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Maxwell's equation which convective derivative

  1. Jul 31, 2014 #1

    I was wondering what people thought of this paper. Please read up to at least page 3 before responding.
    I find it to be pretty convincing up to page 4.

    Thanks for any response.

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    Last edited: Jul 31, 2014
  2. jcsd
  3. Jul 31, 2014 #2


    Staff: Mentor

    It is hard to take him seriously when he thinks that Gauss' law is a statement of the conservation of charge.
  4. Jul 31, 2014 #3
    Maxwell's original 20 equations were in quarternion form. It is likely some mathematical knowledge was lost when it was simplified to vector calculus form. Also, Maxwell equations assume no vacuum polarization, something that is patently false and is not true even in deep space.
  5. Aug 1, 2014 #4
    It's quite well known that Maxwell used full derivative notation rather than partial derivatives for the field values. There are some statements about the history in that paper that I don't agree with. For example, Maxwell did attempt to refit his equations to accommodate moving particles by using Eulerian formulated convective derivatives but didn't feel the attempt was successful and didn't follow up on it. See Olivier Darrigol's "Electrodynamics from Ampere to Einstein". And Helmholtz, not Hertz, was the originator of that type of approach. Hertz might possibly have been the first to employ the simpler Langrangian formulated convective derivatives.

    It's pretty easy to demonstrate that Langrangian formulated convective derivatives used as the author shows make the Maxwell equations invariant across Galilean inertial frames. And also covariant when switching roles between receiver and emitter. But to arrive at mathematics that is equivalent to the Lorentz transformation you need to consider other things. The author presents equation 19 which seems entirely ad hoc. It seems to give him what he wants, but the rationale for invoking it or a derivation is lacking.
  6. Aug 1, 2014 #5
    P.S. Maxwell also did, at one point, append the Lorentz force law or at least a portion of it to the equations which we now know as "Ampere's law" or "Faraday's law" (sorry I can't remember which). That's a topic in his treatise.
  7. Aug 1, 2014 #6


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    I've not analyzed the quoted preprint in detail, but it seems to be flawed, because Maxwell theory is local classical relativistic field theory, and as such it should not contain matter-related quantities, particularly the fluid-velocity fields at other places than the sources (i.e., charge and current distributions). As such it is very well founded in its great success in describing the observations. As far as we know, it's only to be modified due to quantum effects

    It is clear that the Maxwell equations alone are not a closed set of equations. In addition you need the dynamics of the matter. This can be derived, including the Lorentz-force law, from energy-momentum balance equations or even more elegantly using the Hamilton principle of least action.
    Last edited: Aug 1, 2014
  8. Aug 1, 2014 #7
    PhilDSP: I don't understand equation (19) either. In my original post I said I found it convincing up to pg. 4. I don't know why he finds a Galilean invariant form of Maxwell's equations and then goes onto use the Lorentz transformations. He loses me there. Up to pg. 4, however, it was making a lot of sense. I don't see why you shouldn't use the convective term. The change in the local B field is covered by the partial with respect to time, while the convective term covers the change in B (per unit time) due to the fact that the moving observer (detector) is changing position within the B field.
    I see Thomas Phipps derives the corresponding wave equations from these altered Maxwell's equations and finds (I guess obviously) that the speed of light obeys standard Galilean relativity.
    I found the beginning of this paper to be interesting anyway. Thanks for the feedback
  9. Aug 1, 2014 #8
    It looks like the author is interested in showing that a mapping can be made between fields defined through equations exhibiting Galilean frame invariance and fields defined through equations exhibiting inertial frame covariant relationships via the LT. Mathematically, he wants to demonstrate that a homomorphism exists. That's not an entirely new concept. Louis de Broglie succeeded in doing that for wave parameters.
  10. Aug 2, 2014 #9


    Staff: Mentor

    This looks like a good place to close this discussion. Physics Essays is considered a very low quality journal which is not well accepted by professional physicists, and giving a paper there this much "air time" is already generous.
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