- History of special relativity
The

**History of special relativity**consists of many theoretical and empirical results of physicists likeHendrik Lorentz andHenri Poincaré , which culminated in the theory ofspecial relativity proposed byAlbert Einstein , and subsequent work of physicists likeHermann Minkowski .**Introduction**Although

Isaac Newton based his theory on absolute space and time, he also adhered to thePrinciple of relativity ofGalileo Galilei . This stated all observers who move uniformly relative to each other are equal and no absolute state of motion can be attributed to any observer. During the 19th century the ether Theory was widely accepted, mostly in the form given byJames Clerk Maxwell . According to Maxwell "all" optical and electrical phenomena propagate in a medium. Thus it seemed possible to determine "absolute" motion relative to the aether and therefore to disprove Galileo's Principle.Those experiments and their failure lead to the development of the Maxwell-Lorentzian Electrodynamics by

Hendrik Lorentz .Henri Poincaré formally completed this by stating the Relativity Principle as a general law of nature, includingElectrodynamics andGravitation .Albert Einstein eventually devisedSpecial Relativity (SR) by completely re-interpreting Lorentzian Electrodynamics by changing the concepts of space and time and abolishing the aether. This paved the way toGeneral Relativity . Subsequent work ofHermann Minkowski laid the foundations of Relativistic Field Theories.**Prehistory****The search for the ether**1816-1851 — Around that time it was an established fact that

light consists ofwave s, propagating in a medium called theluminiferous aether . Regarding the mutual influence of matter and aether, two theories were considered: The one ofAugustin-Jean Fresnel , who developed a Stationary Aether Theory in which light propagates as a transverse wave and aether was partially dragged with a certain coefficient by matter. Based on this assumption, Fresnel was able to explain theAberration of light and many optical phenomena.Fresnel (1816)] Whittaker (1951), 107ff]George Gabriel Stokes , contrary to Fresnel, stated in 1845 that the aether was "fully" dragged by matter. In his model the aether might be (by analogy with pine pitch) rigid at very high frequencies and fluid at lower speeds. Thus the Earth could move through it fairly freely, but it would be rigid enough to support light.Stokes (1845)] Whittaker (1951), 386f] Fresnel's theory was preferred because his dragging coefficient was confirmed by theFizeau experiment ofHippolyte Fizeau in 1851, who measured the speed of light in moving liquids.Fizeau (1851)] Janssen/Stachel (2004), 4-15]again didn't yield the expected positive result, and was in sharp contrast to the experiment of 1886, which spoke for Fresnel's stationary aether.Michelson (1887)] Janssen/Stachel (2004), 19-20]

**Maxwell's electrodynamics**1861-1864 — After considerable work of many scientists like

Michael Faraday and Lord Kelvin, it wasJames Clerk Maxwell who developed an accurate theory ofelectromagnetism by deriving a set of equations inelectricity ,magnetism andinductance , namedMaxwell's equations . He first proposed that light was in fact undulations (Electromagnetic radiation ) in the "same" aetherial medium that is the cause of electric and magnetic phenomena. However, Maxwell's theory was unsatisfactory regarding the optics of moving bodies.Maxwell (1864)] Whittaker (1951), 240ff]1881 —

J. J. Thomson recognized, during his development of Maxwell's Theory, that charged bodies are harder to set in motion than uncharged bodies. He also noticed that the mass of a body "in motion" is increased by a constant quantity. Electrostatic fields behave as if they add an "electromagnetic mass" beside the mechanical mass to the bodies. I.e., according to Thomson, electromagnetic energy corresponds to a certain mass. In modern notations, Thomson's relation is "m" = (4/3)"E"/"c"^{2}, where m is the electromagnetic mass and E is the electromagnetic energy.Thomson (1881)] Whittaker (1951), 306ff; (1953) 51f] Miller (1981), 46]1889 —

Oliver Heaviside continued the 1881 work of Thomson and recognized that the increase of the mass of a body is not constant and varies with higher velocity. Additionally he determined that the electrostatic fields were contracted in the line of motion (Heaviside Ellipsoid), which leads to physically undetermined conditions at the speed of light.Heaviside (1889)] Miller (1981), 99-100]1889 —

George FitzGerald offered an explanation of the negative result of the Michelson-Morley experiment. He speculated that the intermolecular forces are possibly of electrical origin so that also material bodies would contract in the line of motion (length contraction ) like it was calculated by Heaviside for electrostatic fields. However, Fitzgerald's idea remained widely unknown and was not discussed beforeOliver Lodge published a summary of the idea in 1892.Fitzgerald (1889)] Brown (2001)]1890 — After

Heinrich Hertz in 1887 had proven the existence of electromagnetic waves, he (and, similar to him, Heaviside) in 1890 further developed Maxwell's theory.Hertz (1890a)] Hertz (1890b)] The "Maxwell-Hertz" or "Heaviside-Hertz" Equations subsequently formed an important basis for the further development of electrodynamics. Hertz assumed, like Stokes, that the aether was completely carried along by the bodies - which was not in accordance with Fizeau's experiments. At the beginning of the 20th century his theory was also directly disproved by other experiments and was replaced by the theory of Lorentz.Whittaker (1951), 319ff] Janssen/Stachel (2004), 20] Hertz was one of the last proponents of the "mechanical world-view", according to which all electromagnetic processes should be reduced to mechanical impact and contact actions.Miller (1981), 46]**Electron theories and Lorentz transformation**1887 —

Woldemar Voigt investigated the Doppler Effect for waves propagating in an incompressible elastic medium and deduced for the first time relativistic transformation relations, which have some similarity to the 'Lorentz Transformation'. He started from the corresponding partial differential equation. He assumed a wave expression as a solution of it and inserted in the argument the most general form of theGalilean Transformation , which accounts for both a rotation of coordinates and a shift in time. The Relativistic Transformation relations for some special cases he deduced then by subjecting the Galilei transformed wave expression to the partial differential wave equation. Voigt distinguished strictly between transformation relations valid for "longitudinal" waves and transformation relations valid for "transverse" waves (such as electromagnetic waves). The Voigt-Transformation predicted the negative result of the Michelson-Morley Experiment, but the equations were not symmetrical. However, Voigt's work was completely ignored by his contemporaries.Voigt (1887)] Miller (1981), 114-115]and the measurements of the Fresnel drag coefficient by Hippolyte Fizeau in moving and resting liquids as well. However, Lorentz’s local time was not the time measured by watches, but only an auxiliary mathematical tool. However Lorentz recognized the fact that his theory violated the principle of action and reaction, since the aether acts on matter, but matter cannot act on the immobile aether.Lorentz (1895)] Janssen (1995), Ch. 3.1]

1897 —

Joseph Larmor created a model very similar to Lorentz's. However, he went a step further and extended the Lorentz Transformation for second order terms. So Larmor was the first to put the Lorentz Transformation in an algebraically equivalent form, which is used to this day. He noticed on that occasion, that not only can length-contraction be derived from it, but he also calculated some sort ofTime Dilation for electron orbits.Larmor (1897)] Larmor specified his considerations in 1900.Larmor (1900)] Macrossan (1986)]1899 — Lorentz extended his transformation for second order terms and noted a (mathematical) Time Dilation effect as well. The integration of the speed-dependence of masses recognized by Thomson was especially important for his theory. He noticed that the mass not only varied due to speed, but is also dependent on the direction, and he introduced what Abraham later called "longitudinal" and "transverse" mass. (The transversal mass corresponds to what later was called

Relativistic Mass ).Lorentz (1899)] Janssen (1995), Ch. 3.4]1900 —

Wilhelm Wien assumed (following the works of Thomson andGeorge Frederick Charles Searle ) that the "entire" mass is of electromagnetic origin and the formula for the mass-energy-relationship is "m" = (4/3)"E"/"c"^{2}. This was formulated in the context that all forces of nature are electromagnetic ones (the Electromagnetic World View). Wien stated that, if it is assumed that gravitation is an electromagnetic effect too, then there has to be a proportionality between electromagnetic energy, inertial mass and gravitational mass.Wien (1900)] Miller (1981), 46, 103]1900 —

Emil Cohn created an alternative Electrodynamics in which he, as one of the first, discarded the existence of the aether (at least in the previous form) and would use, likeErnst Mach , the fixed stars as a reference frame instead.Cohn (1900)] Due to internal failures (like different light speeds in different directions) his theory was superseded by Lorentz's and Einstein's.Janssen/Stachel (2004), 31-32]1901-1903 — Walter Kaufmann was the first to confirm the velocity dependence of electromagnetic mass by analyzing the ratio e/m (where e is the charge and m the mass) of

cathode ray s. He found that the value of e/m decreased with the speed, showing that, assuming the charge constant, the mass of the electron increased with the speed. He also believed that those experiment confirmed the assumption of Wien, that there is no "real" mechanical mass, but only the "apparent" electromagnetic mass, or in other words, the mass of all bodies is of electromagnetic origin.Kaufmann (1902)] Miller (1981), 47-54]1902 —

Max Abraham , who was a supporter of the electromagnetic world view, quickly offered an explanation for Kaufmann's experiments by deriving expressions for the electromagnetic mass. Like Lorentz in 1899, he noticed that the mass also depends on the direction and coined the names Longitudinal and Transverse Mass. In contrast to Lorentz, he didn't believe in the Contraction Hypothesis, and therefore his mass terms differed from those of Lorentz. Kaufmann's experiments were, however, not precise enough to distinguish between the theories of Lorentz and Abraham. Following Poincaré, Abraham introduced the concept of "Electromagnetic Momentum" which is proportional to "E"/"c"^{2}. But in contrast to Poincaré, he considered it as a "real" physical entity.Abraham (1902)] Abraham (1903)] Miller (1981), 61-67]1904 — In April, Lorentz came very near to creating a Lorentz-covariant formulation of Electrodynamics (although he didn't succeeded completely). Like Wien and Abraham, he argued that there exists only electromagnetic mass, not mechanical mass, and derived the correct expression for longitudinal and transverse mass. So he could easily explain the negative result of the

Trouton-Noble experiment , in which a charged parallel-plate capacitor moving through the aether should orient itself perpendicular to the motion. Another important step was the postulate that the Lorentz Transformation has to be valid for non-electrical forces as well.Lorentz (1904)] Janssen (1995), Ch. 3.3, 3.4]1904 —

Friedrich Hasenöhrl suggested that part of the mass of a body (which he called apparent mass) can be thought of as radiation bouncing around a cavity. The apparent mass of radiation depends on the temperature (because every heated body emits radiation) and is proportional to its energy, and he first concluded that "m" = (8/3)"E"/"c"^{2}. However, Abraham and Hasenöhrl himself in 1905 changed the result to "m" = (4/3)"E"/"c"^{2}, the same value for the electromagnetic mass for a body at rest. However, Hasenöhrl stated that this energy-apparent-mass relation only holds as long a body radiates, i.e., if the temperature of a body is greater than 0 K.Hasenöhrl (1904)] Hasenöhrl (1904)] Miller (1981), 359-360]**Relativity principle and light constancy**did based on observations of the moons of Jupiter. Poincaré also noted that the propagation speed of light can be (and in practice often is) used to define simultaneity between spatially separate events. He concluded by saying, that "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."Poincare (1898)] Galison (2003)]

1900 — Like in 1895, Poincaré argued that experiments like that of Michelson-Morley show the impossibility of detecting the absolute motion of matter or the relative motion of matter in relation to the aether. He called this the "principle of relative motion."Poincare (1900a)] Katzir (2005), 272-275] In the same year he interpreted Lorentz's 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 aether, synchronize their clocks by optical signals.Poincare (1900b)] Since they believe themselves to be at rest, they must consider only the transmission time of the signals and then cross-reference their observations to examine whether their clocks are synchronous. However, from the point of view of an observer at rest in the aether, the clocks are not synchronous and indicate the local time "t"′ = "t" − "vx"/"c"

^{2}. But because the moving observers do not know anything about their movement, they do not recognize this. So, contrary to Lorentz, Poincaré-defined local time can be measured and indicated by clocks.Darrigol (2005), 10-11] In the same work Poincaré recognized that electromagnetic energy behaves like a fictitious fluid with mass density of "m" = "E"/"c"^{2}(or "E" = "mc"^{2}) and defined a fictitious electromagnetic momentum as well. However, he arrived at a radiation paradox which was fully explained by Einstein in 1905.Darrigol (2005), 18-21]1901 —

Menyhért Palágyi presented a philosophical model, according to which space and time were only two sides of some sort of "spacetime". He used time as a imaginary fourth dimension, which he already gave the form "it" (where "i" = √−1). However, there exists no connection between his philosophy and Lorentz's Electrodynamics, because, contrary to Lorentz's local time, Palagyi's time coordinate is not connected to the speed of light. He also rejected any connection with the already-existing constructions of n-dimensional spaces and non-Euclidean geometry. (Characteristically, Palágyi later rejected also the spacetime constructions of Minkowski and Einstein, which were developed in the spirit of non-Euclidean geometry).Palagyi (1901)]1902 — Poincaré published the philosophical and popular-scientific book "Science and Hypothesis", which included:Poincare (1902)]

*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 aether, and also some arguments supporting the aether

*many remarks on the non-Euclidean geometry.1903-1904 - In November, Wien recognized an important consequence of the velocity dependence of mass. He argued that superluminal velocities were impossible, because that would require an infinite amount of energy.Wien 1904a] And in June 1904, after he had read Lorentz's 1904 paper, he noticed the same in relation to length contraction, because at superluminal velocities the factor √1-v²/c² becomes imaginary.Wien 1904b] Miller (1981), Chap. 1, Footnote 57]

1904 — In July, Abraham demonstrated a defect of Lorentz's theory. On one side the theory obeys the relativity principle, and on the other side the electromagnetic origin of all forces is assumed. Abraham showed, that both assumptions were incompatible, because in Lorentz's theory of the contracted electrons, non-electric forces were needed in order to guarantee the stability of matter. However, in Abraham's theory of the rigid electron, no such forces were needed. Thus the question arose whether the Electromagnetic conception of the world (compatible with Abraham's theory) or the Relativity Principle (compatible with Lorentz's Theory) was correct.Abraham (1904)] Miller (1981), 75ff]

1904 — In a September lecture in

St. Louis named , Poincaré defined (in modification of Galileo’s Relativity Principle and Lorentz's Theorem of Corresponding States) the following principle: "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." He also specified his clock synchronization method and explained the possibility of a "new method" or "new mechanics", in which no velocity can surpass that of light for "all" observers. However, he critically noted that the Relativity Principle, Newton's action and reaction, theConservation of Mass and theConservation of Energy are not fully established and are even threatened by some experiments.Poincare (1904)] Katzir (2005), 275-277]1904 — In November, Cohn discovered some important physical interpretations of the Lorentz transformations. If rods and clocks are at rest in the Lorentzian ether, they show the true length and time, and if they are moving, they show contracted and dilated values. And like Poincaré, Cohn defined local time as the time, which is based on the assumption of isotropic propagation of light. Contrary to Lorentz and Poincaré it was noticed by Cohn, that the separation of "real" and "apparent" coordinates is artificial, because no experiment can distinguish between them. In addition, Cohn believed that the Lorentz transformed quantities were only valid for optical phenomena, but mechanical clocks would indicate the "real" time.Cohn (1904)] Janssen/Stachel (2004), 31-32]

1905 — On 5 June,

Henri Poincaré submitted the summary of a work which closed the existing gaps of Lorentz's work. (This short paper contained the results of a more complete work which was published in January 1906). He showed that Lorentz's equations of electrodynamics were not fully Lorentz-covariant. So he pointed out the group characteristics of the transformation, and he corrected Lorentz's formulae for the transformations ofcharge density and current density (which implicitly contained the relativisticvelocity-addition formula , which he elaborated in May in a letter to Lorentz). Poincaré used for the first time the term "Lorentz transformation", and he gave them the symmetrical form which is used to this day. He introduced a non-electrical binding force to ensure the stability of the electrons and to explain length contraction. He also sketched a Lorentz-invariant model of gravitation (including gravitational waves) by extending the validity of Lorentz-invariance to non-electrical forces.Poincare (1905)] Miller (1981), 79-86] Katzir (2005), 280-288]1905 — Eventually Poincaré (independently of Einstein) finished a substantially extended work of his June-paper (the so called „Palermo paper“, received July 23, printed December 14, published January 1906 ).Poincare (1906)] 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 theLorentz group , and he showed that the combination "x"^{2}+ "y"^{2}+ "z"^{2}− "c"^{2}"t"^{2}is invariant. While elaborating his gravitational theory, he said the Lorentz transformation is merely a rotation in four-dimensional space about the origin, by introducing "ct"√−1 as a fourth imaginary coordinate (contrary to Palagyi, he included the speed of light). He used an early form offour-vector s. (It's notable that at the paper's end he wrote that the discovery of magneto-cathode ray s byPaul Ulrich Villard (1904) seems to threaten the entire theory of Lorentz. However, this problem was quickly solved).Walter (2007), Ch. 1]**pecial relativity****Einstein 1905**;Electrodynamics of moving bodiesIn September 1905 (received June 30), Albert Einstein published his annus mirabilis paper on what is now called Special Relativity.Einstein (1905a)] This paper contains — in the mathematical sense and with exception of the relativistic Doppler effect and aberration — no new results, but "the derivation and the interpretation were radically new". Because of his axiomatic method, Einstein was able to derive all results on a few pages, while his predecessors needed many years of long, complicated work to arrive at the same mathematical formalism.

Einstein identified two fundamental principles, the

Principle of Relativity and the "Principle of the Constancy of Light", each founded on empirical observation. 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 Lorentz's electrodynamics and 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. Einstein's paper also includes a fundamental new definition of space and time (all time and space coordinates in all reference frames are equal, so there is no "true" or "apparent" time) and the abolition of the aether.Darrigol (2005), 15-18] Janssen (1995), Ch. 4]It's notable that Einstein's paper contains no references to other papers. However, many historians of science like Holton,Holton (1988)] Miller,Miller (1981)] Stachel,Stachel (1982)] have tried to find out possible influences on Einstein. Regarding the Relativity Principle, Einstein's

moving magnet and conductor problem (possibly after reading a book ofAugust Föppl ) and the negative aether drift experiments (possibly the Michelson-Morley experiment) were important for him to accept that principle. Another possible source is Poincaré's "Science and Hypothesis", where he described the Principle of Relativity and which was read by him in 1904.Darrigol (2004), 624] Another source were the writings ofMax Abraham , from whom he borrowed the terms "Maxwell-Hertz equations" and "longitudinal and transverse mass".Miller (1981), 86-92] Regarding the Principle of the Constancy of Light, Einstein himself stated that Lorentz's theory (or the Maxwell-Lorentz electrodynamics) had considerable influence on his thinking. He said in 1909 and 1912 that he borrowed that principle from Lorentz's stationary ether (which implies validity of Maxwell's equations and the constancy of light in the ether frame), but he recognized that this principle together with the principle of relativity makes the ether useless.Einstein (1909)] Einstein (1912)] Born (1956), 193] As he wrote in 1907 and in later papers, the apparent contradiction between those principles can be solved if it is realized that Lorentz's local time is not an auxiliary quantity, but can simply be defined as "time" and is connected withsignal velocity . Before Einstein, also Poincaré developed a similar physical interpretation of local time and noticed the connection to signal velocity, but contrary to Einstein he continued to argue that clocks in the aether show the true time, and moving clocks show the apparent time.Einstein (1908a)] Eventually, in 1953 Einstein described the advances of his theory (although Poincaré already stated in 1905 that Lorentz invariance is a general condition for any physical theory):;Mass-energy equivalenceAlready in §10 of his paper on electrodynamics, Einstein used the formula:$E\_\{kin\}=mc^2left(frac1\{sqrt\{1-frac\{v^2\}\; \{c^2\}-1\; ight)$for the kinetic energy of an electron (similar formulas were already used before Einstein by Wien, Poincaré, Abraham, Lorentz, and Hasenöhrl; see the description above). In elaboration of this, in November 1905 (received September 27) Einstein was the first to suggest that when a material body lost energy (either radiation or heat) of amount "E", its mass decreased by the amount "E"/"c"

^{2}. So, he solved Poincaré's radiation paradox from 1900. This led to the famousmass–energy equivalence formula: "E" = "mc"^{2}. Einstein considered the equivalency equation to be of paramount importance because it showed that a massive particle possesses an energy, the "rest energy", distinct from its classical kinetic and potential energies.Einstein (1905b)] Darrigol (2005), 18-21]**Further development**1905–1906 — Walter Kaufmann was probably the first who referred to Einstein's work. He compared the theories of Lorentz and Einstein, and, although he said Einstein's method is to be preferred, he argued that both theories are observationally equivalent. Therefore, he spoke of the relativity principle as the "Lorentz-Einsteinian" basic assumption. The "Lorentz-Einstein-Theory" term was also used by others for some years. Kaufmann now announced the results of his new experiments. They represented, in his opinion, a clear refutation of the relativity principle and the Lorentz-Einstein-Theory, and a confirmation of Abraham's theory. For some years, Kaufmann's experiments represented a weighty objection against the relativity principle.Kaufmann (1905, 1906)] Miller (1981), 334-352]

changed it to "relativity theory". Also simply the term "relativity principle" was used for that theory. All of those terms were used by different physicists alternately in the next years.Miller (1981), 88]

1906 — Einstein showed that the inertia of energy (mass-energy-equivalence) is a necessary and sufficient condition for the conservation of the

center of mass theorem. On that occasion, he argued that the content of Poincaré's 1900 paper and his own paper is mainly the same.Einstein (1906)] Darrigol (2005), 18-21]1907 —

Kurd von Mosengeil extended Hasenöhrl's calculation of black-body-radiation in a cavity under consideration of Einstein's theory and set an important cornerstone for relativistic thermodynamics.Mosengeil (1907)] Based on Mosengeil's work also, also Planck derived the mass-energy-equivalence. He acknowledged the priority of Einstein's 1905 work on $E=mc^2$, however, Planck judged his own approach as more general than Einstein's one.Planck (1908)] Miller (1981), 359-367]1907 — Already in 1895 Lorentz succeeded in deriving Fresnel's dragging coefficient and consequently the result of the Fizeau-Experiment with the aid of his concept of local time for terms on the order of v/c. Eventually in 1907

Jakob Laub , and, completelyMax von Laue , derived the coefficient for terms of all orders by using the relativistic velocity addition law.Laub (1907)] Laue (1907)] Janssen (1995), Ch. 3.1]1907 — Einstein discussed the question of whether, in rigid bodies, as well as in all other cases, the velocity of information can exceed the speed of light, and explained that information could be transmitted under these circumstances into the past, and then causality would be violated. Since this contravenes radically against every experience, superluminal velocities are thought impossible. He added that a dynamics of the

rigid body must be created in the framework of SR. (Like Planck and Bucherer, Einstein now also used the expression relativity theory).Einstein (1907)] Miller (1981), 245-253]1907-1908 — In an important overview article on the relativity principle, Einstein described SR as a "union of Lorentz's theory and the relativity principle", including the fundamental assumption that Lorentz's local time can be described as real time. For the first time he predicted the

Transverse Doppler effect . He presented another derivation of mass-energy equivalence, and, in this context, he pronounced the postulate that gravitational and inertial mass are equivalent, and since inertial mass depends on its energy content, this is also applicable to gravitational mass. And by combining SR with that new equivalence principle, he argued that the application of the constancy of the speed of light to define simultaneity is restricted to small localities. He also concluded that rays of light are bent in a gravitational field, and that clocks go faster in a higher gravitational potential.of 1908 he only mentioned Voigt, Lorentz and Einstein.Walter (1999a), 56-58] At the beginning, Einstein and Laub (like Poincaré) rejected the four-dimensional electrodynamics of Minkowski as too complicated and published a "more elementary", non-four-dimensional derivation of the basic-equations for moving bodies. Einstein (1908b)] But it was Minkowski's formalism which a) showed that special relativity is a complete and consistent theory, and b) served as a basis for further development of relativity.Walter (1999a), 49]

1908–1914 — Following Kaufmann, other physicists like

Alfred Bucherer (1908),Bucherer (1908)] andGünther Neumann (1914)Neumann (1914)] examined the velocity-dependence of mass, and this time it was thought that the "Lorentz-Einstein-theory" is confirmed and Abraham's theory is disproved. However, it was later pointed out that the Bucherer-Neumann experiments were also not precise enough to distinguish between the theories. So it lasted until 1940, when those experiments were repeated with sufficient accuracy for confirming the Lorentz-Einstein formula and disproving Abraham's model.Miller (1981), 334-352]1908–1913 —

Walter Ritz (and others) sketched anemission theory , according to which the speed of light in all reference frames is only constant relative to the source of emission (and not to an aether), whereby he used the Galilei-Transformation instead of the Lorentz-Transformation (i.e., in systems where the source is moving at ± v, the light propagates with the velocity equal to c ± v).Ritz (1908)] Also, Einstein briefly considered such a hypothesis before 1905. So, although this theory violates the constancy of light, it explains the Michelson-Morley-experiment, therefore the experiment only proved the relativity principle, but not the constancy of the speed of light.Norton (2004)] However, an emission theory would require a complete reformulation of electrodynamics, which is not supported by the success of Maxwell's theory. And finally the emission theory is considered to be disproved byWillem de Sitter (1913), who showed that, for the case of a double-star system seen edge-on, light from the approaching star might be expected to travel faster than light from its receding companion and overtake it. If the distance was great enough for an approaching star's "fast" signal to catch up with and overtake the "slow" light that it had emitted earlier when it was receding, then the image of the star system should appear completely scrambled. However, this is not observed.De Sitter (1913)] Pauli (1921), 549-553]1909-1912 — Based on the work of Planck (1906) and

Gilbert Newton Lewis (1909),Richard C. Tolman developed the concept ofrelativistic mass , because he defined mass as the ratio of momentum to velocity, and not as the ratio of force to acceleration. So former definitions of longitudinal and transverse mass became superfluous.Tolman (1912)] Pauli (1921), 634-636]1909 —

Paul Ehrenfest discovered the so calledEhrenfest paradox , according to which the circumference of a rotating disk is shortened because of length contraction by a constant radius.Ehrenfest (1909)] This was in the context of the question, already posed by Einstein (1907), of to what extent the concept of the rigid body is applicable in SR. This question was considered in 1909 byMax Born ,Born (1909)]Gustav Herglotz ,Fritz Noether , and 1911 by Laue.Laue (1911b)] It was recognize by Laue that the classic concept is not applicable in SR since a "rigid" body possesses infinitely manyDegrees of freedom .Pauli (1921), 690-691] It was also discussed byVladimir Varičak whether length contraction is "real" or "apparent", and whether there is a difference between the dynamic contraction of Lorentz and the kinematic contraction of Einstein.Varcak (1909)] However, it was rather a dispute over words because, as Einstein andWolfgang Pauli said, the kinematic length contraction is "apparent" for an co-moving observer, but for an observer at rest it is "real" and the consequences are measurable.Pauli (1921), 556-557]1909-1913 — While it was noted by Minkowski himself, that his space-time formalism can reformulated in a non-euclidean way, he excluded such formulation from his later publications.Walter (1999b)] Some analogies to

Riemannian geometry can be found in the work of Born (1909) on rigid bodies,Pais (1982), Ch. 12b] and in connection with this, Ehrenfest's paradox was an important hint for Einstein in developing his gravitational theory. Other scientists also tried to reformulate special relativity by using non-Euclidean geometry. For example,Alfred Robb (1911) introduced the concept of Rapidity as ahyperbolic function to characterize frame velocity.Robb (1911)]Vladimir Varičak (1912) noticed the similarity toHyperbolic geometry and tried to introduce some hyperbolic functions within special relativity. However, his contributions didn't lead to new physical insights.Varičak (1912)]Edwin Bidwell Wilson andGilbert N. Lewis (1912) introduced a non-euclidean vector-calculus, which later was abandoned by themselves.Lewis/Wilson (1912)] An important discovery related to hyperbolic geometry was made byÉmile Borel (1913), who derived the kinematic basis ofThomas precession .Borel (1913)] However, Minkowski's space-time formalism was preferred over those attempts, and it lasted until the development of general relativity by Einstein, when non-euclidean geometry played an important role within physics.1910–1913 — In a lecture between 1910 and 1912, Lorentz discussed the reciprocity of time dilation and analyzed a clock paradox. Lorentz showed that there is no paradox if one considers that in one system only one clock is used and in the other system two clocks are used. Therefore, the relativity of simultaneity has to be considered.Lorentz (1910)]

Paul Langevin created in 1911 a similar situation with his famoustwin paradox , where he replaced the clocks by twins. Langevin solved the paradox by pointing out the asymmetry of the twins. One twin accelerates and changes direction and, after considering the Doppler effect, Langevin showed that the accelerated twin is younger. However, Langevin himself interpreted this as a hint to the existence of an aether. Langevin (1911)] Although Langevin’s explanation is used in principle until today, his deductions regarding the aether were not accepted. Laue (1913), pointed out that the acceleration can be made arbitrarily small in relation to the inertial motion of the twin.Laue (1913)] So it is much more important that one twin travels within two inertial frames during his journey, while the other twin remains in one frame.Miller (1981), 257-264]1910-1915 — The first derivations of relativity of simultaneity by synchronization with light signals were also simplified.Bjerknes (2002)]

Daniel Frost Comstock in 1910 placed an observer in the middle between two clocks A and B.Comstock (1910)] From this observer a signal is sent to both clocks, and in the frame in which A and B are at rest, they synchronously start to run. But from the perspective of a system in which A and B are moving, clock B is first set in motion, and then comes clock A - so the clocks are not synchronized. Also Einstein created a model in 1917 with an observer in the middle between A and B. However, in his description two signals are sent "from" A and B to the observer. From the perspective of the frame, in which A and B are at rest the signals are sent at the same time and the observer "is hastening towards the beam of light coming from B, whilst he is riding on ahead of the beam of light coming from A. Hence the observer will see the beam of light emitted from B earlier than he will see that emitted from A. Observers who take the railway train as their reference-body must therefore come to the conclusion that the lightning flash B took place earlier than the lightning flash A."Einstein (1917)]1910-1911 — There were some attempts to derive the Lorentz transformation without the postulate of the constancy of the speed of light.

Vladimir Ignatowski for example used for this purpose a) the principle of relativity, b) and homogeneity and isotropy of space c) the requirement of reciprocity.Ignatowsky (1910)]Philipp Frank andHermann Rothe showed that this derivation is incomplete and needs additional assumptions.Frank (1911)] Their own calculation was based on the assumptions that a) the Lorentz transformation forms a homogeneous linear group, b) when changing frames, only the sign of the relative speed changes, c) length contraction solely depends on the relative speed. According to Pauli and Miller, both Ignatowski and Frank/Rothe, were unable to identify the invariant speed in their transformation with the speed of light, therefore they claimed that both both postulates are needed to derive the Lorentz transformation.Pauli (1921), 555-556] Miller (1981), 218-219] However, until today others continued the attempts to derive special relativity without the light postulate.1909-1915 — Eventually, many mathematicians and theoretical physicists accepted the results of special relativity. For example, already in 1909 Planck compared the implications of the modern relativity principle — especially Einstein's relativity of time — with the revolution by the Copernican system.Planck (1910), Chap. 8] Pais (1982), 11a] As a result, the term "Lorentz-Einstein-Theory" wasn't used anymore and only a few physicists like Lorentz, Poincaré, Langevin, still believed in the existence of an aether in any form. Another important reason for accepting special relativity was the extension of Minkowski's space-time formalism by

Arnold Sommerfeld (1910),Sommerfeld (1910a, 1910b)] Laue (1911),Laue (1911a)] and others.Walter (1999a), Ch. 3] At this time, Einstein eventually accepted Minkowski's four-dimensional formalism and used it for his intense work on the foundations ofgeneral relativity (GR). After formulating GR, Einstein in 1915, for the first time, used the expression "special theory of relativity" to distinguish between the theories.**Mathematical background**One might ask, "Did the founders of special relativity need to invent new mathematics for the

mathematical model that is space-time theory?" The answer is that today we see special relativity as a cornerstone of appliedlinear algebra , but at the time Lorentz, Poincaré, Einstein, and Minkowski were doing mathematics, that field was still in its infancy; there were no textbooks on linear algebra as modern vector space and transformation theory, and the matrix notation ofArthur Cayley (that unifies the subject) was yet to catch-on. The actual Lorentz transformations are a mapping concept inherent intessarine multiplication, an idea put forward byJames Cockle in 1848. In his short (34 year) life,William Kingdon Clifford used this multiplication with the evocative name "motor algebra". The lecture "The Principles of the Algebra of Physics" by Alexander MacFarlane in 1891 before theAmerican Association for the Advancement of Science marks the beginning of public discussion of this mathematics in the context of academic physics. The talk was published in the "Proceedings of AAAS", and MacFarlane also promulgated the text in pamphlets.The definitive model put forward in 1908,

Minkowski space , can be viewed as watered-downhyperbolic quaternion s. The algebra arises under the premise that every spacetime subplane has asplit-complex number structure. This premise, taken from MacFarlane's 1891 lecture, sparked a significant response in the 1890s, and a revision by MacFarlane in 1900.In 1912

Gilbert N. Lewis andEdwin Bidwell Wilson provided a deductive approach to thenon-Euclidean geometry supporting the relativistic science. This reductionist view of the relations of points, lines, and other geometric figures in this science is "Synthetic Spacetime" (see external reference).**Priority**Some claim that Poincaré (and Lorentz), not Einstein, are the true founders of special relativity. For more see the article on

relativity priority dispute .**Criticisms**Some criticized Special Relativity for various reasons, such as lack of empirical evidence, internal inconsistencies, rejection of mathematical physics "per se", philosophical reasons. Examples are:

Max Abraham , Friedrich Adler,Henri Bergson ,Herbert Dingle ,Hugo Dingler ,Louis Essen ,Herbert E. Ives ,Emanuel Lasker ,Hjalmar Mellin ,Albert Abraham Michelson ,Menyhért Palágyi ,Walter Ritz ,Georges Sagnac . Other reasons wereAntisemitism within theDeutsche Physik . Examples are:Ernst Gehrcke ,Philipp Lenard ,Johannes Stark ,Bruno Thüring , and, relating to his reception history,Hans Hörbiger (whose "Welteislehre " was referred to as the "German Theory of Relativity" among Right-Wing circles in Germany during the interwar period).One early criticism was the assertion that light simply travels with the earth in a so-called "co-moving luminiferous aether". In the process of traveling through its "immediately surrounding physical reality", the speed light attains appears different for observers who move at different speeds relative to each other, the same as with every other known phenomena.

Critics asserted the Michelson-Morley experiment null result was not the theoretical enigma some scientists believed. So the then-current understanding of light apparently needed to be changed according to this new belief: the medium for light was not rigid after all.

But other critics had already concluded, from stellar aberration, that there had to be a rigid aether which carried the light as the Earth moved through it. The two results suggested contradictory conclusions: was the aether local and fluid, or was it universal and rigid?

Lorentz's solution made the Earth shorter in the direction of travel around the Sun, and later also modified the speed of time. This was criticized by scientists at first, but Einstein's and Minkowski's interpretations inferred Lorentz's hypothesis was the natural consequence of some postulates.

Although there still are critics of relativity outside the scientific mainstream, the overwhelming majority of scientists agree that Special Relativity has been verified in many different ways and there are no inconsistencies within the theory.CosmosMagazine: [

*http://www.cosmosmagazine.com/node/1162 Was Einstein a fake?*] ]**ee also***

Lorentz ether theory

*Aether theories

*History of Lorentz transformations

*Relativity priority dispute

*Mass–energy equivalence **External links***MacTutor Biography|class=HistTopics|id=Special_relativity|title=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://ca.geocities.com/cocklebio/synsptm.html Synthetic Spacetime*]

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