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I am trying to write a paper on how Einstein's special relativity (SR) essentially saved electromagnetism for high school and am confused on how the following two problems were solved.

  1. How did physicists explain the (theoretical) disappearance of the magnetic force on a moving charge by changing the frame of reference? Special relativity saves this by essentially showing that changing frames changes the electric force too, as well as the magnetic, but I am unsure about how this was tackled before

  2. Michelson & Morley disproved the existence of luminiferous ether in 1887, 18 years before SR. Was the world of physics in complete chaos for the next 18 years with the apparent breaking of electromagnetism, or was there a temporary solution?

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  • $\begingroup$ Afaik M&M's result was not considered as an obvious disproof. They tought there was some error in the experiment and tried to fix it, until they lived. $\endgroup$
    – peterh
    Dec 18 '20 at 21:32
  • $\begingroup$ You might find my answer here useful in framing your thinking about the pre-1905 understanding of electromagnetism. $\endgroup$ Dec 18 '20 at 21:41
  • $\begingroup$ Einstein's special relativity (SR) did not "save electromagnetism", it provided a better theoretical framework for what was already there. Lorentz's ether theory had the same change of frame effects, in fact, it was mathematically equivalent to SR. But the explanation was different, it involved dynamic effects on molecular forces in non-ether frames rather than kinematics. See Zahar's paper Why Did Einstein's Programme Supersede Lorentz's? on how frame invariance issues were handled by Lorentz. $\endgroup$
    – Conifold
    Dec 19 '20 at 22:57
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There certainly WERE formulae that correctly described parts of the electromagnetic puzzle, including Fitzgerald-Lorentz contraction of distance, and even some medium-drag light delay experiments with transparent media instead of the fictitious ether.

What special relativity did was to incorporate all the various 'it-works-like-this' rules into a single coherent picture, including generating all magnetic forces from the behaviors of charge; it cut the four Maxwell equations for electricity and magnetism down to two equations, and a principle of relativity... while simultaneously predicting a variety of phenomena regarding space and time. It revolutionized both electricity, AND mechanics, with one concept.

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Special Relativity(SR) didn't save electromagnetism, not even remotely. In fact, all of SR can essentially be derived from classical electromagnetism. That is essentially what Lorentz Ether Theory(LET) is. For example, before SR came into the picture, Lorentz showed that electromagnetic systems, such as matter, would experience length contraction in the direction of movement at speeds close to the speed of light. LET essentially assumes the entire universe consists of electromagnetic systems in an ether(which in this case means a homogeneous medium with a given electric permittivity and magnetic permeability). If you have a moving charge in LET, a Lorentz transformation can be done so that the charge is stationary and the magnetic field disappears. In case you're wondering, LET an SR give the exact same experimental predictions.

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