“Tension” between Electromagnetism and Newton's laws

When talking about the inconsistencies in physics that led up to Einstein's discovery of relativity today's professors always say that Maxwell's discovery of the constant speed of light $c$ created a huge contradiction in physics. (namely: was there a special frame relative to which the speed of light was $c$ OR were the laws of EM wrong).

My question is why didn't the scientists realize something was wrong right when the law saying that the magnetic force on a body was proportional to it's velocity was first proposed? someone had to ask "velocity relative to which observer" right? if they did realize something was wrong, why did they continue to use it in mainstream physics?

• Nobody thought of "observers" back then, it was assumed that Maxwell equations strictly speaking hold in the Newton's absolute space. When the Michelson-Morley experiments failed to show velocity relative to it clever ways were suggested to eliminate the "contradiction", one by Hertz, the other by Fitzgerald, Lorentz and Larmor (who identified the absolute space with ether). There was no widespread sense at the end of 19th century that there was any contradiction left, let alone a "huge" one. But today borrowing sentiments from later developments makes the "history" easier to tell. – Conifold May 14 '17 at 20:05
• someone had to ask "velocity relative to which observer" right? They thought it was relative to the frame of the aether. They also knew ca. 1880-1900 that any observable effect of motion relative to the aether would vanish up to some order in v/c. – Ben Crowell May 14 '17 at 21:51
• "Relative to which observer" is the kind of issue that people became sensitive to only after Einstein partly followed Mach in redefining what constitutes "physical" in special relativity. Of course, experimenters paid attention to frames in practice, but in analysis one could always fall back on absolute space and forget about them. Even the identification of the absolute frame with the ether happened in the aftermath of dealing with the Michelson-Morley experiments, not before, as Hertz's alternative theory shows. – Conifold May 14 '17 at 23:00
• didn't galilean relativity abolish the concept of an absolute space? – alex May 15 '17 at 1:11
• No, Newton introduced the absolute space in Principia and it remained the dominant view of mechanics until after Einstein (anticipated by Mach's criticisms). "Galilean relativity" is a post-Einsteinian term, Newton saw relativity as a superficial appearance over the "true" reality of absolute space, see here. – Conifold May 15 '17 at 20:34

They thought it was relative to the frame of the aether. People like Lorentz also knew ca. 1880-1895 that any observable effect of motion relative to the aether would vanish until you got to at least order $(v/c)^4$. They understood that the electric and magnetic fields would transform when you changed frames. They just didn't know that it was possible to make the form of Maxwell's equations exactly frame-independent by doing what Einstein did in his 1905 paper. It was a very radical and surprising step that Einstein took. Before 1905, people like Lorentz conceived of things like the Lorentz transformation in terms of stresses and strains generated by the motion of matter through the aether.

• did they also think it was relative to the aether even before they knew magnetism had anything to do with light waves? – alex May 16 '17 at 3:14
• By "it," we still mean the velocity appearing in the Lorentz force law, right? The discovery of the Lorentz force and the discovery of electromagnetic waves date to about the same time period. There wasn't a period where magnetism or magnetostatics was well understood and electromagnetic waves were unknown. – Ben Crowell May 16 '17 at 3:34

Concerning Einstein's relativity, there was only one relevant contradiction in physics before 1905: The ether theory had (wrongly) predicted that the speed of light is independent of the speed of the light source while Newton's emission theory of light had (correctly) said that the speed of light does vary with the speed of the source. The Michelson-Morley experiment had confirmed the latter (correct) prediction but Einstein found it profitable to adopt the former (wrong) one as his 1905 second ("light") postulate:

http://philsci-archive.pitt.edu/1743/2/Norton.pdf "The Michelson-Morley experiment is fully compatible with an emission theory of light that CONTRADICTS THE LIGHT POSTULATE."

http://books.google.com/books?id=JokgnS1JtmMC Banesh Hoffmann, Relativity and Its Roots, p.92: "There are various remarks to be made about this second principle. For instance, if it is so obvious, how could it turn out to be part of a revolution - especially when the first principle is also a natural one? Moreover, if light consists of particles, as Einstein had suggested in his paper submitted just thirteen weeks before this one, the second principle seems absurd: A stone thrown from a speeding train can do far more damage than one thrown from a train at rest; the speed of the particle is not independent of the motion of the object emitting it. And if we take light to consist of particles and assume that these particles obey Newton's laws, they will conform to Newtonian relativity and thus automatically account for the null result of the Michelson-Morley experiment without recourse to contracting lengths, local time, or Lorentz transformations. Yet, as we have seen, Einstein resisted the temptation to account for the null result in terms of particles of light and simple, familiar Newtonian ideas, and introduced as his second postulate something that was more or less obvious when thought of in terms of waves in an ether. If it was so obvious, though, why did he need to state it as a principle? Because, having taken from the idea of light waves in the ether the one aspect that he needed, he declared early in his paper, to quote his own words, that "the introduction of a 'luminiferous ether' will prove to be superfluous."

• The ether theory had (wrongly) predicted that the speed of light is independent of the speed of the light source This sounds like you're confused, not expressing yourself clearly, or are not familiar with the experimental facts. The speed of light is independent of the speed of the source. For a review, see Fox, J. G. (1967), "Constancy of the Velocity of Light," J. Opt. Soc. Am. 57, 967-968. A good, conceptually simple test is from in-flight decay of pi0 mesons: Alvager, adsabs.harvard.edu/abs/1964PhL....12..260A It's unfortunate that the OP hastily accepted this incorrect answer. – Ben Crowell May 16 '17 at 1:00

This is an extended comment on the answer of @Pentcho Valev. In his first paper on relativity Einstein does not mention the Micheson-Morley experiment. When asked later he said that this was not of crucial importance for him. As I understand, of prime importance was careful reading of Maxwell and thinking about what Maxwell's theory implies. Maxwell's theory is indeed inconsistent with classical (Galileo) relativity Principle. (In mathematical language, Mazwell's equations are not invariant under the group of Galileo transformations. They are invariant under Lorenz transformations instead.) This logically implies special relativity, if one only believes that Maxwell's equations are correct.(And Maxwell's theory was spectacularly confirmed by Hertz). But only the most profound thinkers clearly understood this (Lorenz, Poincare and Einstein). I mean that these people could PREDICT the outcome of the Michelson-Morley experiment even if it were not made.

So my short answer to the question is: there was a tension, but very few people noticed it.

Remark. Maxwell's book is a real treasure chest and it was read by very few people: http://www.ams.org.ezproxy.lib.purdue.edu/journals/bull/1972-78-05/S0002-9904-1972-12971-9/home.html but Einstin was certainly among them.

• Maxwell's theory is consistent not only with the classical relativity principle, but even with the entire Newtonian mechanics, as Lorentz, Larmor and Poincare showed in detail at the turn of the century. Together with the hypothesis that molecular forces are electromagnetic the combination even predicts the outcome of the Michelson-Morley experiment. Einstein explicitly stated that his light postulate is not implied by Maxwell's electrodynamics, see Zahar's Why Did Einstein's Programme Supersede Lorentz's? I and II – Conifold May 19 '17 at 2:07
• @Conifold: This seems like a good example of a Kuhn-style revolution, similar to heliocentrism. Geocentrism was working fine, and to get more precision all you had to do was pile more epicycles on top of epicycles. Heliocentrism didn't win because it gave better agreement with experiment. – Ben Crowell May 19 '17 at 3:48
• In his first paper on relativity Einstein does not mention the Micheson-Morley experiment. When asked later he said that this was not of crucial importance for him. This is actually not so clear. See Jeroen van Dongen, On the role of the Michelson-Morley experiment: Einstein in Chicago, arxiv.org/abs/0908.1545 – Ben Crowell May 19 '17 at 3:51
• @BenCrowell I think this is partly Zahar's point. Einstein's "paradigm" prevailed after 1905 because it provided better heuristics for developing new successful theories (GR especially), not because of the Michelson-Morley experiment or Galileo/Maxwell "inconsistencies". I'd be more cautious with the parallel to epicycles though, they had an indefinite number of parameters that could fit anything periodic, Lorentz-Larmor-Poincare theory had nothing of the sort, and of course it provided the same accuracy as SR since they share the formalism. Still, on balance it was reasonable to abandon it. – Conifold May 19 '17 at 5:15