matter. It shouldn't be surprising that EM doesn't give you a theory of matter. I maintain there is no conceptual problem with EM, the problem is with your electron model which is unphysical. It might seem reasonable to you, but that's because of your intuition to build up matter from point particles, which is only justified by QFT considerations that came almost a century after EM. [1] A simple matter model often used in GR is dust. I'm sure this would work for EM even better.
- jules 8y ago