Basic concept The Lorentz ether theory, which was developed mainly between 1892 and 1906 by Lorentz and Poincaré, was based on the aether theory of
Augustin-Jean Fresnel,
Maxwell's equations and the electron theory of
Rudolf Clausius. Lorentz's 1895 paper rejected the aether drift theories, and refused to express assumptions about the nature of the aether. It said: As
Max Born later said, it was natural (though not logically necessary) for scientists of that time to identify the
rest frame of the Lorentz aether with the absolute space of
Isaac Newton. The condition of this aether can be described by the
electric field E and the
magnetic field H, where these fields represent the "states" of the aether (with no further specification), related to the charges of the electrons. Thus an abstract electromagnetic aether replaces the older mechanistic aether models. Contrary to Clausius, who accepted that the electrons operate by
actions at a distance, the
electromagnetic field of the aether appears as a mediator between the electrons, and changes in this field can propagate not faster than the
speed of light. Lorentz theoretically explained the
Zeeman effect on the basis of his theory, for which he received the
Nobel Prize in Physics in 1902.
Joseph Larmor found a similar theory simultaneously, but his concept was based on a mechanical aether. A fundamental concept of Lorentz's theory in 1895 was the "theorem of corresponding states" for terms of order
v/
c. This theorem states that a moving observer with respect to the aether can use the same electrodynamic equations as an observer in the stationary aether system, thus they are making the same observations.
Length contraction A big challenge for the Lorentz ether theory was the
Michelson–Morley experiment in 1887. According to the theories of Fresnel and Lorentz, a relative motion to an immobile aether had to be determined by this experiment; however, the result was negative. Michelson himself thought that the result confirmed the aether drag hypothesis, in which the aether is fully dragged by matter. However, other experiments like the
Fizeau experiment and the effect of aberration disproved that model. A possible solution came in sight, when in 1889
Oliver Heaviside derived from
Maxwell's equations that the
magnetic vector potential field around a moving body is altered by a factor of \sqrt{1- v^2 / c^2}. Based on that result, and to bring the hypothesis of an immobile aether into accordance with the Michelson–Morley experiment,
George FitzGerald in 1889 (qualitatively) and, independently of him, Lorentz in 1892 (already quantitatively), suggested that not only the electrostatic fields, but also the molecular forces, are affected in such a way that the dimension of a body in the line of motion is less by the value v^2/(2c^2) than the dimension perpendicularly to the line of motion. However, an observer co-moving with the earth would not notice this contraction because all other instruments contract at the same ratio. In 1895 • The body
contracts in the line of motion and preserves its dimension perpendicularly to it. • The dimension of the body remains the same in the line of motion, but it
expands perpendicularly to it. • The body contracts in the line of motion and expands at the same time perpendicularly to it. Although the possible connection between electrostatic and intermolecular forces was used by Lorentz as a plausibility argument, the contraction hypothesis was soon considered as purely
ad hoc. It is also important that this contraction would only affect the space between the electrons but not the electrons themselves; therefore the name "intermolecular hypothesis" was sometimes used for this effect. The so-called
Length contraction without expansion perpendicularly to the line of motion and by the precise value l=l_0 \cdot \sqrt{1- v^2 / c^2} (where l0 is the length at rest in the aether) was given by Larmor in 1897 and by Lorentz in 1904. In the same year, Lorentz also argued that electrons themselves are also affected by this contraction. For further development of this concept, see the section .
Local time An important part of the theorem of corresponding states in 1892 and 1895 In
The Measure of Time he wrote in 1898: In 1900 Poincaré interpreted local time as the result of a synchronization procedure based on light signals. He assumed that two observers,
A and
B, who are moving in the aether, synchronize their clocks by optical signals. Since they treat themselves as being at rest, they must consider only the transmission time of the signals and then crossing their observations to examine whether their clocks are synchronous. However, from the point of view of an observer at rest in the aether the clocks are not synchronous and indicate the local time t'=t - vx / c^2. But because the moving observers don't know anything about their movement, they don't recognize this. In 1904, he illustrated the same procedure in the following way:
A sends a signal at time 0 to
B, which arrives at time
t. B also sends a signal at time 0 to
A, which arrives at time
t. If in both cases
t has the same value, the clocks are synchronous, but only in the system in which the clocks are at rest in the aether. So, according to Darrigol, Poincaré understood local time as a physical effect just like length contraction – in contrast to Lorentz, who did not use the same interpretation before 1906. However, contrary to Einstein, who later used a similar synchronization procedure which was called
Einstein synchronisation, Darrigol says that Poincaré had the opinion that clocks resting in the aether are showing the true time. also Lorentz noted for the frequency of oscillating electrons "
that in S the time of vibrations be k\varepsilon times as great as in S0", where S0 is the aether frame, S the mathematical-fictitious frame of the moving observer, k is \sqrt{1- v^2 / c^2}, and \varepsilon is an undetermined factor.
Lorentz transformation While
local time could explain the negative aether drift experiments to first order to
v/
c, it was necessary – due to other unsuccessful aether drift experiments like the
Trouton–Noble experiment – to modify the hypothesis to include second-order effects. The mathematical tool for that is the so-called
Lorentz transformation. Voigt in 1887 had already derived a similar set of equations (although with a different scale factor). Afterwards, Larmor in 1897 and Lorentz in 1899 who introduced the so-called "Poincaré stresses" to solve that problem. Those stresses were interpreted by him as an external, non-electromagnetic pressure, which stabilize the electrons and also served as an explanation for length contraction. Although he argued that Lorentz succeeded in creating a theory which complies to the postulate of relativity, he showed that Lorentz's equations of electrodynamics were not fully
Lorentz covariant. So by pointing out the group characteristics of the transformation, Poincaré demonstrated the Lorentz covariance of the Maxwell–Lorentz equations and corrected Lorentz's transformation formulae for
charge density and
current density. He went on to sketch a model of gravitation (incl.
gravitational waves) which might be compatible with the transformations. It was Poincaré who, for the first time, used the term "Lorentz transformation", and he gave them a form which is used up to this day. (Where \ell is an arbitrary function of \varepsilon, which must be set to unity to conserve the group characteristics. He also set the speed of light to unity.) :x^\prime = k\ell\left(x + \varepsilon t\right), \qquad y^\prime = \ell y, \qquad z^\prime = \ell z, \qquad t^\prime = k\ell\left(t + \varepsilon x\right) :k = \frac 1 {\sqrt{1-\varepsilon^2}} A substantially extended work (the so-called "Palermo paper") was submitted by Poincaré on 23 July 1905, but was published in January 1906 because the journal appeared only twice a year. He spoke literally of "the postulate of relativity", he showed that the transformations are a consequence of the
principle of least action; he demonstrated in more detail the group characteristics of the transformation, which he called
Lorentz group, and he showed that the combination x^2+ y^2+ z^2- c^2t^2 is invariant. While elaborating his gravitational theory, he noticed that the Lorentz transformation is merely a rotation in
four-dimensional space about the origin by introducing ct\sqrt{-1} as a fourth, imaginary, coordinate, and he used an early form of
four-vectors. However, Poincaré later said the translation of physics into the language of four-dimensional geometry would entail too much effort for limited profit, and therefore he refused to work out the consequences of this notion. This was later done, however, by Minkowski; see "
The shift to relativity".
Electromagnetic mass J. J. Thomson (1881) and others noticed that electromagnetic energy contributes to the mass of charged bodies by the amount m=(4/3)E/c^2, which was called electromagnetic or "apparent mass". Another derivation of some sort of
electromagnetic mass was conducted by Poincaré (1900). By using the
momentum of electromagnetic fields, he concluded that these fields contribute a mass of E_{em}/c^2 to all bodies, which is necessary to save the
center of mass theorem. As noted by Thomson and others, this mass increases also with velocity. Thus in 1899, Lorentz calculated that the ratio of the electron's mass in the
moving frame and that of the aether frame is k^3 \varepsilon parallel to the direction of motion, and k\varepsilon perpendicular to the direction of motion, where k = \sqrt{1- v^2 / c^2} and \varepsilon is an undetermined factor. The concept of electromagnetic mass is not considered anymore as the cause of mass
per se, because the entire mass (not only the electromagnetic part) is proportional to energy, and can be
converted into different forms of energy, which is explained by Einstein's
mass–energy equivalence.
Gravitation Lorentz's theories In 1900 Lorentz tried to explain gravity on the basis of the Maxwell equations. He first considered a
Le Sage type model and argued that there possibly exists a universal radiation field, consisting of very penetrating em-radiation, and exerting a uniform pressure on every body. Lorentz showed that an attractive force between charged particles would indeed arise, if it is assumed that the incident energy is entirely absorbed. This was the same fundamental problem which had afflicted the other Le Sage models, because the radiation must vanish somehow and any absorption must lead to an enormous heating. Therefore, Lorentz abandoned this model. In the same paper, he assumed like
Ottaviano Fabrizio Mossotti and
Johann Karl Friedrich Zöllner that the attraction of opposite charged particles is stronger than the repulsion of equal charged particles. The resulting net force is exactly what is known as universal gravitation, in which the
speed of gravity is that of light. This leads to a conflict with the law of gravitation by Isaac Newton, in which it was shown by
Pierre Simon Laplace that a finite speed of gravity leads to some sort of aberration and therefore makes the orbits unstable. However, Lorentz showed that the theory is not concerned by Laplace's critique, because due to the structure of the Maxwell equations only effects in the order
v2/
c2 arise. But Lorentz calculated that the value for the perihelion advance of Mercury was much too low. He wrote: In 1908 Poincaré examined the gravitational theory of Lorentz and classified it as compatible with the relativity principle, but (like Lorentz) he criticized the inaccurate indication of the perihelion advance of Mercury. Contrary to Poincaré, Lorentz in 1914 considered his own theory as incompatible with the relativity principle and rejected it.
Lorentz-invariant gravitational law Poincaré argued in 1904 that a propagation speed of gravity which is greater than c is contradicting the concept of local time and the relativity principle. He wrote: However, these attempts were superseded because of Einstein's theory of
general relativity, see "
The shift to relativity". The non-existence of a generalization of the Lorentz ether to gravity was a major reason for the preference for the spacetime interpretation. A viable generalization to gravity has been proposed only 2012 by Schmelzer. The
preferred frame is defined by the
harmonic coordinate condition. The gravitational field is defined by density, velocity and stress tensor of the Lorentz ether, so that the harmonic conditions become
continuity and Euler equations. The
Einstein Equivalence Principle is derived. The
Strong Equivalence Principle is violated, but is recovered in a limit, which gives the Einstein equations of general relativity in harmonic coordinates. == Principles and conventions ==