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# 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". 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 electronsThis 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 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 neighborhood 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.Born (1964), 172ff] 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 emphasized that Joseph Larmor found a similar theory simultaneously, but his concept was based on a mechanical ether.Larmor (1897, 1900)]

;Corresponding statesA 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 (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)Lorentz (1904b)] and completed by Poincaré (1905, 1906)Poincaré (1906)] Poincaré (1905b)] and by Lorentz (1906, 1916)Lorentz (1916)] 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. Michelson (1887)]

In 1889 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 $sqrt\left\{1- v^2 / c^2\right\}$.Heaviside (1889)] To bring the hypothesis of an immobile ether in accordance with the Michelson–Morley experiment, George FitzGerald in 1889Fitzgerald (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 $v^2/\left(2c^2\right)$ 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 explanation 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.The so called Length contraction without expansion perpendicularly to the line of motion and by the precise value $l=l_0 cdot sqrt\left\{1- v^2 / c^2\right\}$ (where l0 is the length at rest in the ether) was given by Larmor in 1897 and by Lorentz in 1904.

Local time

An important part of the theorem of corresponding states in 1892 and 1895 was the local time $t\text{'}=t - vx / c^2$, 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 1887Voigt (1887), p. 44] 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 Fizeau experiment (i.e. 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".Poincaré (1904); Poincaré (1905a), Ch. 8] In 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 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 then 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 $t\text{'}=t - vx / c^2$. 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 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 DarrigolDarrigol (2005), 10-11] 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.

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 [ether] system in the ratio $varepsilon^\left\{-1/2\right\}$ or $\left(1-\left(1/2\right)v^2/c^2\right)$". And in 1899Lorentz (1899)] also Lorentz noticed for the frequency of oscillating electrons "that in S the time of vibrations be $kvarepsilon$ times as great as in S0", where S0 is the ether frame, k is $sqrt\left\{1- v^2 / c^2\right\}$, and $varepsilon$ is an undetermined factor. Janssen (1995), Chap. 3.5.4]

Lorentz transformation

In 1887 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 was in possession of the first order variant of those equations. Larmor in 1897 and Lorentz in 1899 adjusted them to account for second order effects and gave them an algebraically equivalent form to those, which are used up to this day (however, Lorentz used an undetermined factor "l" in his transformation). In 1904 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 June 1905 Poincaré showed that Lorentz 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 he corrected 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.)

:$x^prime = kellleft\left(x + varepsilon t ight\right), qquad y^prime = ell y, qquad z^prime = ell z, qquad t^prime = kellleft\left(t + varepsilon x ight\right)$:$k = frac 1 \left\{sqrt\left\{1-varepsilon^2$

A substantially extended work (the so called „Palermo paper“) 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 $x^2+ y^2+ z^2- c^2t^2$ 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 $ctsqrt\left\{-1\right\}$ 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. This was later done by Minkowski, see "The shift to relativity".Walter (2007), Kap. 1]

Principles and conventions

Constancy of light

Already in his philosophical writing on time measurements (1898) 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, when he recognized that synchronization by light signals in earth's reference frame leads to Lorentz's local time.Galison (2002)] Miller (1981), 186-189] (See the section on "local time" above). And in 1904 Poincaré wrote:

Principle of relativity

In 1895Poincaré (1895)] Katzir (2005), 275-288] 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 had other views, Poincaré in 1900Poincaré (1900a); Poincaré (1902), Ch. 9-10] stood to his opinion and alternately used the expressions "principle of relative motion" and "relativity of space". He criticized Lorentz by saying, that it would be better to create a more fundamental theory, which explains the absence of any ether drift, than to create one hypothesis after the other. In 1902Poincaré (1902), Ch. 13] he used for the first time the expression "principle of relativity". In 1904 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 (according to MillerMiller (1981), 79] based on Lorentz's theorem of corresponding states): "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 the critique of Poincaré from 1900, Lorentz wrote in his famous paper in 1904, where he extended his theorem of corresponding states: "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.Langevin (1905)] 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". However, Poincaré noticed in 1905 that Lorentz's theory of 1904 was not perfectly "Lorentz invariant" in a few equations such as Lorentz's expression for current density (it was admitted by Lorentz in 1921 that these were defects). As this required just minor modifications of Lorentz's work, also Poincaré asserted that Lorentz had succeeded in harmonizing his theory with the principle of relativity: "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] ."French original: "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] "]

In his 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 by Paul Ulrich Villard (1904) seems to threaten itWalter (2007), Chap. 1] ), 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. In 1921 Lorentz credited Poincaré for establishing the principle and postulate of relativity and wrote:Lorentz (1921), pp. 247-261] "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."French original: "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."]

Ether

Poincaré wrote in the sense of his conventionalist philosophy in 1889: Poincaré (1889); Poincaré (1902), Ch. 12] "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:Poincaré (1901a); Poincaré (1902), Ch. 6] "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: "Does our ether actually exist ? We know the origin of our belief in the ether. If light takes several years to reach us from a distant star, it is no longer on the star, nor is it on the earth. It must be somewhere, and supported, so to speak, by some material agency." And referring to the Fizeau experiment, he even wrote: "The ether is all but in our grasp." He also said the ether is necessary to harmonize Lorentz's theory with Newton's third law. Even in 1912 in a paper called "The Quantum theory", Poincaré ten times used the word "ether", and described light as "luminous vibrations of the ether".Poincaré 1912; Poincaré 1913, Ch. 6]

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. Addressing the question if a new convention of space and time is needed he wrote in 1912:Poincaré (1913), Ch. 2] "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.Lorentz (1913), p. 75]

Mass, energy and speed

Rest mass and energy

It was recognized by J. J. Thomson in 1881Thomson (1881)] 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).Searle (1896)] 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),Wien (1900)] Max Abraham (1902),Abraham (1902, 1903, 1904)] and Lorentz (1904) 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 $m=\left(4/3\right)E/c^2$ (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. Abraham (1903) argued, that non-electrical binding forces were necessary within Lorentz's electrons model. And in 1904 he noticed 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 and 1906 introduced some sort of pressure of non-electrical nature, which contributes the amount $-\left(1/3\right)E/c^2$ to the mass of the bodies, and therefore the 4/3-factor vanishes. Max von Laue showed in 1910 that Poincaré's model is formally correct, but it is only one of many possible and equivalent compensation mechanisms.Janssen/Mecklenburg (2007)]

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 $kvarepsilon$ perpendicular to the direction of motion, where $k = sqrt\left\{1- v^2 / c^2\right\}$ and $varepsilon$ is an undetermined factor. Lorentz wrote in 1899 by using the term „ions“ for the basic constituents of matter:

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. Lorentz himself expanded his 1899 ideas in his famous 1904 paper, where he set the factor $varepsilon$ to unity. 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 (1901), but the experiments were not precise enough, to distinguish between them.Kaufmann (1902, 1906)]

In 1904 Paul Langevin Langevin (1904)] 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). And Poincaré wrote in 1904, that because of the variability of mass the conservation of mass and the aren'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. Poincaré (1902), Ch. 14]

The mass concept of Lorentz (incl. longitudinal and transverse mass) was incorporated into special relativity by Einstein (1905)Einstein (1905a)] and Max Planck (1906).Planck (1906)] In 1905 Kaufmann conducted another series of experiments, which confirmed Abraham's theory, but contradicted what Kaufmann called the "Lorentz-Einstein theory". However, in the following years experiments by Alfred Bucherer (1908), Neumann (1914) and others seemed to confirm Lorentz's mass formula.Bucherer (1908)] However, it was later pointed out, that the Bucherer-Neumann experiments were also not precise enough to distinguish between the theories. So Abraham's theory was disproved not before 1940. Miller (1981), 334-352] Later a similar concept was also used as relativistic mass by reputable physicists like Max BornBorn (1964), 238] and Wolfgang PauliPauli (1921), 634-636] 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) Maxwell (1874)] and Adolfo Bartoli (1876) Bartoli (1876)] found out that the existence of tensions in the ether like the radiation pressure follows from the electromagnetic theory.Lorentz recognized in 1895 that this is also the case in his theory. So if the ether is able to set bodies in motion, the demands that the ether must be set in motion by matter as well. However, Lorentz pointed out that 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 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 $E/c^2$ (in other words $m=E/c^2$). 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. Therefore he argued that also in this case there has to be another compensating mechanism in the ether.ref group=B>Miller (1981), 41ff] Darrigol (2005), 18-21]

Poincaré came back to this topic in 1904. This time rejected his own solution that motions in the ether can compensate the motion of matter, because any such motion is unobservable and therefore scientifically worthless. He also abandoned the concept that energy carries mass and wrote in connection to the above mentioned recoil:

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. 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 $E/c^2$ and $E/c$ per cm2. Contrary to Lorentz and Poincaré, who considered that momentum as a fictitious force, he argued that it is a real physical entity. In 1904, Friedrich Hasenöhrl concluded that radiation contributes to the inertia of bodies, and inertia depends on temperature as well.Hasenöhrl (1904, 1905)] He derived the formula $m=\left(8/3\right)E/c^2$, where m is the "apparent mass" due to radiation. This was corrected in 1905 by Abraham and him to $m=\left(4/3\right)E/c^2$ (the same formula as for the electromagnetic mass, see section „Rest mass and energy“).Miller (1981), 359-360]

Gravitation

Lorentz's theories

In 1900Lorentz (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 1908Poincaré (1908a); Poincaré (1908b) Book 3, Ch. 3] 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 (1914) primary sources]

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, 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. Following Poincaré, also Minkowski (1908) and Arnold Sommerfeld (1910) tried to establish a lorentz-invariant gravitational law.Walter (2007)] However, these attempts were superseded because of Einstein's theory of general relativity, see "The shift to relativity".

The shift to relativity

Special relativity

In 1905, Albert Einstein published his paper on what is now called special relativity. 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:

# that the laws by which physical processes occur are the same with respect to any system of inertial coordinates (the principle of relativity), and
# 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 Poincaré 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 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 Poincaré 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.] ). Therefore, special relativity very quickly gained wide acceptance among physicists, and the 19th century concept of a luminiferous ether was no longer considered useful.Darrigol (2005), 15-18] Janssen (1995), Kap. 4]

Einstein's 1905 presentation of special relativity was soon supplemented, in 1907, by Hermann Minkowski, who showed that the relations had a very natural interpretationSee Whittaker's History of the Aether, in which he writes "the great advances made by Minkowski were connected with his formulation of physics in terms of a four-dimensional manifold... in order to represent natural phenomena without introducing contingent elements, it is necessary to abandon the customary three-dimensional system of coordinates and to operate in four dimensions". See also Pais's Subtle is the Lord, in which it says of Minkowski's interpretation "Thus began the enormous simplification of special relativity". See also Miller's "Albert Einstein's Special Theory of Relativity" in which it says "Minkowski's results led to a deeper understanding of relatvity theory".] 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"). Minkowski (1909)] Walter (1999)] The utility and naturalness of the representations by Einstein and Minkowski contributed to the rapid acceptance of special relativity, and to the corresponding loss of interest in Lorentz's ether theory.

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 unsatisfactory.Einstein (1907)] And in 1910Einstein (1909)] and 1912Einstein (1912)] 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. 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. However, Lorentz disagreed that it was "ad-hoc" and he argued in 1913 that there is little difference between his theory and the negation of a preferred reference frame, as in the theory of Einstein and Minkowski, so that it is a matter of taste which theory one prefers..

Mass–energy equivalence

It was derived by Einstein (1905) as a consequence of the relativity principle, that inertia of energy is actually represented by $E/c^2$, but in contrast to Poincaré's 1900-paper Einstein recognized, that matter itself loses or gain mass during the emission or absorption.Einstein (1905b)] So the mass of any form of matter is equal to a certain amount of energy, which can be converted into and re-converted from other forms of energy. This is the mass–energy equivalence, represented by $E=mc^2$. So Einstein didn't have to introduce "fictitious" masses and also avoided the perpetual motion problem, because according to DarrigolDarrigol (2005), 18-21] , Poincaré's radiation paradox can simply be solved by applying Einstein's equivalence. If the light source loses mass during the emission by $E/c^2$, the contradiction in the momentum law vanishes without the need of any compensating effect in the ether.

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 all problems. On that occasion, Einstein referred to Poincaré's 1900-paper and wrote:Einstein (1906)]

Also Poincaré's rejection of the reaction principle due to the violation of the mass conservation law can be avoided through Einstein's $E=mc^2$, because mass conservation appears as a special case of the energy conservation law.

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.Walter 2007] This theory is based on principles like the equivalence principle, the general principle of relativity, the principle of general covariance, geodesic motion, local Lorentz covariance (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:Einstein (1922)]

Priority

Some claim that Poincaré and Lorentz are the true founders of special relativity, but not Einstein. For more Details see the article on Relativity priority dispute.

Later activity and Current Status

Viewed as a theory of elementary particles, Lorentz's electron/ether theory was superseded during the first few decades of the 20th century, first by quantum mechanics and then by quantum field theory. As a general theory of dynamics, Lorentz and Poincare had already (by about 1905) found it necessary to invoke the principle of relativity itself in order to make the theory match all the available empirical data. By this point, the last vestiges of a substantial ether had been eliminated from Lorentz's "ether" theory, and it become both empirically and deductively equivalent to special relativity. The only difference was the metaphysicalLorentz commented that the difference between his and Einstein's view was purely metaphysical, and could be left to the metaphysicians.] postulate of a unique absolute rest frame, which was empirically undetectable and played no role in the physical predictions of the theory. As a result, the term "Lorentz ether theory" is sometimes used today to refer to a neo-Lorentzian interpretation of special relativity. The prefix "neo" is used in recognition of the fact that the interpretation must now be applied to physical entities and processes (such as the standard model of quantum field theory) that were unknown in Lorentz's day.

Subsequent to the advent of special relativity, only a small number of individuals have advocated the Lorentzian approach to physics. Many of these, such as Herbert E. Ives (who, along with G. R. Stilwell, performed the first experimental confirmation of time dilation) have been motivated by the belief that special relativity is logically inconsistent, and so some other conceptual framework is needed to reconcile the relativitic phenomena. For example, Ives wrote "The 'principle' of the constancy of the velocity of light is not merely 'ununderstandable', it is not supported by 'objective matters of fact'; it is untenable..."Herbert E. Ives, "Revisions of the Lorentz Transformations", October 27, 1950] . However, the logical consistency of special relativity (as well as its empirical success) is well established, so the views of such individuals are considered unfounded within the mainstream scientific community.

A few physicists, while recognizing the logical consistency of special relativity, have nevertheless argued in favor of the absolutist neo-Lorentzian view. Some (like John Stewart Bell) have asserted that the metaphysical postulate of an undetectable absolute rest frame has pedagogical advantages J. Bell, How to Teach Special Relativity] , while others have suggested that a neo-Lorentzian interpretation would be preferable in the event that any evidence of a failure of Lorentz invariance were ever detected.It should also be mentioned that the flexibility of the neo-Lorentzian interpretation is regarded as a weakness, rather than a strength, according to the usual view that equates the strength of a scientific theory with its falsibiability. A theory that can be easily modified to accommodate any contingency is considered weaker than one that could be strictly falsified by any of a large number of empirical tests (and of course that passes all those tests).] However, no evidence of such violation has ever been found (despite strenuous efforts) → see Test theories of special relativity.

* Mathpages: [http://www.mathpages.com/rr/s1-05/1-05.htm Corresponding States] , [http://www.mathpages.com/rr/s3-06/3-06.htm The End of My Latin] , [http://www.mathpages.com/rr/s8-08/8-08.htm Who Invented Relativity?] , [http://www.mathpages.com/home/kmath305/kmath305.htm Poincaré Contemplates Copernicus] , [http://www.mathpages.com/home/kmath571/kmath571.htm Whittaker and the Aether] , [http://www.mathpages.com/home/kmath601/kmath601.htm Another Derivation of Mass-Energy Equivalence]

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