He continued that as long as a consistent explanation is missing as to how those forces and potentials act together on the electron, Lorentz's system of hypotheses is incomplete and doesn't satisfy the relativity principle.
In special relativity, the space and time coordinates depend on the inertial observer's frame of reference, and the luminiferous aether plays no role in the physics.
Alfred Bucherer and Paul Langevin (1904) developed another model, in which the electron is contracted in the line of motion, and dilated in the transverse direction, so that the volume remains constant.
Eventually, Kaufmann published his results in December 1905 and argued that they are in agreement with Abraham's theory and require rejection of the "basic assumption of Lorentz and Einstein" (the relativity principle).
Max Planck (1906) alluded to inconsistencies in the theoretical interpretation of the data, and Adolf Bestelmeyer (1906) introduced new techniques, which (especially in the area of low velocities) gave different results and which cast doubts on Kaufmann's methods.
Following an old argument by Pierre-Simon Laplace, Poincaré (1904) alluded to the fact that Newton's law of universal gravitation is founded on an infinitely great speed of gravity.
[B 16] Insufficient knowledge of the basics of special relativity, especially the application of the Lorentz transformation in connection with length contraction and time dilation, led and still leads to the construction of various apparent paradoxes.
However, the self-consistency of the reciprocity of time dilation had already been demonstrated long before in an illustrative way by Lorentz (in his lectures from 1910, published 1931[A 21]) and many others—they alluded to the fact that it is only necessary to carefully consider the relevant measurement rules and the relativity of simultaneity.
Smoot explained that "one problem to overcome was the strong prejudice of good scientists who learned the lesson of the Michelson and Morley experiment and Special Relativity that there were no preferred frames of reference."
"[B 20] The theory of complete aether drag, as proposed by George Gabriel Stokes (1844), was used by some critics as Ludwig Silberstein (1920) or Philipp Lenard (1920) as a counter-model of relativity.
For example, the Sagnac effect is based on the independence of light speed from the source velocity, and the image of Double stars should be scrambled according to this model—which was not observed.
However, as pointed out by Willem de Sitter in 1916, Mach's principle is not completely fulfilled in general relativity because there exist matter-free solutions of the field equations.
While this charge was rejected (among others) by Hermann Weyl, in an inaugural address given at the University of Leiden in 1920, shortly after the Bad Nauheim debates, Einstein himself acknowledged that according to his general theory of relativity, so-called "empty space" possesses physical properties that influence matter and vice versa.
However, as Weyl pointed out, it is incorrect to handle a rotating extended system as a rigid body (neither in special nor in general relativity)—so the signal velocity of an object never exceeds the speed of light.
Another criticism that was raised by both Lenard and Gustav Mie concerned the existence of "fictitious" gravitational fields in accelerating frames, which according to Einstein's Equivalence Principle are no less physically real than those produced by material sources.
In 1920 he argued that the deflection of light by the sun, as observed by Arthur Eddington et al. (1919), is not necessarily a confirmation of general relativity, but may also be explained by the Stokes-Planck theory of complete aether drag.
[A 37][B 35][B 36][C 20] Some proponents of Philosophy of Life, Vitalism, Critical realism (in German speaking countries) argued that there is a fundamental difference between physical, biological and psychological phenomena.
For example, Henri Bergson (1921), who otherwise was a proponent of special relativity, argued that time dilation cannot be applied to biological organisms, therefore he denied the relativistic solution of the twin paradox.
[A 42][A 3] Some academic scientists, especially experimental physicists such as the Nobel laureates Philipp Lenard and Johannes Stark, as well as Ernst Gehrcke, Stjepan Mohorovičić, Rudolf Tomaschek and others criticized the increasing abstraction and mathematization of modern physics, especially in the form of relativity theory, and later quantum mechanics.
Therefore, Wazeck (who studied some German examples) gave to these "free researchers" the name "world riddle solver" ("Welträtsellöser", such as Arvid Reuterdahl, Hermann Fricke or Johann Heinrich Ziegler).
It was significant for many "free researchers" (especially the monists) to explain all phenomena by intuitive and illustrative mechanical (or electrical) models, which also found its expression in their defense of the aether.
The enormous self-confidence of the "free researchers" is noteworthy, since they not only believed themselves to have solved the great riddles of the world, but many also seemed to expect that they would rapidly convince the scientific community.
Physicists like Gehrcke, some philosophers, and the "free researchers" were so obsessed with their own ideas and prejudices that they were unable to grasp the basics of relativity; consequently, the participants of the discussions were talking past each other.
Similarly, popular criticism in the Soviet Union and China, which partly was politically organized, rejected the theory not because of factual objections, but as ideologically motivated as the product of western decadence.
[A 49] Reacting to this underlying mood, Einstein himself openly speculated in a newspaper article that in addition to insufficient knowledge of theoretical physics, antisemitism at least partly motivated their criticisms.
Gehrcke's book on "The mass suggestion of relativity theory" (1924) was not antisemitic itself, but it was praised by the far-right press as describing an alleged typical Jewish behavior, which was also imputed to Einstein personally.
For example, Hans Reichenbach wrote a report in the entertainment section of a newspaper, describing the book as "a magnificent collection of naive mistakes" and as "unintended droll literature".
[A 56][6] Albert von Brunn interpreted the book as a pamphlet "of such deplorable impotence as occurring elsewhere only in politics" and "a fallback into the 16th and 17th centuries" and concluded “it can only be hoped that German science will not again be embarrassed by such sad scribblings”.
On the other hand, no antisemitic expression can be found in the book, and it also included contributions of some authors of Jewish ancestry (Salomo Friedländer, Ludwig Goldschmidt, Hans Israel, Emanuel Lasker, Oskar Kraus, Menyhért Palágyi).
Therefore, fundamental criticism (like that of Herbert Dingle, Louis Essen, Petr Beckmann, Maurice Allais and Tom van Flandern) has not been taken seriously by the scientific community, and due to the lack of quality of many critical publications (found in the process of peer review) they were rarely accepted for publication in reputable scientific journals (except for a few articles by, say, Mansuripur[10] and Javanshiry[11] regarding some paradoxes in the definition of, respectively, the Lorentz force and force (general form) in special relativity).