My watch list
my.chemeurope.com

# Lorentz ether theory

What is now called Lorentz Ether theory ("LET") has its roots in Hendrik Lorentz's "Theory of electrons", which was the final point in the development of the classical aether theories at the end of the 19th and at the beginning of the 20th century. An extension of the theory was developed in particular by Henri Poincaré, who coined the name "The New Mechanics" for Lorentz's theory. One of its features was to explain why no experiments had been able to detect any motion relative to an immobile aether, which was done by introducing the Lorentz transformation. 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. Introducing the effects of length contraction and time dilation in a "preferred" frame of reference leads to the Lorentz transformation and therefore it is not possible to distinguish between LET and SR by experiment. However, in LET the existence of an undetectable ether is assumed and the validity of the relativity principle seems to be only coincidental, which is one reason why SR is commonly preferred over LET.

## Historical development

### Basic concept

Ether and electrons

This 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.[1] Lorentz introduced a strict separation between matter (electrons) and ether, whereby in his model the ether is completely motionless, and it won't be set in motion in the neighbourhood of ponderable matter. 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 ether with the absolute space of Isaac Newton.[2] The condition of this ether can be described by the electric field E and the magnetic field H, where these fields represent the "states" of the ether (with no further specification), related to the charges of the electrons. Thus an abstract electromagnetic ether replaces the older mechanistic ether models. Contrary to Clausius, who accepted that the electrons operate by actions at a distance, the electromagnetic field of the ether 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. It must be empathized that Joseph Larmor found a similar theory simultaneously, but his concept was based on a mechanical ether.[3]

Corresponding states

A fundamental concept of Lorentz's theory in 1895[4] was the "theorem of corresponding states" for terms of order v/c. This theorem states that a moving observer (relative to the ether) in his „fictitious“ field makes the same observations as a resting observers in his „real“ field. This theorem was extended for terms of all orders by Lorentz (1904)[5] and completed by Poincaré (1905, 1906)[6][7] and by Lorentz (1906, 1916)[8] in order to obey the principle of relativity.

### Length contraction

A big challenge for this theory was the Michelson–Morley experiment in 1887. According to the theories of Fresnel and Lorentz a relative motion to an immobile ether had to be determined by this experiment, however, the result was negative. [9]

In 1888 Oliver Heaviside derived from the Maxwell equations that the electrostatic field around a moving, spherical body is contracted in the line of motion by the factor $\sqrt{1- v^2 / c^2}$.[10] To bring the hypothesis of an immobile ether in accordance with the Michelson–Morley experiment, George FitzGerald in 1889[11] (qualitatively) and independently of him Lorentz in 1892[12] (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 v2 / (2c2) 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[4] Lorentz proposed three possible explanation for this relative contraction:[13]

• 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.

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 ether) was given by Larmor in 1897[3] and by Lorentz in 1904.[5]

### Local time

An important part of the theorem of corresponding states was the local time t' = tvx / c2, where t is the time coordinate for an observer resting in the ether, and t' is the time coordinate for an observer moving in the ether. (Woldemar Voigt used the same expression for local time already in 1887[14] in connection with the Doppler effect and an incompressible medium.) 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. With the help of this concept Lorentz could explain the aberration of light, the Doppler effect and the measurements of the Fresnel drag coefficient by Hippolyte Fizeau in moving and resting liquids as well.

In contrast, Poincaré saw more than a mathematical trick in the definition of local time, which he called Lorentz's "most ingenious idea".[15] In 1898 he wrote:[16]

 “ We do not have a direct intuition for simultaneity, just as little as for the equality of two periods. If we believe to have this intuition, it is an illusion. We helped ourselves with certain rules, which we usually use without giving us account over it [...] We choose these rules therefore, not because they are true, but because they are the most convenient, and we could summarize them while saying: „The simultaneity of two events, or the order of their succession, the equality of two durations, are to be so defined that the enunciation of the natural laws may be as simple as possible. In other words, all these rules, all these definitions are only the fruit of an unconscious opportunism.“[17] ”

In 1900 Poincaré interpreted local time as the result of a synchronisation procedure based on light signals. He assumed that 2 observers A and B which are moving in the ether, synchronize their clocks by optical signals. Since they believe to be at rest they must consider only the transmission time of the signals and than crossing their observations to examine whether their clocks are synchronous. However, from the point of view of an observer at rest in the ether the clocks are not synchronous and indicate the local time t' = tvx / c2. But because the moving observers don't know anything about their movement, they don't recognize this.[18] In 1904 he illustrated the same procedure in the following way: A sends a signal at the time 0 to B, which arrives at the time t. B also sends a signal at the time 0 to A, which arrives at the 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 ether. So according to Darrigol[19] and Jannsen,[20] Poincaré understood local time as a physical effect just like length contraction - in contrast to Lorentz, who used the same interpretation not before 1906. However, contrary to Einstein, who later used a similar synchronisation procedure which was called Einstein synchronisation, he still was the opinion that only clocks resting in the ether are showing the „true“ time.[15]

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),[3] who wrote that "individual electrons describe corresponding parts of their orbits in times shorter for the [ether] system in the ratio $\varepsilon^{-1/2}$ or (1 − (1 / 2)v2 / c2)". And in 1899[21] also Lorentz noticed 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 ether frame, k is $\sqrt{1- v^2 / c^2}$, and $\varepsilon$ is an undetermined factor. [20]

### Lorentz transformation

Further information: History of lorentz transformations

In 1887[14] Voigt derived a similar form of equations (with a wrong scale factor), which later were known as the Lorentz transformation. Based on his theorem of corresponding states, also Lorentz in 1895[4] was in possession of the first order variant of those equations. Larmor in 1897[3] and Lorentz in 1899[21] adjusted them to account for second order effects and gave them a algebraically equivalent form to those, which are used up to this day (however, Lorentz used an undetermined factor l in his transformation). In 1904[5] Lorentz came very near to create such a theory, where all forces between the molecules, whatever their nature may be, are affected by the Lorentz transformation (in which Lorentz set the factor l to unity) in the same manner as electrostatic forces. This step had become necessary due to other unsuccessful ether drift experiments like the Trouton–Noble experiment.

However, on 5 Juni 1905[7] Poincaré showed that Lorentz equations of electrodynamics were not fully Lorentz covariant. So by pointing out the group characteristics of the transformation Poincaré demostrated the Lorentz covariance of the Maxwell-Lorentz equations by correcting Lorentz's formulae for the transformations of charge density and current density. He also sketched a model of gravitation (incl. gravitational waves) which might be compatible with the transformations. Poincaré used for the first time 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“)[6] was submitted by Poincaré on 23 July 1905, but was published on January 1906, because the journal only appeared two times in 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 x2 + y2 + z2c2t2 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 metry would entail too much effort for limited pro?t, and therefore he refused to work out the consequences of this notion.[22] This was later done by Minkowski, see "The shift to relativity".

### Principles and conventions

#### Light postulate

Already in his philosophical writing on time measurements (1898)[16] Poincaré wrote that astronomers like Ole Rømer, in determining the speed of light, simply assume that light has a constant speed, and that this speed is the same in all directions. Without this postulate it would not be possible to infer the speed of light from astronomical observations, as Rømer did based on observations of the moons of Jupiter. Poincaré went on to note that Rømer also had to assume that Jupiter's moons obey Newton's laws, including the law of gravitation, whereas it would be possible to reconcile a different speed of light with the same observations if we assumed some different (probably more complicated) laws of motion. According to Poincaré, this illustrates that we adopt for the speed of light a value that makes the laws of mechanics as simple as possible. (This is an example of Poincaré's conventionalist philosophy.) Poincaré also noted that the propagation speed of light can be (and in practice often is) used to define simultaneity between spatially separate events. However, in that paper he did not go on to discuss the consequences of applying these "conventions" to multiple relatively moving systems of reference. This next step was done by Poincaré in 1900,[18] when he recognized that synchronisation by light signals in earth's reference frame leads to Lorentz's local time. (See the section on "local time" above).

#### Principle of relativity

Already in 1895[23] Poincaré argued that experiments like that of Michelson-Morley show that it seems to be impossible to detect the absolute motion of matter or the relative motion of matter in relation to the ether. And although most physicists at this time believed that the "principle of relative motion" was incompatible with the ether, Poincaré stated in 1900[24] that he did not believe that the relative speed of the earth to the ether will ever be measured. In 1904[15] he appreciated the work of the mathematicians, who saved what he now called the "principle of relativity" with the help of hypotheses like local time, but he confessed that this venture was possible only by an accumulation of hypotheses. And he defined the principle in this way:

 “ The principle of relativity, according to which the laws of physical phenomena must be the same for a stationary observer as for one carried along in a uniform motion of translation, so that we have no means, and can have none, of determining whether or not we are being carried along in such a motion. ”

Referring to a critique of Poincaré in 1900,[24] who said that it would be better to create a more fundamental theory than to create one hypothesis after the other, Lorentz wrote in his famous paper in 1904, where he extended his theorem of corresponding states:[5]

 “ [p.811] Surely, the course of inventing special hypotheses for each new experimental result is somewhat artificial. It would be more satisfactory, if it were possible to show, by means of certain fundamental assumptions, and without neglecting terms of one order of magnitude or another, that many electromagnetic actions are entirely independent of the motion of the system. ”

One of the first assessments of Lorentz's paper was by Paul Langevin in May 1905.[25] According to him, this extension of the electron theories of Lorentz and Larmor led to "the physical impossibility to demonstrate the translational motion of the earth". Although Poincaré showed in 1905,[7] that Lorentz didn't completed his task, he attributed this postulate to Lorentz:

 “ [p. 489]: It appears that this impossibility of demonstrating the absolute motion of the earth is a general law of nature. [..] Lorentz tried to complete and modify his hypothesis in order to harmonize it with the postulate of complete impossibility of determining absolute motion. He has succeeded in doing so in his article [Lorentz, 1904b].[26] ”

In the Palermo paper (1906), Poincaré called this "the postulate of relativity“, and although he stated that it was possible this principle might be disproved at some point (and in fact he mentioned at the paper's end that the discovery of magneto-cathode rays seems to threaten it), he believed it was interesting to consider the consequences if we were to assume the postulate of relativity was valid without restriction. This would imply that all forces of nature (not just electromagnetism) must be invariant under the Lorentz transformation.[6] In 1921 Lorentz credited Poincaré for establishing the principle and postulate of relativity and wrote:[27]

 “ I have not established the principle of relativity as rigorously and universally true. Poincaré, on the other hand, has obtained a perfect invariance of the electro-magnetic equations, and he has formulated 'the postulate of relativity', terms which he was the first to employ.[28] ”

#### Ether

Poincaré wrote in the sense of his conventionalist philosophy in 1889: [29]

 “ Whether the ether exists or not matters little - let us leave that to the metaphysicians; what is essential for us is, that everything happens as if it existed, and that this hypothesis is found to be suitable for the explanation of phenomena. After all, have we any other reason for believing in the existence of material objects? That, too, is only a convenient hypothesis; only, it will never cease to be so, while some day, no doubt, the ether will be thrown aside as useless. ”

He also denied the existence of absolute space and time by saying in 1901:[30]

 “ 1. There is no absolute space, and we only conceive of relative motion ; and yet in most cases mechanical facts are enunciated as if there is an absolute space to which they can be referred. 2. There is no absolute time. When we say that two periods are equal, the statement has no meaning, and can only acquire a meaning by a convention. 3. Not only have we no direct intuition of the equality of two periods, but we have not even direct intuition of the simultaneity of two events occurring in two different places. I have explained this in an article entitled "Mesure du Temps" [1898]. 4. Finally, is not our Euclidean geometry in itself only a kind of convention of language? ”

However, Poincaré himself never abandoned the ether hypothesis and stated in 1900,[24] that the ether is needed to explain where the ray of light is after leaving the source and before reaching the receiver. In order not to give up the comfort of the simplicity of the mechanical laws of nature and because in mechanics all conditions must be determined by preceding conditions, a material carrier is needed. And although he admitted the relative and conventional character of space and time, he believed that the classical convention is more "convenient" and continued to distinguish between "true" time in the ether and "apparent" time in moving systems. Adressing the question if a new convention of space and time is needed he wrote in 1912:[31]

 “ Shall we be obliged to modify our conclusions? Certainly not; we had adopted a convention because it seemed convenient and we had said that nothing could constrain us to abandon it. Today some physicists want to adopt a new convention. It is not that they are constrained to do so; they consider this new convention more convenient; that is all. And those who are not of this opinion can legitimately retain the old one in order not to disturb their old habits, I believe, just between us, that this is what they shall do for a long time to come. ”

Also Lorentz argued during his lifetime that in all frames of reference this one has to be preferred, in which the ether is at rest. Clocks in this frame are showing the "real“ time and simultaneity is not relative. However, if the correctness of the relativity principle is accepted, it is impossible to find this system by experiment.[32]

### Mass, energy and speed

#### Rest mass and energy

It was recognized by J. J. Thomson in 1881[33] that a charged body is harder to set in motion than an uncharged body, which was worked out on more detail by Heaviside (1889) and George Frederick Charles Searle (1896).[34] So the electrostatic energy behaves as having some sort of electromagnetic mass, which can increase the normal mechanical mass of the bodies. This was discussed in connection with the proposal of the electrical origin of matter, and Wilhelm Wien (1900),[35] Max Abraham (1902),[36] and Lorentz (1904)[5] came to the conclusion that the total mass of the bodies is identical to its electromagnetic mass. And because the em-mass depends on the em-energy, the formula for the energy-mass-relation given by Wien (1900) was m = (4 / 3)E / c2 (Abraham and Lorentz used similar expressions). Wien stated, that if it is assumed that gravitation is an electromagnetic effect too, than there has to be a proportionality between em-energy, inertial mass and gravitational mass. However, it was not recognized that energy can transport inertia from one body to another and that mass can be converted into energy, which was explained by Einstein's mass–energy equivalence - see „The shift to relativity“.

The idea of an electromagnetic nature of matter had to be given up, however, in the course of the development of relativistic mechanics. It turned out that different results occurred, dependent on whether the em-mass is calculated from the energy or from the momentum, and the 4/3-factor had to be compensated as well. To solve those problems, and also to explain the stability of Lorentz's matter-electron configuration, Poincaré in 1905[7] and 1906[6] introduced some sort of pressure of non-electrical nature, which contributes the amount − (1 / 3)E / c2 to the mass of the bodies, and therefore the 4/3-factor vanishes. Max von Laue showed in 1910 that Poincaré's model is only one of many possible compensation mechanisms.[20]

#### Mass and speed

Thomson, Heaviside and Searle also noticed that inertia depends on the speed of the bodies as well. In 1899 Lorentz calculated that the ratio of the electron masses of the moving frame and the ether 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. Lorentz wrote in 1899 by using the term „ions“ for the basic constituents of matter: [21]

 “ [p. 442]: states of motion, related to each other in the way we have indicated, will only be possible if in the transformation of S0 into S the masses of the ions change; even this must take place in such a way that the same ion will have different masses for vibrations parallel and perpendicular to the velocity of translation. ”

This theory was further developed by Abraham (1902), who first used the terms longitudinal and transverse mass for Lorentz's two masses. However, Abraham's expressions were more complicated than those of Lorentz.[36] Lorentz himself expanded his 1899 ideas in his famous 1904 paper, where he set the factor $\varepsilon$ to unity.[5] So, according to this theory no body can reach the speed of light because the mass becomes infinitely large at this velocity. The predictions of those theories were supported by the experiments of Walter Kaufmann (1902), but the experiments were not precise enough, to distinguish between them.[37]

Poincaré wrote in 1904, that because of the variability of mass the conservation of mass isn't valid anymore. In a later edition of his book Science and Hypothesis in 1906 he concluded that in case matter is of electromagnetic origin, and because matter and mass are inseparably connected, matter doesn't exist at all and electrons are only concavities in the ether. In 1908 Poincaré illustrated this kind of inertia by a body which moves in a liquid. If the body changes the direction it suffers resistance, afterwards it moves in straight lines, because the resistance is compensated by some sort of wake (in that case the electromagnetic fields). With each acceleration this energy must be supplied too.[38]

The mass concept of Lorentz (incl. longitudinal and transverse mass) was incorporated into special relativity by Einstein (1905)[39] and Max Planck (1906).[40] In 1905 Kaufmann conducted another series of experiments, which confirmed Abraham's theory, but contradicted what Kaufmann called the "Lorentz-Einstein theory".[41] However, in the following years experiments by Bucherer (1908) and others confirmed Lorentz's mass formula.[42] Later a similar concept was also used as relativistic mass by reputable physicists like Max Born[2] and Wolfgang Pauli[43] and is sometimes used in physics textbooks up to this day, although the expression invariant mass is preferred.

#### Inertia of energy

James Clerk Maxwell (1874) [44] and Adolfo Bartoli (1876) [45] found out that the existence of tensions in the ether like the radiation pressure follows from the electromagnetic theory. Lorentz recognized in 1895[4] that this is also the case in his theory. So if the ether is able to set bodies in motion, the action/reaction principle demands that the ether must be set in motion by matter as well. However, Lorentz pointed out the this is impossible, because any tension in the ether requires the mobility of the ether parts, which in not possible in his immobile ether. This represents a violation of the reaction principle which was accepted by Lorentz consciously. He continued by saying, that one can only speak about fictitious tensions, since they are only mathematical models in his theory to ease the description of the electrodynamic interactions.

In 1900[18] Poincaré studied the conflict between the action/reaction principle and Lorentz's theory. He tried to determine whether the center of gravity still moves with a uniform velocity when electromagnetic fields are included. He noticed that the action/reaction principle does not hold for matter alone, but that the electromagnetic field has its own momentum. The electromagnetic field energy behaves like a fictitious fluid („fluide fictif“) with a mass density of E / c2 (in other words m = E / c2). If the center of mass frame (COM-frame) is defined by both the mass of matter and the mass of the fictitious fluid, and if the fictitious fluid is indestructible - it's neither created or destroyed - then the motion of the center of mass frame remains uniform. But electromagnetic energy is not indestructible and can be converted into other forms of energy, and therefore loses its mass (which was the reason why Poincaré regarded em-energy as a "fictitious" fluid rather than a "real" fluid). So Poincaré assumed that there exists a non-electric energy fluid at each point in the ether, into which electromagnetic energy can be transformed and which also carries a mass proportional to the energy. In this way, the motion of the COM-frame (incl. matter, em-energy and non-electrical energy) remains uniform. Poincaré said that one should not be too surprised by these assumptions, since they are only mathematical fictions.

But Poincaré's resolution led to a paradox when changing frames: if a Hertzian oscillator radiates in a certain direction, it will suffer a recoil from the inertia of the fictitious fluid. In the framework of Lorentz's theory Poincaré performed a Lorentz boost to the frame of the moving source. He noted that energy conservation holds in both frames, but that the law of conservation of momentum is violated. This would allow perpetual motion, a notion which he abhorred. The laws of nature would have to be different in the frames of reference, and the relativity principle would not hold.[19]

Poincaré came back to this topic in „Science and Hypothesis“ (1902) and „The Value of Science“ (1905). This time he rejected the possibility that energy carries mass and thereby rejected his own solution, that motions in the ether can compensate the motion of matter:[15]

 “ What then will happen according to the theory? The apparatus will recoil as if it were a cannon and the projected energy a ball, and that contradicts the principle of Newton, since our present projectile has no mass; it is not matter, it is energy. ”

Besides this radiation paradox (1) he also discussed two other problematic effects: (2) non-conservation of mass implied by Abraham's and Lorentz's theory of variable mass, and Kaufmann's experiments on the mass of fast moving electrons and (3) the non-conservation of energy in the radium experiments - however, for the latter he cited William Ramsay's proposal that radium is transformed because it contains an enormous amount of energy. Even in 1908, he rejected the idea that energy is carrying mass and used the same arguments as in 1904 in order to show that the reaction principle is not valid in the new mechanics.[38] Those problems were later solved through Einstein's mass–energy equivalence - see "The shift to relativity".

Following Poincaré, Abraham introduced the term „electromagnetic momentum“ to maintain the reaction principle, whereby the field density per cm3 is E / c2 and E / c per cm2.[36] In 1904, Friedrich Hasenöhrl concluded that radiation contributes to the inertia of bodies, and inertia depends on temperature as well.[46] He derived the formula m = (8 / 3)E / c2, where m is the "apparent mass" due to radiation. This was corrected in 1905 by Abraham and him to m = (4 / 3)E / c2 (the same formula as for the electromagnetic mass, see section „Mass and speed“).

### Gravitation

#### Lorentz's theories

In 1900[47] 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 an universal radiation field, consisting of very penetrating em-radiation, and exerting an 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:

 “ The special form of these terms may perhaps be modified. Yet, what has been said is sufficient to show that gravitation may be attributed to actions which are propagated with no greater velocity than that of light. ”

In 1908[38] 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.[48]

#### 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: [15]

 “ What would happen if we could communicate by signals other than those of light, the velocity of propagation of which differed from that of light? If, after having regulated our watches by the optimal method, we wished to verify the result by means of these new signals, we should observe discrepancies due to the common translatory motion of the two stations. And are such signals inconceivable, if we take the view of Laplace, that universal gravitation is transmitted with a velocity a million times as great as that of light? ”

However, in 1905 and 1906 Poincaré pointed out the possibility of a gravitational theory, in which changes propagate with the speed of light and which is Lorentz covariant. He pointed out that in such a theory the gravitational force not only depends on the masses and their mutual distance, but also on their velocities and their position due to the finite propagation time of interaction. On that occasion Poincaré introduced four-vectors.[7] Following Poincaré, also Minkowski (1908) and Arnold Sommerfeld (1910) tried to establish a lorentz-invariant gravitational law.[22] However, these attempts were superseded because of Einstein's theory of general relativity, see "The shift to relativity".

### The shift to relativity

#### Special relativity

Main article: History of special relativity

In 1905, Albert Einstein published his paper on what is now called special relativity.[39] In this paper, by examining the fundamental meanings of the space and time coordinates used in physical theories, Einstein showed that the "effective" coordinates given by the Lorentz transformation were in fact the inertial coordinates of relatively moving frames of reference. From this followed all of the physically observable consequences of LET, along with others, all without the need to postulate an unobservable entity (the ether). Einstein identified two fundamental principles, each founded on experience, from which all of Lorentz's electrodynamics follows:

1. that the laws by which physical processes occur are the same with respect to any system of inertial coordinates (the principle of relativity), and
2. that light propagates at an absolute speed of c in terms of any system of inertial coordinates ("principle of the constancy of light“)

Taken together (along with a few other tacit assumptions such as isotropy and homogeneity of space), these two postulates lead uniquely to the mathematics of special relativity. Lorentz and Poincare had also adopted these same principles, as necessary to achieve their final results, but didn't recognize that they were also sufficient, and hence that they obviated all the other assumptions underlying Lorentz's initial derivations (many of which later turned out to be incorrect [49]). Therefore, special relativity very quickly gained wide acceptance among physicists, and the 19th century concept of a luminiferous ether was no longer considered useful.

Einstein's 1905 presentation of special relativity was soon supplemented, in 1907, by Hermann Minkowski, who showed that the relations had a very natural interpretation in terms of a unified four-dimensional "spacetime" in which absolute intervals are seen to be given by an extension of the Pythagorean theorem. (Already in 1906 Poincaré anticipated some of Minkowski's ideas, see the section "Lorentz-transformation"). [50] The naturalness and utility of the representation by Einstein and Minkowski contributed to the rapid acceptance of special relativity, and to the corresponding loss of interest in Lorentz's ether theory.

Lorentz argued in 1913, that there is little difference between his ether theory and the negation of a preferred reference frame, as in the theory of Einstein and Minkowski, and therefore according to him it is a matter of taste which theory one prefers.[32] However, in 1907 Einstein criticized the "ad hoc" character of Lorentz's contraction hypothesis in his theory of electrons, because according to him it was only invented to rescue the hypothesis of an immobile ether. Einstein thought it necessary to replace Lorentz's theory of electrons by assuming that Lorentz's "local time" can simply be called "time", and he stated that the immobile ether as the theoretical fundament of electrodynamics was unsatifactory.[51] Minkowski ironically said that for Lorentz the contraction hypothesis is only a "gift from above". And although Lorentz's hypothesis is "completely equivalent with the new concept of space and time", Minkowski held that it becomes much more comprehensible in the framework of the new spacetime physics.

#### Mass–energy equivalence

It was derived by Einstein (1905) as a consequence of the relativity principle, that inertia of energy is actually represented by E / c2, but in contrast to Poincaré's 1900-paper Einstein recognized, that matter itself loses or gain mass during the emission or absorption.[52] So the mass of any form of matter is equal to a certain amount of energy, which can converted into and re-converted from other forms of energy. This is the mass–energy equivalence, represented by E = mc2. So Einstein didn't have to introduce "fictitious" masses and also avoided the perpetual motion problem, because according to Darrigol[19], Poincaré's radiation paradox can simply be solved by applying Einstein's equivalence. If the light source loses mass during the emission by E / c2, the contradiction in the momentum law vanishes.

Similar to Poincaré, Einstein concluded in 1906 that the inertia of (electromagnetic) energy is a necessary condition for the center of mass theorem to hold in systems, in which electromagnetic fields and matter are acting on each other. Based on the mass–energy equivalence he showed that emission and absorption of em-radiation and therefore the transport of inertia solves the problem. On that occasion, Einstein referred to Poincaré's 1900-paper and wrote:[53]

 “ Although the simple formal views, which must be accomplished for the proof of this statement, are already mainly contained in a work by H. Poincaré [Lorentz-Festschrift, p. 252, 1900], for the sake of clarity I won't rely on that work.[54] ”

Also Poincaré's rejection of the reaction principle due to the violation of the mass conservation law can be avoided through Einstein's E = mc2, because mass conservation appears as a special case of the energy conservation law.

#### General relativity

Main article: History of general relativity

The attempts of Lorentz and Poincaré (and other attempts like those of Abraham and Gunnar Nordström) to formulate a theory of gravitation, were superseded by Einstein's theory of general relativity. [22] This theory is based on principles like the equivalence principle, the general principle of relativity, the principle of general covariance, geodesic motion, local Lorentz invariance (the laws of special relativity apply locally for all inertial observers), and that spacetime curvature is created by stress-energy within the spacetime.

In 1920 Einstein compared Lorentz's ether with the "gravitational ether" of general relativity. He said that immobility is the only mechanical property of which the ether has not been deprived by Lorentz, but contrary to the luminiferous and Lorentz's ether the ether of general relativity has no mechanical property, not even immobility:[55]

 “ The ether of the general theory of relativity is a medium which is itself devoid of all mechanical and kinematical qualities, but helps to determine mechanical (and electromagnetic) events. What is fundamentally new in the ether of the general theory of relativity as opposed to the ether of Lorentz consists in this, that the state of the former is at every place determined by connections with the matter and the state of the ether in neighbouring places, which are amenable to law in the form of differential equations; whereas the state of the Lorentzian ether in the absence of electromagnetic fields is conditioned by nothing outside itself, and is everywhere the same. The ether of the general theory of relativity is transmuted conceptually into the ether of Lorentz if we substitute constants for the functions of space which describe the former, disregarding the causes which condition its state. Thus we may also say, I think, that the ether of the general theory of relativity is the outcome of the Lorentzian ether, through relativation. ”

#### Priority

Main article: Relativity priority dispute
Lorentz

In a paper that was written in 1914 and published in 1921,[56] Lorentz appreciated the Palermo paper (1906)[6] of Poincaré on relativity. Lorentz stated:

 “ Indeed I have not given the most appropriate transformation for some physical quantities encountered in the formulae. This was done by Poincaré and later by Einstein and Minkowski. [..] I had not thought of the straight path leading to them, since I considered there was an essential difference between the reference systems x, y, z, t and x', y', z', t'. In one of them were used - such was my reasoning - coordinate axes with a defnite position in ether and what could be termed true time; in the other, on the contrary, one simply dealt with auxiliary quantities introduced with the aid of a mathematical trick. [..] I have not established the principle of relativity as rigorously and universally true. Poincaré, on the other hand, has obtained a perfect invariance of the electro-magnetic equations, and he has formulated 'the postulate of relativity', terms which he was the first to employ. [..] Let's add that while thus correcting the imperfections of my work he never blamed me for them.[57] ”

However, a 1916 reprint of his main work "The theory of electrons"[8] contains notes (written in 1909 and 1915) in which Lorentz sketched the differences between his results and that of Einstein as follows:

 “ [p. 230]: the chief difference [is] that Einstein simply postulates what we have deduced, with some difficulty and not altogether satisfactorily, from the fundamental equations of the electromagnetic field. [p. 321]: The chief cause of my failure was my clinging to the idea that the variable t only can be considered as the true time and that my local time t' must be regarded as no more than an auxiliary mathematical quantity. In Einstein's theory, on the contrary, t' plays the same part as t; if we want to describe phenomena in terms of x', y', z', t' we must work with these variables exactly as we could do with x, y, z, t. ”

Regarding the fact, that in this book Lorentz only mentioned Einstein and not Poincaré in connection with a) the synchronisation by light signals, b) the reciprocity of the Lorentz transformation, and c) the relativistic transformation law for charge density, Janssen comments:[20]

 “ [p.90]: My guess is that it has to do with the fact that Einstein made the physical interpretation of the Lorentz transformation the basis for a remarkably clear and simple discussion of the electrodynamics of moving bodies, whereas Poincaré’s remarks on the physical interpretation of Lorentz transformed quantities may have struck Lorentz as inconsequential philosophical asides in expositions that otherwise closely followed his own. I also have a sense that Lorentz found Einstein’s physically very intuitive approach more appealing than Poincaré’s rather abstract but mathematically more elegant approach. ”

And at a conference on the Michelson-Morley experiment in 1927 at which Lorentz and Michelson were present, Michelson suggested that Lorentz was the initiator of the theory of relativity. Lorentz then replied:[58]

 “ I considered my time transformation only as a heuristic working hypothesis. So the theory of relativity is really solely Einstein's work. And there can be no doubt that he would have conceived it even if the work of all his predecessors in the theory of this field had not been done at all. His work is in this respect independent of the previous theories. ”
Poincaré

Poincaré attributed the development of the new mechanics almost entirely to Lorentz. He only mentioned Einstein in connection with the photoelectric effect, but not in connection with special relativity. For example, in 1912 Poincaré raises the question whether „the mechanics of Lorentz“ will still exist after the development of the quantum theory. He wrote: [59]

 “ In all instances in which it differs from that of Newton, the mechanics of Lorentz endures. We continue to believe that no body in motion will ever be able to exceed the speed of light ; that the mass of a body is not a constant, but depends on its speed and the angle formed by this speed with the force which acts upon the body; that no experiment will ever be able to determine whether a body is at rest or in absolute motion either in relation to absolute space or even in relation to the ether. ”
Einstein

In his well-known „History of the theories of ether and electricity“ from 1953, E. T. Whittaker claimed that relativity is the creation of Lorentz and Poincaré and attributed to Einstein's papers only little importance.[60] However, the predominant majority of the historians of science like Abraham Pais,[61] John Stachel[62] or Olivier Darrigol[19] and physicists like Born[2] or Pauli[43] have other points of view. It's true that Lorentz and Poincaré developed the mathematics of special relativity, and many scientists originally spoke about the „Lorentz-Einstein theory“. But Einstein was the first (contrary to Lorentz and Poincaré) to banish the (classical) ether out of physics, which lead to a fundamental new approach to physics.

Einstein wrote in 1907[51] that one needed only to realize that an auxiliary quantity that was introduced by Lorentz and that he called "local time" can simply be defined as "time." And in 1910[63] and 1912[64] Einstein explained that he borrowed the principle of the constancy of light from Lorentz's immobile ether, but he recognized that this principle together with the principle of relativity makes the ether useless and leads to special relativity. It is also known[65] that he read Poincaré's 1902-book „Science and hypothesis“ before 1905, which included:

• philosophical assessments on the relativity of space, time, and simultaneity
• the opinion that a violation of the relativity principle can never be detected
• the possible non-existence of the ether
• many remarks on the non-Euclidean geometry.

Einstein refers to Poincaré in connection with the inertia of energy in 1906[53] and the non-Euclidean geometry in 1921,[55] but not in connection with the Lorentz transformation, the relativity principle or the synchronisation procedure by light signals. However, in the last years before Einstein's death he acknowledged some of Poincaré's contributions (according to Darrigol, maybe because his biographer Pais in 1950 sent him a copy of Poincarè's Palermo paper, which he hadn't read before). Einstein wrote in 1953:

 “ There is no doubt, that the special theory of relativity, if we regard its development in retrospect, was ripe for discovery in 1905. Lorentz had already recognized that the transformations named after him are essential for the analysis of Maxwell’s equations, and Poincaré deepened this insight still further. Concerning myself, I knew only Lorentz's important work of 1895 [...] but not Lorentz's later work, nor the consecutive investigations by Poincaré. In this sense my work of 1905 was independent. ”

## Recent activity

### Neo-Lorentzian interpretations

Today LET is often treated as some sort of "neo-Lorentzian" interpretation of special relativity. For example, Reza Mansouri and Roman Ulrich Sexl (1977)[66] created a "test theory" of special relativity, in order to establish the framework for examinations about the validity of the Lorentz symmetry and the existence of a preferred frame of reference. By setting the speed of light to unity they chose the following coefficients of the transformation between reference frames:

$t=aT+\varepsilon x$
x = b(XvT)

Where T, X are coordinates measured in the (preferred) ether frame, and t, x are coordinates measured in a moving frame, and therefore 1 / a(v) is time dilation and b(v) is length contraction. By supposing $1/a(v)=b(v)=1/\sqrt{1-v^2}$ the Lorentz transformation follows. Then they discussed different methods of clock synchronisation.

1. Internal clock synchronisation including the Poincaré-Einstein synchronisation and synchronisation by slow clock transport. If it is assumed that time dilation has the exact relativistic value, both methods are equivalent in all reference frames, independent of the question if there is an ether or not.
2. External clock synchronisation by choosing a "preferred" reference frame (like the CMB) and using the clocks of this frame to synchronize the clocks in all other frames. This means that in all frames the clocks are synchronous, nevertheless also in this case the ether theory is equivalent to special relativity, if the effects of time dilation and length contraction have the exact relativistic value.

So Sexl/Mansouri spoke about the "remarkable result that a theory maintaining absolute simultaneity is equivalent to special relativity." However they preferred SRT over an ether theory, because the latter "destroys the internal symmetry of a physical theory".

### Breaking Lorentz symmetry?

However, there are some models, which predict a violation of the Lorentz symmetry and which have some similarity to LET, although they are not the same. Modern measurements empirically seems to discredit such theories. A 2007 study sensitive to 10-16 employed two simultaneous interferometers over a year's observation: Optical in Berlin, Germany at 52°31'N 13°20'E and microwave in Perth, Australia at 31°53'S 115°53E. Such an aether background (leading to Lorentz violation) could never be at rest relative to both of them. [67]

Affine (Einstein-Cartan theory), teleparallelism (Weitzenböck) and noncommutative (Alain connes) gravitation theories wholly contain General Relativity as a restricted case (isotropic vacuum, Equivalence Principle = true). They also allow a Lorentz-violating chiral vacuum background (anisotropic vacuum) in which the Equivalence Principle has parity violations in the mass sector (e.g., enantiomorphic mass distributions - atom locations - in opposite parity space groups P3121 and P3221 chemically identical crystals). This is experimentally unexamined.

## Bibliography

### Primary sources

• Abraham, M. (1902), " ", Göttinger Nachrichten: 20-41
• Abraham, M. (1903), " ", Annalen der Physik 10: 105-179
• Bartoli, A. (1876), " ", Nuovo Cimento (1884) 15: 196-202
• Bucherer, A. H. (1908), " ", Physikalische Zeitschrift 9 (22): 755-762
• Einstein, A. (1905a), " ", Annalen der Physik 17: 891-921 English translation
• Einstein, A. (1905b), " ", Annalen der Physik 18: 639–643 English translation.
• Einstein, A. (1906), " ", Annalen der Physik 20: 627-633
• Einstein, A. (1907), " ", Jahrbuch der Radioaktivität und Elektronik 4: 411-462
• Einstein, A. (1909), " ", Physikalische Zeitschrift 10 (22): 817-825
• Einstein, A. (1912), " ", Annalen der Physik 38: 1059-1064
• Einstein, A. (1922), , London: Methuen & Co. This work includes the English translations of "Ether and the theory of relativity (1920)" and "Geometry and experience (1921)".
• FitzGerald, G.F. (1889), " ", Science 13: 390
• Hasenöhrl, F. (1904), " ", Annalen der Physik 15: 344-370
• Hasenöhrl, F. (1905), " ", Annalen der Physik 16: 589-592
• Heaviside, O. (1888), " ", Electrician 22: 147-148 Reprinted in "Electrical papers II".
• Kaufmann, W. (1902), " ", Physikalische Zeitschrift 4 (1b): 54-56
• Kaufmann, W. (1905), " ", Annalen der Physik (1906) 19: 487-553
• Langevin, P. (1905), " ", Comptes Rendus 140: 1171–1173
• Larmor, J. (1897), " ", Phil. Trans. Roy. Soc. 190: 205-300
• Lorentz, H.A. (1892), , in Zeeman, P., Fokker, A.D., , vol. 4, The Hague: Nijhoff, 1937, pp. 219-223
• Lorentz, H.A. (1895), , Leiden: E.J. Brill
• Lorentz, H.A. (1899), " ", Proc. Roy. Soc. Amst. 1: 427-442
• Lorentz, H.A. (1900), " ", Proc. Roy. Soc. Amst. 2: 559-574
• Lorentz, H.A. (1904a), " ", Encyclopädie der mathematischen Wissenschaften 5 (2): 145-288
• Lorentz, H.A. (1904b), " ", Proc. Roy. Soc. Amst. 6: 809-831
• Lorentz, H.A & Einstein, A. & Minkowski, H. (1913), , Leipzig & Berlin: B.G. Teubner
• Lorentz, H.A (1914), " ", Scientia 16: 28-59
• Lorentz, H.A (1916), , Leipzig & Berlin: B.G. Teubner
• Lorentz, H.A. (1921), " ", Acta Mathematica 38: 293-308 Reprinted in Poincaré, Oeuvres, tome XI, S. 247-261.
• Lorentz, H.A. (1928), " ", The Astrophysical Journal 68: 345-351
• Mansouri R., Sexl R.U. (1977), " ", General. Relat. Gravit. 8 (7): 497–513
• Maxwell, J.C (1873), , London: Macmillan & Co., pp. 391
• Michelson, A. A., Morley, E.W. (1887), " ", American Journal of Science 34: 333-345
• Minkowski, H. (1909), " ", Physikalische Zeitschrift 10: 75-88
• Planck, M. (1906), " ", Deutsche Physikalische Gesellschaft 8: 136–141
• Poincaré, H. (1889), , vol. 1, Paris: G. Carré & C. Naud Preface partly reprinted in "Science and Hypothesis", Ch. 12.
• Poincaré, H. (1895), " ", L'Èclairage électrique 5: 5-14. Reprinted in Poincaré, Oeuvres, tome IX, pp. 395-413
• Poincaré, H. (1898), " ", Revue de métaphysique et de morale 6: 1-13 Reprinted in "The Value of Science", Ch. 2.
• Poincaré, H. (1900), " ", Revue générale des sciences pures et appliquées 11: 1163-1175. Reprinted in "Science and Hypothesis", Ch. 9-10.
• Poincaré, H. (1900), " ", Archives néerlandaises des sciences exactes et naturelles 5: 252-278. Reprinted in Poincaré, Oeuvres, tome IX, pp. 464-488
• Poincaré, H. (1901), " ", Bibliothèque du Congrès international de philosophie: 457-494. Reprinted in "Science and Hypothesis", Ch. 6-7.
• Poincaré, H. (1901), , Paris: Gauthier-Villars
• Poincaré, H. (1902), , London and Newcastle-on-Cyne (1905): The Walter Scott publishing Co.
• Poincaré, H. (1904), " ", Bull. Amer. Math. Soc. (2000) 37: 25-38 Reprinted in "The value of science" (1905a).
• Poincaré, H. (1905a),
• Poincaré, H. (1905b), " ", Comptes Rendus 140: 1504-1508 Reprinted in Poincaré, Oeuvres, tome IX, S. 489-493.
• Poincaré, H. (1906), " ", Rendiconti del Circolo matematico Rendiconti del Circolo di Palermo 21: 129-176 Reprinted in Poincaré, Oeuvres, tome IX, pages 494-550. Partial English translation in Dynamics of the electron.
• Poincaré, H. (1908a), " ", Revue générale des sciences pures et appliquées 19: 386-402 Reprinted in Poincaré, Oeuvres, tome IX, S. 551-586 and in "Science and Method" (1908).
• Poincaré, H. (1908b),
• Poincaré, H. (1909), " ", Comptes Rendus des Sessions de l’Association Française pour l’Avancement des Sciences (Paris): 38-48
• Poincaré, H. (1910), , , Leipzig und Berlin: B.G.Teubner, pp. 41-47
• Poincaré, H. (1911), , Leipzig & Berlin: B.G. Teubner
• Poincaré, H. (1913), , New York: Dover Publication (1963)
• Searle, G.F.C. (1896), " ", Phil. Trans. Roy. Soc. 187: 675-718
• Thomson, J.J. (1881), " ", Phil. Mag. 11: 229
• Voigt, W. (1887), " ", Göttinger Nachrichten (no. 2): 41-51
• Wien, W. (1900), " ", Annalen der Physik (1901) 5: 501-513

### Secondary sources

• Born, M. (1964/2003), , Berlin-Heidelberg-New York: Springer, pp. 172-194, ISBN 3-540-00470-x
• Brown, H. R. (2001), " ", American Journal of Physics 69 (10): 1044-1054
• Darrigol, O. (2000), , Oxford: Clarendon Press, ISBN 0198505949
• Darrigol, O. (2004), " ", Isis 95 (4): 614-626
• Darrigol, O. (2005), " ", Séminaire Poincaré 1: 1-22
• Galison, P. (2003), , New York: W.W. Norton, ISBN 0393326047
• Janssen, M. (Dissertation, 1995): A Comparison between Lorentz's Ether Theory and Special Relativity in the Light of the Experiments of Trouton and Noble: Title/TOC, Intro, Intro (Part I), Chapter 1, Chapter 2, Intro (Part 2), Chapter 3, Chapter 4, References
• Jannsen, M. (2002), " ", Phys. perspect. 4: 421–446
• Jannsen, M., Mecklenburg, M. (2007), , in V. F. Hendricks, et.al., Interactions: Mathematics, Physics and Philosophy (Dordrecht: Springer): 65–134
• Katzir, S. (2005), " ", Phys. perspect. 7: 268–292
• Keswani, G.H., Kilmister, C.W. (1983), " ", Brit. J. Phil. Sci. 34: 343-354
• Macrossan, M. N. (1986), " ", Brit. J. Phil. Sci. 37: 232-234
• Norton, J.D. (2004), " ", Archive for History of Exact Sciences 59: 45-105
• Pais, A. (1982), , New York: Oxford University Press, ISBN 0-19-520438-7
• Pauli, W. (1921), " ", Encyclopädie der mathematischen Wissenschaften 5 (2): 539-776
• Scribner, C. (1964), " ", American Journal of Physics 32: 672–678
• Stachel, J. (2002), , Boston: Birkhäuser, ISBN 0-8176-4143-2
• Walter, S. (2007), , in Renn, J., The Genesis of General Relativity 3: 193–252
• Whittaker, E.T. (1910), , Dublin: Longman, Green and Co., pp. 411-466
• Whittaker, E.T. (1951-1953), , London: Nelson
• Zahar, E. (1973), " ", Brit. J. Phil. Sci. 24 (2): 95-123, 223-262

## Endnotes

1. ^ Whittaker (1910), secondary sources
2. ^ a b c Born (2003), secondary sources
3. ^ a b c d Larmor (1897), primary sources, p. 229
4. ^ a b c d Lorentz (1895), primary sources
5. ^ a b c d e f Lorentz (1904b), primary sources
6. ^ a b c d e Poincaré (1906), primary sources
7. ^ a b c d e Poincaré (1905b), primary sources
8. ^ a b Lorentz (1916), primary sources
9. ^ Michelson (1887), primary sources
10. ^ Heaviside (1888), primary sources
11. ^ Fitzgerald (1889), primary sources
12. ^ Lorentz (1892), primary sources
13. ^ Brown (2001), secondary sources
14. ^ a b Voigt (1887), p. 44, primary sources
15. ^ a b c d e Poincaré (1904); Poincaré (1905a), Ch. 8, primary sources
16. ^ a b Poincaré (1898); Poincaré (1905a), Ch. 2, primary sources
17. ^ Nous n’avons pas l’intuition directe de la simultanéité, pas plus que celle de l’égalité de deux durées. Si nous croyons avoir cette intuition, c’est une illusion. Nous y suppléons à l’aide de certaines règles que nous appliquons presque toujours sans nous en rendre compte. [...] Nous choisissons donc ces règles, non parce qu’elles sont vraies, mais parce qu’elles sont les plus commodes, et nous pourrions les résumer en disant: « La simultanéité de deux événements, ou l’ordre de leur succession, l’égalité de deux durées, doivent être définies de telle sorte que l’énoncé des lois naturelles soit aussi simple que possible. En d’autres termes, toutes ces règles, toutes ces définitions ne sont que le fruit d’un opportunisme inconscient. »
18. ^ a b c Poincaré (1900b), primary sources
19. ^ a b c d Darrigol (2006), secondary sources
20. ^ a b c d Jannsen (1995), Ch. 3, secondary sources
21. ^ a b c Lorentz (1899), primary sources
22. ^ a b c Walter (2007), secondary sources
23. ^ Poincaré (1895), primary sources
24. ^ a b c Poincaré (1900a); Poincaré (1902), Ch. 10, primary sources
25. ^ Langevin (1905), primary sources
26. ^ Il semble que cette impossibilité de démontrer le mouvement absolu soit une loi générale de la nature [..] Lorentz a cherché à more compléter et à more modifier son hypothèse de façon à la mettre en concordance avec le postulate de l' impossibilité complète de la détermination du mouvement absolu. C'est ce qu'il a réussi dans son article intitulé [Lorentz, 1904b]
27. ^ Lorentz (1921), pp. 247-261, primary sources
28. ^ je n'ai pas établi le principe de relativité comme rigoureusement et universellement vrai. Poincaré, au contraire, a obtenu une invariance parfaite des équations de l’électrodynamique, et il a formule le « postulat de relativité » , termes qu’il a été le premier a employer.
29. ^ Poincaré (1889); Poincaré (1902), Ch. 12, primary sources
30. ^ Poincaré (1901a); Poincaré (1902), Ch. 6, primary sources
31. ^ Poincaré (1913), Ch. 2, primary sources
32. ^ a b Lorentz (1913), p. 75, primary sources
33. ^ Thomson (1881), primary sources
34. ^ Searle (1896), primary sources
35. ^ Wien (1900), primary sources
36. ^ a b c Abraham (1902,1903), primary sources
37. ^ Kaufmann (1902), primary sources
38. ^ a b c Poincaré (1908a); Poincaré (1908b), 3rd book, primary sources
39. ^ a b Einstein (1905a), primary sources
40. ^ Planck (1906), primary sources
41. ^ Kaufmann (1905), primary sources
42. ^ Bucherer (1908), primary sources
43. ^ a b Pauli (1921), secondary sources
44. ^ Maxwell (1874), primary sources
45. ^ Bartoli (1876), primary sources
46. ^ Hasenöhrl (1904, 1905), primary sources
47. ^ Lorentz (1900), primary sources
48. ^ Lorentz (1914) primary sources
49. ^ The three best known examples are (1) the assumption of Maxwell's equations, and (2) the assumptions about finite structure of the electron, and (3) the assumption that all mass was of electromagnetic origin. Maxwell's equations were subsequently found to be invalid and were replaced with quantum electrodynamics, although one particular feature of Maxwell's equations, the invariance of a characteristic speed, has remained. The electron's mass is now regarded as a pointlike particle, and Poincare already showed in 1905 that it is not possible for all the mass of the electron to be electromagnetic in origin. This is how relativity invalidated the 19th century hopes for basing all of physics on electromagnetism.
50. ^ Minkowski (1909), primary sources
51. ^ a b Einstein (1907), primary sources
52. ^ Einstein (1905b), primary sources
53. ^ a b Einstein (1906), primary sources
54. ^ Trotzdem die einfachen formalen Betrachtungen, die zum Nachweis dieser Behauptung durchgeführt werden müssen, in der Hauptsache bereits in einer Arbeit von H. Poincaré enthalten sind [Lorentz-Festschrift, p. 252, 1900], werde ich mich doch der Übersichtlichkeit halber nicht auf jene Arbeit stützen.
55. ^ a b Einstein (1922), primary sources
56. ^ Lorentz (1921), pp. 247-261, primary sources
57. ^ En effet, pour certaines des grandeurs physiques qui entrent dans les formules, je n'ai pas indique la transformation qui convient le mieux. Cela a été fait par Poincaré et ensuite par M. Einstein et Minkowski. [..] C'est que je n'avais pas songé a la voie directe qui y conduit, et cela tient a ce que j'avais l’idée qu'il y a une différence essentielle entre les systèmes x, y, z, t et x', y’, z’, t’. Dans l’un on se sert - telle était ma pensée - d'axes des coordonnées qui ont une position fixe dans l’éther et de ce qu'on peut appeler le « vrai » temps; dans l’autre système, au contraire, on aurait affaire a de simples grandeurs auxiliaires dont l’introduction n'est qu'un artifice mathématique. [..] mais je n'ai pas établi le principe de relativité comme rigoureusement et universellement vrai. Poincaré, au contraire, a obtenu une invariance parfaite des équations de l’électrodynamique, et il a formule le « postulat de relativité » , termes qu’il a été le premier a employer. [..] Ajoutons qu'en corrigeant ainsi les imperfections de mon travail il ne me les a jamais reprochées.
58. ^ Lorentz (1928), p. 10, primary sources
59. ^ Poincaré (1913), Ch. 6, primary sources
60. ^ Whittaker (1953), secondary sources
61. ^ Pais (1982), secondary sources
62. ^ Stachel (2002), secondary sources
63. ^ Einstein (1909), primary sources
64. ^ Einstein (1912), primary sources
65. ^ Darrigol (2004), secondary sources, p. 624
66. ^ Mansouri/Sexl (1977), primary sources
67. ^ Physics Today 57(7) 40 (2004), No electromagnetic aether, Lorentz violation models, Lorentz and CPT violation theory, No electromagnetic Lorentz_violation
Non-mainstream
• Logunov, A.A. (2004): Henri Poincaré and relativity theory