History of special relativity

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Although Isaac Newton based his theory on absolute space and time, he also adhered to the Principle of relativity of Galileo 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 Aether Theory was widely accepted, mostly in the form given by James 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, including Electrodynamics and Gravitation. Albert Einstein eventually devised Special Relativity (SR) by completely re-interpreting Lorentzian Electrodynamics by changing the concepts of space and time and abolishing the aether. This paved the way to General Relativity. Subsequent work of Hermann Minkowski laid the foundations of Relativistic Field Theories.

Contents 1 From aether to relativity principle 2 Einstein (1905) 3 Further development after 1905 4 Mathematical background 5 Priority 6 Criticisms of special relativity 7 See also 8 Secondary sources 9 Primary sources 10 Weblinks

[edit] From aether to relativity principle

1816 — Augustin-Jean Fresnel 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 the Aberration of light and many optical phenomena.^[1]

1845 — George Gabriel Stokes, contrary to Fresnel, stated 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.^[2]

1851 — Both theories were considered, but Fresnel's theory was favoured because his dragging coefficient was confirmed by the experiments of Armand Hippolyte Louis Fizeau, who measured the speed of light in moving liquids.^[3][4][5]

1861-1864 — James Clerk Maxwell developed a set of equations in electricity, magnetism and inductance, named Maxwell'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.^[6]

1881 — Albert Abraham Michelson tried to measure the relative motion of earth and Aether (Aether-Wind), as it was expected in Fresnel’s theory, by using an interferometer. However, he could not determine any relative motion, so he interpreted the result as a confirmation of the thesis of Stokes.^[7]

1881 — J. J. Thomson recognized, during his development of Maxwell's Theory, that charged bodies are harder to set in motion than uncharged bodies. 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.^[8]

1886 — Hendrik Lorentz showed Michelson's 1881 experiment calculations were wrong and therefore the experiment was not conclusive. This was admitted by Michelson himself.^[9] Lorentz also showed that a complete drag of the aether as in Stokes' Theory is self-contradictory.^[4][5]

1886 — Michelson and Edward Morley performed an experiment to check Fizeau’s experiment, which measured Fresnel's dragging coefficient in a moving liquid. Fresnel's theory was confirmed very exactly on that occasion. Michelson was now of the opinion that a nearly stationary aether is confirmed.^[10]

1887 — Michelson and Morley published the results of repeating Michelson's 1881-experiment. The now famous Michelson-Morley experiment didn't yield the expected positive result, and was in sharp contrast to the 1886 Michelson and Morley experiment, which spoke for Fresnel's stationary aether. However, Stokes's alternative of a fully-dragged aether was hardly justifiable either, because of Lorentz's 1886 arguments.^[11]

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 the Galilean 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 following Michelson-Morley Experiment, but the equations were not symmetrical. However, Voigt's work was completely ignored by his contemporaries.^[12]

1889 — Oliver Heaviside continued the 1881 work of Thomson and recognized that the mass of a body is increased, not only when it is charged, but the electromagnetic mass is also increased due to 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.^[13]

1889 — Following Heaviside, George FitzGerald suggested that also material bodies contract in the line of motion (length contraction), which could explain the negative result of the Michelson-Morley experiment.^[14]

1890 — After Heinrich Hertz in 1887 had proven the existence of electromagnetic waves,^[4] he (and, similar to him, Heaviside) in 1890 further developed Maxwell's theory.^[15][16] The "Maxwell-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 experiments. At the beginning of the 20th century his theory was also directly disproved by experiment and was replaced by the theory of Lorentz. 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.^[5]

1892 — Lorentz set the foundations of Lorentz Aether/Electron Theory, by assuming the existence of electrons as the source of electromagnetic fields and by replacing the "Maxwell-Hertz" Equations by the "Maxwell-Lorentz" Equations. In his model, the aether is completely motionless and, contrary to Fresnel's theory, also is not partially dragged by matter. He gave no statements about the mechanical nature of the aether and the electromagnetic processes, but, vice-versa, tried to explain the mechanical processes by electromagnetic ones and therefore created an abstract Electromagnetic Aether. In the framework of his theory, Lorentz calculated, like Heaviside, the contraction of the electrostatic fields.^[17] In the same year he proposed length contraction independently from Fitzgerald in order to explain the Michelson-Morley experiment. For plausibility reasons, Lorentz referred to the analogy of the contraction of electrostatic fields. However, even Lorentz admitted that that was not a necessary reason and length-contraction consequently remained as a purely ad-hoc hypothesis.^[18]

1895 — Lorentz introduced the "Theorem of Corresponding States" for terms on the order of v/c. This theorem states that a moving observer (relative to the aether) in his „fictitious“ field makes the same observations as a resting observers in his „real“ field. An important part of it was local time t′ = t − vx/c², which paved the way to the Lorentz Transformation and which he introduced independently of Voigt. 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. 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.^[19]

1895 — Henri Poincaré judged that, despite the violation of the Reaction Principle, the theory of Lorentz is the least defective of all theories of electrodynamics. Because, contrary to the other theories, it can explain the Fizeau experiment and the Conservation of Electricity and Magnetism. Contrary to Lorentz, who only wanted to explain the negative (optical) aether drift experiments of first order to v/c, Poincaré (based on the Michelson-Morley experiment) was of the opinion that it is only possible to observe relative motions of matter, but not absolute motion nor motion relative to the aether.^[20]

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 of Time Dilation for electron orbits.^[21] Larmor specified his considerations in 1900.^[22] In 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).^[23]

1898 — In the second half of the 19th century there were many attempts to develop a world-wide clock network synchronized by electrical signals. On that occasion, the finite propagation speed of light had to be considered as well.^[24] So Henri Poincaré drew some important consequences of this process and explained that astronomers, 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 be impossible to infer the speed of light from astronomical observations, as Ole Rømer 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."^[25]

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."^[26] 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. 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/c². 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.^[27] In the same work Poincaré recognized that electromagnetic energy behaves like a fictitious fluid with mass density of m = E/c² (or E = mc²) and defined a fictitious electromagnetic momentum as well. However, he arrived at a radiation paradox which was fully explained by Einstein in 1905.^[28]

1900 — Wilhelm Wien assumed (following the works of Thomson and George Frederick Charles Searle) that the entire mass is of electromagnetic origin and the formula for the mass-energy-relationship is m = (4/3)E/c². 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.^[29]

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, like Ernst Mach, the fixed stars as a reference frame instead.^[30] Due to internal failures (like different light speeds in different directions) his theory was superseded by Lorentz's and Einstein's.

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).^[31]

1901-1903 — Walter Kaufmann was the first to confirm the velocity dependence of mass.^[32]

1902 — Max Abraham submitted an explanation for Kaufmann's experiments and, following Lorentz, he 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, in contrast to Poincaré, he considered as a real physical entity which is proportional to E/c².^[33][34]

1902 — Poincaré published the philosophical and popular-scientific book "Science and Hypothesis", which included:^[35]

• 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
• many remarks on the non-Euclidean geometry.

1904 — In May, 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. Another important step was the postulate that the Lorentz Transformation has to be valid for non-electrical forces as well.^[36]

1904 — Cohn, following the work of Lorentz, (like Poincaré) noticed that local time was not only a mathematical construct, but was the result of synchronizing moving clocks by light signals. Cohn believed that this is only valid for optical phenomena, but mechanical clocks would indicate the "real" time.^[37] Also Abraham criticized that Lorentz's theory of the contracted electrons is not compatible with the electromagnetic conception of the world, since non-electric forces are needed in order to guarantee the stability of matter. 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.^[38]

1904 — In a September lecture in St. Louis, 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, the Conservation of Mass and the Conservation of Energy are not fully established and are even threatened by some experiments.^[39]

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/c². However, Abraham and Hasenöhrl himself in 1905 changed the result to m = (4/3)E/c², 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.^[40][41]

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 of charge density and current density (which implicitly contained the relativistic velocity-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.^[42]

[edit] Einstein (1905)

Special relativity

In September 1905 (received June 30), Albert Einstein published his annus mirabilis paper on what is now called Special Relativity.^[43] 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 experience. 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.

It's notable that Einstein's paper contains no references to other papers. However, many historians of science like Holton or Miller 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 of August Föppl) and the negative aether drift experiments (possibly the Michelson-Morley experiment) were important for him to accept that principle.^[44][45] Another possible source is Poincaré's Science and Hypothesis, where he described the Principle of Relativity and which was read by him in 1904.^[46][47] 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.^[48][49] 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 with signal 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.^[50] 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):^[51]

“

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. [..] The new feature of it was the realization of the fact that the bearing of the Lorentz transformation transcended its connection with Maxwell's equations and was concerned with the nature of space and time in general. A further new result was that the "Lorentz invariance" is a general condition for any physical theory. This was for me of particular importance because I had already previously found that Maxwell's theory did not account for the micro-structure of radiation and could therefore have no general validity.

”

Mass–energy equivalence

Already in §10 of his paper on electrodynamics, Einstein used the formula

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/c². So, he solved Poincaré's radiation paradox from 1900. This led to the famous mass–energy equivalence formula: E = mc². 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.^[52]

[edit] Further development after 1905

1905–1906 — Independently of Einstein, Poincaré published a substantially extended work of his June-paper in January 1906 (the so called „Palermo paper“, received July 23, 1905, and printed December 14, 1905). 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 the Lorentz group, and he showed that the combination x² + y² + z² − c²t² 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 of four-vectors. (It's notable that at the paper's end he wrote that the discovery of magneto-cathode rays by Paul Ulrich Villard (1904) seems to threaten the entire theory of Lorentz. However, this problem was quickly solved).^[53]

1905–1906 — Kaufmann was probably the first who referred to Einstein's work.^[47] 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.^[54]

1906 — Max Planck published his first work on relativity, in which he described Einstein's theory as a "generalization" of Lorentz's theory. Planck seemed to be the first who used the term "Lorentz-Einstein-Theory" together with the term "relative theory" (Relativtheorie), in contrast to the "sphere theory" (Kugeltheorie) of Abraham.^[47] In the following discussion of that paper, Adolf Heinrich Bucherer changed it to "relativity theory". Those three terms were used by different physicists alternately in the next years. In his electrodynamics paper, Einstein made a slight mistake in calculating the transverse mass of the electron. Planck corrected this and showed that the expression was equivalent to that used by Lorentz in 1899. Planck also defined for the first time the relativistic momentum.

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.^[55]

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.^[56] Based on Mosengeil's work also, also Planck derived the mass-energy-equivalence. He acknowledged the priority of Einstein's 1905 work on E = mc², however, Planck judged his own approach as more general than Einstein's one.^[57]

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, more exactly Max von Laue, derived the coefficient for terms of all orders by using the relativistic velocity addition law.^[58][59] The Fizeau experiment was also very important for Einstein's views before 1905, because, in his opinion, it showed the classical velocity addition law had to be changed.^[45]

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).^[60] And in an important overview article on the relativity principle in the same year, he 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. 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.^[50]

1907-1908 — Poincaré’s attempt of a four-dimensional reformulation of the new mechanics was rejected by himself in 1907, because in his opinion the translation of physics into the language of four-dimensional metry would entail too much effort for limited profit.^[53] So it was Hermann Minkowski, who worked out the consequences of that notion. Minkowski completed, for example, the concept of four vectors; he created the Minkowski diagram for the depiction of space-time; and most notably he presented a four-dimensional formulation of electrodynamics. However, like Poincaré, his attempt to formulate a Lorentz-invariant law of gravity failed.^[61] In 1907 Minkowski named four predecessors who contributed to the formulation of the relativity principle: Lorentz, Einstein, Poincaré and Planck. However, in his famous lecture Raum und Zeit of 1908 he only mentioned Voigt, Lorentz and Einstein.^[53]

1908 — 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. ^[62] 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.

1908–1938 — Following Kaufmann, other physicists like Bucherer (1908),^[63] Neumann (1914)^[64] 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 Abraham's theory was not disproved before 1938.^[47]

1908–1913 — Walter Ritz (and others) sketched an emission 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).^[65] Also, Einstein briefly considered such a hypothesis before 1905.^[45] 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. 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 by Willem 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.^[66]

1909 — Paul Ehrenfest presented a paradox named after him, according to which the circumference of a rotating disk is shortened because of length contraction by a constant radius.^[67] 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 by Max Born, Gustav Herglotz, Fritz Noether, and 1911 by Laue. It was recognize by Laue that the classic concept is not applicable in SR since a "rigid" body possesses infinitely many Degrees of freedom.^[68] It was also discussed by Vladimir Varicak 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.^[69] However, it was rather a dispute over words because, as Einstein and Wolfgang 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.^[68] At the end, Ehrenfest's paradox was an important hint for Einstein in developing his gravitational theory using non-Euclidean geometry.

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.^[70] Paul Langevin created in 1911 a similar situation with his famous twin 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. ^[71] Although Langevin’s explanation is used in principle until today, his deductions regarding the aether were not accepted. Max von Laue (1913), pointed out that the acceleration can be made arbitrarily small in relation to the inertial motion of the twin.^[72] 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.^[47]

1910-1915 — The first derivations of relativity of simultaneity by synchronization with light signals were also simplified.^[73] Daniel Frost Comstock in 1910 and following him Robert Daniel Carmichael in 1912, placed an observer in the middle between two clocks A and B.^[74][75] 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 1916 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."^[76]

1910-1911 — There were some attempts to derive the Lorentz transformation without the postulate of the constancy of the speed of light. Waldemar von Ignatowsky for example used for this purpose a) the principle of relativity, b) and homogeneity and isotropy of space c) the requirement of reciprocity.^[77] Philipp Frank and Hermann Rothe showed that this derivation is incomplete and needs additional assumptions.^[78] 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. Both Ignatowsky and Frank/Rothe, however, were unable to identify the invariant speed in their transformation with the speed of light. Therefore, until today, both postulates are needed to derive the Lorentz transformation.^[68]

1912 — Richard C. Tolman developed the concept of relativistic 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.^[79]

1909–1915 — Born, Abraham, Gilbert Newton Lewis, Laue and Arnold Sommerfeld extended Minkowski's space-time physics and introduced a modern vector notation.^[53] The naturalness and utility of this representation contributed to the rapid acceptance of special relativity, and to the corresponding loss of interest in Lorentz's aether theory. The term "Lorentz-Einstein-Theory" wasn't used anymore and only a few physicists like Lorentz, Poincaré, Langevin and Planck, still believed in the existence of an aether in any form. At this time, Einstein eventually accepted Minkowski's four-dimensional formalism and used it for his intense work on the foundations of general relativity (GR). After formulating GR, Einstein in 1915, for the first time, used the expression "special theory of relativity" to distinguish between the theories.

[edit] 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 applied linear 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 of Arthur Cayley (that unifies the subject) was yet to catch-on. The actual Lorentz transformations are a mapping concept inherent in tessarine multiplication, an idea put forward by James 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 the American 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-down hyperbolic quaternions. The algebra arises under the premise that every spacetime subplane has a split-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.

[edit] 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.

[edit] Criticisms of special relativity

Some criticized Special Relativity for various reasons, such as lack of empirical evidence, internal inconsistencies, rejection of mathematical physics per se, philosophical reasons, and anti-Semitism within the Deutsche Physik. Examples are: Max Abraham, Walter Ritz, Georges Sagnac, Menyhért Palágyi, Hugo Dingler, Emanuel Lasker, Philipp Lenard, Johannes Stark, Ernst Gehrcke, Henri Bergson, Hjalmar Mellin, Herbert Dingle, Louis Essen, and Herbert E. Ives.

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.^[80]

[edit] See also

• Lorentz ether theory
• Aether theories
• History of Lorentz transformations
• Relativity priority dispute
• Mass–energy equivalence

[edit] Secondary sources

[edit] Primary sources

[edit] Weblinks

• O'Connor, John J. & Robertson, Edmund F., “Special relativity”, MacTutor History of Mathematics archive 
• Mathpages: Corresponding States, The End of My Latin, Who Invented Relativity?, Poincaré Contemplates Copernicus