What is now often called Lorentz ether theory (LET) has its roots in Hendrik Lorentz's "theory of electrons", which marked the end of the development of the classical aether theories at the end of the 19th and at the beginning of the 20th century.
Lorentz's initial theory was created between 1892 and 1895 and was based on removing assumptions about aether motion. It explained the failure of the negative aether drift experiments to first order in v/c by introducing an auxiliary variable called "local time" for connecting systems at rest and in motion in the aether. In addition, the negative result of the Michelson–Morley experiment led to the introduction of the hypothesis of length contraction in 1892. However, other experiments also produced negative results and (guided by Henri Poincaré's principle of relativity) Lorentz tried in 1899 and 1904 to expand his theory to all orders in v/c by introducing the Lorentz transformation. In addition, he assumed that non-electromagnetic forces (if they exist) transform like electric forces. However, Lorentz's expression for charge density and current were incorrect, so his theory did not fully exclude the possibility of detecting the aether. Eventually, it was Henri Poincaré who in 1905 corrected the errors in Lorentz's paper and actually incorporated non-electromagnetic forces (including gravitation) within the theory, which he called "The New Mechanics". Many aspects of Lorentz's theory were incorporated into special relativity (SR) with the works of Albert Einstein and Hermann Minkowski.
Today LET is often treated as some sort of "Lorentzian" or "neo-Lorentzian" interpretation of special relativity. The introduction of length contraction and time dilation for all phenomena in a "preferred" frame of reference, which plays the role of Lorentz's immobile aether, leads to the complete Lorentz transformation (see the Robertson–Mansouri–Sexl test theory as an example), so Lorentz covariance doesn't provide any experimentally verifiable distinctions between LET and SR. The absolute simultaneity in the Mansouri–Sexl test theory formulation of LET implies that a one-way speed of light experiment could in principle distinguish between LET and SR, but it is now widely held that it is impossible to perform such a test. In the absence of any way to experimentally distinguish between LET and SR, SR is widely preferred over LET, due to the superfluous assumption of an undetectable aether in LET, and the validity of the relativity principle in LET seeming ad hoc or coincidental.
Historical development
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.Whittaker (1951), 386ff 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.Born (1964), 172ff 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 1895Lorentz (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 . 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 1892Lorentz (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 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 Lorentz proposed three possible explanations for this relative contraction:Brown (2001) 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 (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.Miller (1981), 70–75, For further development of this concept, see the section .Lorentz (1904b)
Local time An important part of the theorem of corresponding states in 1892 and 1895 was the local time , where t is the time coordinate for an observer resting in the aether, and t' is the time coordinate for an observer moving in the aether. (Woldemar Voigt had previously used the same expression for local time in 1887 in connection with the Doppler effect and an incompressible medium.) With the help of this concept Lorentz could explain the aberration of light, the Doppler effect and the Fizeau experiment (i.e. measurements of the Fresnel drag coefficient) by Hippolyte Fizeau in moving and also resting liquids. While for Lorentz length contraction was a real physical effect, he considered the time transformation only as a heuristic working hypothesis and a mathematical stipulation to simplify the calculation from the resting to a "fictitious" moving system. Contrary to Lorentz, Poincaré saw more than a mathematical trick in the definition of local time, which he called Lorentz's "most ingenious idea".Poincaré (1904); Poincaré (1905a), Ch. 8 In The Measure of Time he wrote in 1898:Poincaré (1898); Poincaré (1905a), Ch. 2
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 . But because the moving observers don't know anything about their movement, they don't recognize this.Poincaré (1900b) 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,Darrigol (2005), 10–11 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.
However, at the beginning it was unknown that local time includes what is now known as time dilation. This effect was first noticed by Larmor (1897), who wrote that "individual electrons describe corresponding parts of their orbits in times shorter for the [aether] system in the ratio or ". And in 1899Lorentz (1899) also Lorentz noted for the frequency of oscillating electrons "that in S the time of vibrations be times as great as in S0", where S0 is the aether frame, S the mathematical-fictitious frame of the moving observer, k is , and is an undetermined factor.Janssen (1995), Chap. 3.5.4
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 derived equations in a form algebraically equivalent to those which are used up to this day, although Lorentz used an undetermined factor l in his transformation. In his paper Electromagnetic phenomena in a system moving with any velocity smaller than that of light (1904) Lorentz attempted to create such a theory, according to which all forces between the molecules are affected by the Lorentz transformation (in which Lorentz set the factor l to unity) in the same manner as electrostatic forces. In other words, Lorentz attempted to create a theory in which the relative motion of earth and aether is (nearly or fully) undetectable. Therefore, he generalized the contraction hypothesis and argued that not only the forces between the electrons, but also the electrons themselves are contracted in the line of motion. However, Max Abraham (1904) quickly noted a defect of that theory: Within a purely electromagnetic theory the contracted electron-configuration is unstable and one has to introduce non-electromagnetic force to stabilize the electrons – Abraham himself questioned the possibility of including such forces within the theory of Lorentz.