Welcome to ornacle.com on July 6 2009.
This is an internet experiment running to monitor browsing habbits of individuals through wikipedia contents.

History of special relativity

From Wikipedia, the free encyclopedia

Jump to: navigation, search
"History of relativity" redirects here. For the history of general relativity, see history of general relativity.
Sister project Wikisource has original works on the topic:

The history of special relativity consists of many theoretical results and empirical findings obtained by physicists like Hendrik Lorentz and Henri Poincaré. It culminated in the theory of special relativity proposed by Albert Einstein, and subsequent work of physicists like Hermann Minkowski.

Contents

[edit] Introduction

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 ether 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.

[edit] Prehistory

[edit] Electrodynamics and aether drift

[edit] Aether models and Maxwell's equations

Due to the works of Thomas Young (1804) and Augustin-Jean Fresnel (1816), it was an established fact that light propagates as a transverse wave within an elastic medium called luminiferous aether. However, it was still distinguished between optical and electrodynamical phenomena so it was necessary to create specific aether models for all phenomena. But attempts to unify those models or to create a complete mechanical description of them were failing.[1] But after considerable work of many scientists like Michael Faraday and Lord Kelvin, it was James Clerk Maxwell (1864) who developed an accurate theory of electromagnetism by deriving 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. However, Maxwell's theory was unsatisfactory regarding the optics of moving bodies, and while he was able to present a complete mathematical model, a coherent mechanical description of the aether was still missing.[2]

J. J. Thomson (1881) 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. This was interpreted as some form of self-inductance of the electromagnetic field.[3][4] Thomson's work was continued and perfected by George FitzGerald, Oliver Heaviside (1888), and George Frederick Charles Searle (1896, 1897). For the electromagnetic mass they gave — in modern notation — the formula m = (4/3)E/c2, where m is the electromagnetic mass and E is the electromagnetic energy. Heaviside and Searle also recognized that the increase of the mass of a body is not constant and varies with higher velocity. Consequently, Searle noted the impossibility of superluminal velocities, because an infinite amount of energy is needed to supersede the speed of light. Additionally Heaviside and Searle 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.[5]

1890 — After Heinrich Hertz in 1887 had proven the existence of electromagnetic waves, Maxwell's theory was widely accepted. In addition, Heaviside and Hertz further developed the theory and introduced modernized versions of Maxwell's equations. The "Maxwell-Hertz" or "Heaviside-Hertz" Equations subsequently formed an important basis for the further development of electrodynamics, whereby it is Heaviside's notation which is used until today. Hertz assumed, like George Gabriel Stokes, that the aether was completely carried along by the bodies - which was not in accordance with Fizeau's experiment. At the beginning of the 20th century his theory was also directly disproved by other experiments and was replaced by the theory of Lorentz.[6][7] 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.[8]

[edit] Search for the aether

Regarding the relative motion and the mutual influence of matter and aether, two theories were considered: The one of 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 the Aberration of light and many optical phenomena.[9] But 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.[10] Fresnel's theory was preferred because his dragging coefficient was confirmed by the Fizeau experiment of Hippolyte Fizeau in 1851, who measured the speed of light in moving liquids.[11]

Albert Abraham Michelson

Albert Abraham Michelson (1881) tried to measure the relative motion of earth and Aether (Aether-Wind), as it was expected in Fresnel’s theory, by using an interferometer. He could not determine any relative motion, so he interpreted the result as a confirmation of the thesis of Stokes.[12] However, Hendrik Lorentz (1886) showed Michelson's calculations were wrong and therefore the experiment was not conclusive. This was admitted by Michelson himself. In addition, Lorentz also showed that a complete drag of the aether as in Stokes' Theory is self-contradictory, and therefore he supported an aether theory similar to Fresnel's.[13] So Michelson and Edward Morley (1886) performed an experiment to check Fresnel's theory by repeating the Fizeau experiment. Fresnel's dragging coefficient was confirmed very exact on that occasion, and Michelson was now of the opinion that Fresnel's stationary aether theory is correct.[14] To clarify the situation, Michelson and Morley (1887) repeated Michelson's 1881-experiment. The now famous Michelson-Morley experiment 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.[15]

Woldemar Voigt (1887) 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'. The Voigt-Transformations include the Lorentz factor 1/\sqrt{1-v^{2}/c^{2}} for the y- and z-coordinates, and a new time variable t' = t − vx / c2 which later was called "local time". The transformation left the Wave equation in free space unchanged, and explained the negative result of the Michelson-Morley Experiment. On the other hand, the equations are not symmetrical, thus violating the principle of relativity. However, Voigt's work was completely ignored by his contemporaries.[16][17]

1889 — George FitzGerald offered another explanation of the negative result of the Michelson-Morley experiment. Contrary to Voigt, 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 before Oliver Lodge published a summary of the idea in 1892.[18] Also Lorentz (1892b) 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.[19][20]

[edit] Theory of electrons

[edit] Lorentz's theory

Hendrik Antoon Lorentz

Lorentz (1892a) set the foundations of Lorentz Aether/Electron Theory, by assuming the existence of electrons which he separated from the aether, 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. An important consequence of this notion was that the velocity of light is totally independent of the velocity of the source. Lorentz 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.[21] Lorentz (1895) also introduced what he called 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 Fizeau experiment 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.[22]

Joseph Larmor (1897, 1900) 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. Larmor specified his considerations in 1900.[17][23] Independently of Larmor, also Lorentz (1899) 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).[24]

Wilhelm Wien (1900) assumed (following the works of Thomson, Hearviside, and 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.[25] In the same paper Henri Poincaré (1900b) found another way of combining the concepts of mass and energy. He 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.[26]

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. Due to internal failures (like different light speeds in different directions) his theory was superseded by Lorentz's and Einstein's.[27]

[edit] Dynamics of the electron

Walter Kaufmann (1901) 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 rays. 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.>[28]

Max Abraham (1902, 1903), 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/c2. But in contrast to Poincaré, he considered it as a real physical entity.[29]

[edit] Relativity principle and light constancy

[edit] Absolute space and time

Some scientists started to criticize Newton's definitions of absolute space and time.[30][31][32] For example, Carl Neumann (1870) introduced a "Body alpha", which represents some sort of rigid and fixed body for defining inertial motion. Ernst Mach (1883) argued that absolute time and space are meaningless and only relative motion is a useful concept. He also said that even accelerated motion such as rotation could be related to the fixed stars without using Newton's absolute space. Based on the definition of Neumann, Heinrich Streintz (1883) argued that if gyroscopes don't measure any signs of rotation, then one can speak of inertial motion which is related to a "Fundamental body" and a "Fundamental Coordinate System". Eventually, Ludwig Lange (1885) was the first to coin the expression inertial frame of reference and inertial time scale as operational replacements for absolute space and time, by defining "a reference frame in which a mass point thrown from the same point in three different (non co-planar) directions follows rectilinear paths each time it is thrown is called a inertial frame".

There were also some attempts to use time as a Fourth Dimension.[33][34] This was done as early as 1754 by Jean le Rond d'Alembert in the Encyclopédie, as it was done by some authors in the 19th century like H. G. Wells in his novel The Time Machine (1895). And in 1901 a philosophical model was published by Menyhért Palágyi, in which space and time were only two sides of some sort of "spacetime".[35] He used time as a imaginary fourth dimension, which he gave the form it (where i = √−1). However, Palagyi's time coordinate is not connected to the speed of light like it is in Lorentz's theory. He also rejected any connection with the existing constructions of n-dimensional spaces and non-Euclidean geometry and consequently rejected the spacetime formalism of Einstein and Minkowski - so Palagyi's criticism is considered to be misguided and his model has little in common with special relativity.[36]

[edit] Principle of relative motion and clock synchronization

Henri Poincaré

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. So Henri Poincaré (1898) in his paper The Measure of Time 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."[37]

Poincaré (1895, 1900a) 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."[38] 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.[39]

In his recommendation of Lorentz for the Nobel Prize in 1902, Poincaré argued that Lorentz has convincingly explained the negative outcome of the known the aether-drift experiments by inventing the "diminished time", i.e. that two events at different place could appear as simultaneous, although they are not simultaneous in reality.[40] In the same year he published the philosophical and popular-scientific book "Science and Hypothesis", which included:

  • philosophical assessments on the relativity of space, time, and simultaneity
  • the opinion that a violation of the Relativity Principle can never be detected
  • the possible non-existence of the aether, and also some arguments supporting the aether
  • many remarks on the non-Euclidean geometry.

Like Poincaré, Alfred Bucherer (1903) believed in the validity of the relativity principle within the domain of electrodynamics. Contrary to Poincaré he assumed that this implies the nonexistence of the aether. However, the theory which was created by Bucherer later in 1906 was incorrect and not self-consistent. Also any form of relativity of space and time was absent within this theory.[41]

[edit] Lorentz's 1904 model

In his paper Electromagnetic phenomena in a system moving with any velocity smaller than that of light, Lorentz (1904) was following the suggestion of Poincaré and attempted to create a formulation of Electrodynamics, which explains the failure of all known ether drift experiments, i.e. the relativity principle. He tried to prove the validity of the Lorentz transformation for all orders, 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. And using the electromagnetic momentum, he could 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.[42]

Wien (1903) 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 — which was already noted by Searle (1897). 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.[43]

Abraham (1904) 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.[44]

In a September 1904 lecture in St. Louis named The Principles of Mathematical Physics, 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.[45]

Cohn (1904) 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, at least within Lorentz's theory. Therefore, Cohn believed that the Lorentz transformed quantities were only valid for optical phenomena, but mechanical clocks would indicate the "real" time.[46]

Friedrich Hasenöhrl (1904) 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. 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. However, Abraham and Hasenöhrl himself in 1905 changed the result to m = (4/3)E/c2, the same value as for the electromagnetic mass for a body at rest.[47]

[edit] Poincaré's Dynamics of the electron

On 5 June 1905, 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 (the so called "Poincaré stresses") 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.[48][49]

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 ). He spoke literally of „the postulate of relativity“. He showed that the transformations are a consequence of the Principle of Least Action and developed the properties of the Poincaré stresses. 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), and he used an early form of four-vectors. 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. But this problem was quickly solved.[50] However, Poincaré continued to refer to an (undetectable) aether and to distinguish between "apparent" and "real" coordinates, so most historians of science argue that Poincaré failed to invent what is now called special relativity.[51]

[edit] Special relativity

[edit] Einstein 1905

[edit] Electrodynamics of moving bodies

Albert Einstein, 1921

In September 1905 (received June 30), Albert Einstein published his annus mirabilis paper on what is now called Special Relativity. Einstein's paper 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.

Because of his axiomatic method, Einstein was able to derive all results of his predecessors - and in addition the formulas for the Relativistic Doppler effect and Relativistic aberration - 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.[52][53]

It's notable that Einstein's paper contains no references to other papers. However, many historians of science like Holton,[54] Miller,[55] Stachel,[56] have tried to find out possible influences on Einstein. Einstein himself stated that his thinking was influenced by the empiricist philosophers David Hume and Ernst Mach. Regarding the Relativity Principle, the moving magnet and conductor problem (possibly after reading a book of August Föppl) and the various negative aether drift experiments were important for him to accept that principle — but he denied any significant influence of the most important experiment: the Michelson-Morley experiment.[56] Other possible sources are Poincaré's Science and Hypothesis, where he described the Principle of Relativity and which was read by Einstein in 1904,[57] and the writings of Max Abraham, from whom he borrowed the terms "Maxwell-Hertz equations" and "longitudinal and transverse mass".[58]

Regarding his views on Electrodynamics and the Principle of the Constancy of Light, Einstein himself stated that Lorentz's theory of 1895 (or the Maxwell-Lorentz electrodynamics) and also the Fizeau experiment 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.[59] 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. 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):[59]

“ 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. ”

[edit] Mass-energy equivalence

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

E_{kin}=mc^2\left(\frac1{\sqrt{1-\frac{v^2} {c^2}}}-1\right)

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.[60]

[edit] Early reception

[edit] First assessments

Walter Kaufmann (1905, 1906) 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 name "Lorentz-Einstein-Theory" was used by others for some years as well.[61] Shortly after that, Max Planck published his first work on relativity, in which he described Einstein's theory as a "generalization" of Lorentz's theory. According to Miller, Planck in 1906 seems to be the first who used the term "relative theory" (Relativtheorie) together with the term "Lorentz-Einstein-Theory" — in contrast to the "sphere theory" (Kugeltheorie) of Abraham. In the following discussion of that paper, Alfred Bucherer changed it to "relativity theory". In addition, Einstein himself and many others simply referred to the new method as the "relativity principle". All of those expressions were used by different physicists alternately in the next years.[62]

[edit] Kaufmann-Bucherer experiments

Kaufmann (1905, 1906) announced the results of his new experiments on the charge to mass ratio, i.e. the velocity dependence of mass. 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. Following Kaufmann, other physicists like Alfred Bucherer (1908), and Günther Neumann (1914) also examined the velocity-dependence of mass, and this time it was thought that the "Lorentz-Einstein theory" and the relativity principle is confirmed, and Abraham's theory is disproved. However, it was later pointed out that the Kaufmann-Bucherer-Neumann experiments only showed a qualitative mass increase of moving electron, but they were not precise enough to distinguish between the models of Lorentz-Einstein and Abraham. So it lasted until 1940, when those experiments were repeated with sufficient accuracy for confirming the Lorentz-Einstein formula and disproving Abraham's model.[63]

[edit] Relativistic momentum and mass

Max Planck

Planck (1906a) defined the relativistic momentum and gave the correct values for the longitudinal and transverse mass by correcting a slight mistake of the expression given by Einstein in 1905. Planck's expressions were in principle equivalent to those used by Lorentz in 1899.[64] Based on the work of Planck, the concept of relativistic mass was developed by Gilbert Newton Lewis and Richard C. Tolman (1908, 1909) by defining mass as the ratio of momentum to velocity. So the older definition of longitudinal and transverse mass, in which mass was defined as the ratio of force to acceleration, became superfluous. Finally, Tolman (1912) interpreted relativistic mass simply as the mass of the body.[65] However, many modern textbooks on relativity don't use the concept of relativistic mass anymore, and mass is considered as an invariant quantity.

[edit] Mass and energy

Einstein (1906) 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 (1900b) and his own paper is mainly the same.[66] Kurd von Mosengeil, by extending Hasenöhrl's calculation of black-body-radiation in a cavity, set an important cornerstone for relativistic thermodynamics - on that occasion Mosengeil derived the same expression for the additional mass of a body due to electromagnetic radiation as Hasenöhrl. Based on Mosengeil's work, also Planck derived the mass-energy-equivalence, and considered the binding forces within matter as well. 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.[67]

[edit] Dragging coefficient

Already in 1895 Lorentz succeeded in deriving Fresnel's dragging coefficient with the aid of his concept of local time for terms on the order of v/c. Eventually Jakob Laub, and, completely Max von Laue (1907), derived the coefficient for terms of all orders by using the relativistic velocity addition law. So the Fizeau experiment can also be interpreted as a confirmation of special relativity.[68]

[edit] Additional works by Einstein

Einstein (1907) 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). In another paper, Einstein proposed a method for detecting the Transverse Doppler effect, and in fact, that effect was measured in 1938 by Herbert E. Ives and G. R. Stilwell (Ives–Stilwell experiment).[69]

And in an important overview article on the relativity principle (1908a), 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. 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.

[edit] Emission theories of light

Walter Ritz (1908) 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). Also, Einstein briefly considered such a hypothesis before 1905. So this theory obeys the relativity principle and although it violates the constancy of light, it explains the Michelson-Morley-experiment. So the experiment cannot be considered as a direct proof of the constancy of the speed of light in all reference frames.[70] However, the solution provided by special relativity is preferred over an emission theory, for such a 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.[71] However, due to extinction that argument is invalid for optical wavelengths, but it was shown by Brecher (1977) that even at X-ray wavelengths, the velocity of light is independent of the velocity of the stars. Other effects that rule out the theory are the Sagnac effect and the experiments by Alväger, et al. (1964), who measured the velocity of γ-rays after the decay of π0-mesons - the result show that the velocity of light is independent of the source.

[edit] Relativity of simultaneity

The first derivations of relativity of simultaneity by synchronization with light signals were also simplified.[72] Daniel Frost Comstock (1910) placed an observer in the middle between two clocks A and B. 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 (1917) created a model 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."

[edit] Spacetime physics

[edit] Minkowski's spacetime

Hermann Minkowski

Poincaré’s attempt of a four-dimensional reformulation of the new mechanics was not continued by himself, because in his opinion that would entail too much effort.[50] So it was Hermann Minkowski (1907), who worked out the consequences of that notion. That was based on the work of many mathematicians of the 19th century like Arthur Cayley (1859), who contributed to Group theory, Invariant theory and Projective geometry.[73] Using similar methods, Minkowski succeeded in formulating a geometrical interpretation of the Lorentz transformation. He completed, for example, the concept of four vectors; he created the Minkowski diagram for the depiction of space-time; he was the first to use expressions like world line, proper time, Lorentz invariance/covariance, etc.; and most notably he presented a four-dimensional formulation of electrodynamics. Similar to Poincaré he tried to formulate a Lorentz-invariant law of gravity, but that work was superseded by Einstein's elaborations on gravitation.

In 1907 Minkowski named four predecessors who contributed to the formulation of the relativity principle: Lorentz, Einstein, Poincaré and Planck. And in his famous lecture Space and Time (1908) he mentioned Voigt, Lorentz and Einstein. Minkowski himself considered Einstein's theory as a generalization of Lorentz's and credited Einstein for completely stating the relativity of time, but he criticized his predecessors for not fully developing the relativity of space. However, modern historians of science argue that Minkowski's claim for priority was unjustified. That is because Minkowski (like Wien or Abraham) adhered to the electromagnetic world-picture and apparently didn't fully understand the difference between Lorentz's electron theory and Einstein's kinematics.[74][75] In 1908, Einstein and Laub 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. 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.[76] Eventually, also Einstein (1912) agreed on the importance of Minkowski's spacetime formalism and used it for his intense work on the foundations of general relativity.

[edit] Vector notation and closed systems

Minkowski's space-time formalism was extended and therefore was quickly accepted.[75] For example, Arnold Sommerfeld (1910) replaced Minkowski's matrix notation by an elegant vector notation and coined the terms "four vector" and "six vector". He also introduced a trigonometric formulation of the relativistic velocity addition rule, which according to Sommerfeld, removes much of the strangeness of that concept. Other important contributions were made by Laue (1911, 1913), who used the spacetime formalism to create a relativistic theory of deformable bodies and elementary particle theory.[77][78] He extended Minkowski's expressions for electromagnetic processes to all possible forces and thereby clarified the concept of mass-energy-equivalence. Laue also showed that non-electrical forces are needed for ensure the proper Lorentz transformation properties and for the stability of matter - he could show that the "Poincaré stresses" are a natural consequence of relativity theory so that the electron be a closed system.

[edit] Reciprocity of time dilation and twin paradox

Lewis and Tolman (1909) described the reciprocity of time dilation by using two light clocks A and B, traveling with a certain relative velocity to each other. The clocks consist of two plane mirrors parallel to one another and to the line of motion. Between the mirrors a light signal is bouncing, and for the observer resting in the same reference frame as A, the period of clock A is the distance between the mirrors divided by the speed of light. But if the observer looks at clock B, he sees that within that clock the signal traces out a longer, angled path, thus clock B is slower than A. However, for the observer moving alongside with B the situation is completely in reverse: Clock B is faster and A is slower. Also Lorentz (1910-1912) discussed the reciprocity of time dilation and analyzed a clock "paradox", which apparently occurs as a consequence of the reciprocity of time dilation. Lorentz showed that there is no paradox if one considers that in one system only one clock is used, while in the other system two clocks are necessary. So the relativity of simultaneity has to be considered as well.

Max von Laue

A similar situation was created by Paul Langevin in 1911 with what was later called the "twin paradox", where he replaced the clocks by persons (Langevin never used the word "twins" but his description contained all other features of the paradox). Langevin solved the paradox by alluding to the fact that one twin accelerates and changes direction, so Langevin could show that the symmetry is broken and the accelerated twin is younger. However, Langevin himself interpreted this as a hint to the existence of an aether. 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. 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. Laue was also the first to visualize the situation using Minkowski diagrams - he demonstrated how the world lines of inertially moving bodies maximize the proper time elapsed between two events.[79]

[edit] Rigid bodies and the Ehrenfest paradox

Paul Ehrenfest (1909) formulated the so called Ehrenfest paradox, according to which the circumference of a rotating disk is shortened because of length contraction by a constant radius. 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.[80] It was also discussed by Vladimir 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. 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.[81]

[edit] Lorentz transformation without second postulate

There were some attempts to derive the Lorentz transformation without the postulate of the constancy of the speed of light. Vladimir Ignatowski (1910) for example used for this purpose a) the principle of relativity, b) and homogeneity and isotropy of space c) the requirement of reciprocity. Philipp Frank and Hermann Rothe (1911) argued that this derivation is incomplete and needs additional assumptions. 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. However, according to Pauli and Miller such models were insufficient to identify the invariant speed in their transformation with the speed of light — for example, Ignatowski was forced to recourse to electrodynamics to include the speed of light. So Pauli and others argued that both both postulates are needed to derive the Lorentz transformation.[82][83] However, until today, others continued the attempts to derive special relativity without the light postulate.

[edit] Non-euclidean reformulations of special relativity

While it was noted by Minkowski (1907) himself, that his space-time formalism can reformulated in a non-euclidean way, he excluded such formulation from his later publications.[84] Some analogies to Riemannian geometry can be found in the work of Born (1909) on rigid bodies,[85] 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, in the lines of Sommerfeld's trigonometric formulation, Alfred Robb (1911) introduced the concept of Rapidity as a hyperbolic angle to characterize frame velocity. Vladimir Varičak (1912) noticed the similarity to Hyperbolic geometry and tried to introduce some hyperbolic functions within special relativity. Edwin Bidwell Wilson and Gilbert N. Lewis (1912) introduced a non-euclidean vector-calculus. However, the contributions of Varičak, Wilson, or Lewis didn't lead to new physical insights. An important discovery related to hyperbolic geometry was made by Émile Borel (1913), who derived the kinematic basis of Thomas precession. Overall these attempts produced little in the way of new results to justify the effort involved and so Minkowski's space-time remained the preferred formalism[84]. In 1988, Abraham Ungar brought new insight to the non-euclidean perspective with new investigations of Thomas precession and Einstein's velocity addition law leading to the development of a new form of hyperbolic trigonometry called gyrotrigonometry based on so-called gyrovectors[86]. One of the insights of the new gyrovector approach is a rethinking of the concept of relativistic mass which had fallen out of fashion with some authors because it did not sit well with the Minkowski formulation[87].

[edit] Acceptance of special relativity

Eventually, most mathematicians and theoretical physicists accepted the results of special relativity. For example, already Planck (1909) compared the implications of the modern relativity principle — especially Einstein's relativity of time — with the revolution by the Copernican system.[88] As a result, the fundamental difference between the dynamical approach of Lorentz and the kinematical of Einstein was pointed out, and the term "Lorentz-Einstein-Theory" wasn't used anymore. Only a few theoretical physicists like Lorentz, Poincaré, Abraham, Langevin, still believed in the existence of an aether in any form.[89] Another important reason for accepting special relativity was the extension of Minkowski's space-time formalism around 1910-1913[75] 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

Today special relativity is seen as an application of linear algebra, but at the time special relativity was being developed the field of linear algebra 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) had not yet come into widespread use. In retrospect, we can see that the Lorentz transformations are simply hyperbolic rotations, as explicitly noted by Minkowski.

[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

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, Harald Nordenson, Hugo Dingler, Louis Essen, Herbert E. Ives, Emanuel Lasker, Hjalmar Mellin, Albert Abraham Michelson, Menyhért Palágyi, Walter Ritz, Georges Sagnac. Other reasons were Antisemitism within the Deutsche 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 phenomenon.

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.[90]

[edit] References

[edit] Primary sources

  • Alväger, Farley, Kjellmann, Walle (1964), "Test of the second postulate of special relativity in the GeV region", Phys. Rev. Letters 12 (3): 260–262, doi:10.1016/0031-9163(64)91095-9 
  • Brecher, Kenneth (1977), "Is the Speed of Light Independent of the Velocity of the Source?", Phys. Rev. Letters 39 (17): 1051–1054, doi:10.1103/PhysRevLett.39.1051 
  • Ehrenfest, Paul (1909), "Gleichförmige Rotation starrer Körper und Relativitätstheorie", Physikalische Zeitschrift 10: 918 
  • Ignatowsky, Waldemar von (1910), Physikalische Zeitschrift 11: 172 
  • Laue, Max von (1911b), "Zur Diskussion über den starren Körper in der Relativitätstheorie", Physikalische Zeitschrift 12: 85–87 
  • Laue, Max von (1913), Das Relativitätsprinzip (2 ed.), Braunschweig: Vieweg 
  • Lorentz, Hendrik Antoon (1886), "De l’influence du mouvement de la terre sur les phénomènes lumineux", Archives néerlandaises des sciences exactes et naturelles 21: 103–176 
  • Lorentz, Hendrik Antoon (1900), "Considerations on Gravitation", Proceedings of the Royal Netherlands Academy of Arts and Sciences 2: 559–574 
  • Lorentz, Hendrik Antoon (1910/1931), Lecture on theoretical physics, Vol.3, London: MacMillan 
  • Lorentz, Hendrik Antoon (1921), "Deux Memoirs de Henri Poincaré sur la Physique Mathematique", Acta Mathematica 38: 293–308, doi:10.1007/BF02392073 ; See Online Oeuvres tome XI, S. 247–261.
  • Michelson, Albert Abraham & Morley, Edward Williams (1886), "Influence of Motion of the Medium on the Velocity of Light", American Journal of Science 31: 377–386 
  • Mosengeil, Kurd von (1907), "Theorie der stationären Strahlung in einem gleichförmich bewegten Hohlraum", Annalen der Physik 327 (5): 867–904, doi:10.1002/andp.19073270504 
  • Palagyi, Menyhért (1901), Neue Theorie des Raumes und der Zeit, Leipzig: Wilhelm Engelmann 
  • Planck, Max (1907), "Zur Dynamik bewegter Systeme", Sitzungsberichte der Königlich-Preussischen Akademie der Wissenschaften, Berlin Erster Halbband (29): 542-570 
  • Planck, Max (1910/1915), Eight lectures on theoretical physics, delivered at Columbia University in 1909, New York: Columbia University Press 
  • Poincaré, Henri (1889), Théorie mathématique de la lumière, 1, Paris: G. Carré & C. Naud  Preface partly reprinted in "Science and Hypothesis", Ch. 12.
  • Poincaré, Henri (1901a), "Sur les principes de la mécanique", Bibliothèque du Congrès international de philosophie: 457–494 . Reprinted in "Science and Hypothesis", Ch. 6-7.
  • Poincaré, Henri (1904), "L'état actuel et l'avenir de la physique mathématique", Bulletin des sciences mathématiques 28 (2): 302–324  English translation in Poincaré, Henri (1904/1906), "The Principles of Mathematical Physics", in Rogers, Howard J., Congress of arts and science, universal exposition, St. Louis, 1904, 1, Boston and New York: Houghton, Mifflin and Company, pp. 604–622  Reprinted in (1905a), Ch. 7-9.
  • Poincaré, Henri (1910), "La Mécanique Nouvelle (Göttingen, 1909)", Sechs Vorträge über ausgewählte Gegenstände aus der reinen Mathematik und mathematischen Physik, Leipzig und Berlin: B.G.Teubner, pp. 41–47 
  • Poincaré, Henri (1912), "L'hypothèse des quanta", Revue scientifique 17: 225–232  Reprinted in Poincaré 1913, Ch. 6.
  • Sommerfeld, Arnold (1910), "Zur Relativitätstheorie I: Vierdimensionale Vektoralgebra", Annalen der Physik 337 (9): 749–776, doi:10.1002/andp.19103370904 
  • Sommerfeld, Arnold (1910), "Zur Relativitätstheorie II: Vierdimensionale Vektoranalyis", Annalen der Physik 338 (14): 649–689, doi:10.1002/andp.19103381402 
  • Stokes, George Gabriel (1845), "On the Aberration of Light", Philosophical Magazine 27: 9–15 
  • Tolman, Richard Chase (1912), "The mass of a moving body", Philosophical Magazine 23: 375–380 
  • Varičak, Vladimir (1911), "Zum Ehrenfestschen Paradoxon", Physikalische Zeitschrift 12: 169 
  • Voigt, Woldemar (1887), "Ueber das Doppler'sche Princip", Nachrichten von der Königl. Gesellschaft der Wissenschaften und der Georg-Augusts-Universität zu Göttingen (2): 41–51 

[edit] Secondary sources

  • Born, Max (1964), Einstein's Theory of Relativity, Dover Publications, ISBN 0486607690 
  • Boyce Gibson, William Ralph (1928), "The Philosophy of Melchior Palagyi. (I) Space-Time and the Criticism of Relativity", Journal of Philosophical Studies 3 (9): 15–28 
  • Darrigol, Olivier (2000), Electrodynamics from Ampére to Einstein, Oxford: Clarendon Press, ISBN 0198505949 
  • Darrigol, Olivier (2004), "The Mystery of the Einstein-Poincaré Connection", Isis 95 (4): 614–626, doi:10.1086/430652 
  • Einstein, Albert (1989), "The Swiss Years: Writings, 1900-1909", in Stachel, John et al., The Collected Papers of Albert Einstein, 2, Princeton: Princeton University Press, ISBN 0-691-08526-9 
  • Galison, Peter (2003), Einstein's Clocks, Poincaré's Maps: Empires of Time, New York: W.W. Norton, ISBN 0393326047 
  • Goenner, Hubert (2008), "On the history of geometrization of space-time", 414. Heraeus-Seminar . arΧiv:0811.4529
  • Hentschel, Klaus (1990), Interpretationen und Fehlinterpretationen der speziellen und der allgemeinen Relativitätstheorie durch Zeitgenossen Albert Einsteins, Basel - Boston - Bonn: Birkhäuser, ISBN 3764324384 
  • Holton, Gerald (1988), Thematic Origins of Scientific Thought: Kepler to Einstein, Harvard University Press, ISBN 0674877470 
  • Katzir, Shaul (2005), "Poincaré’s Relativistic Physics: Its Origins and Nature", Phys. Perspect. 7: 268–292, doi:10.1007/s00016-004-0234-y 
  • Miller, Arthur I. (1981), Albert Einstein’s special theory of relativity. Emergence (1905) and early interpretation (1905–1911), Reading: Addison–Wesley, ISBN 0-201-04679-2 
  • Pais, Abraham (1982), Subtle is the Lord: The Science and the Life of Albert Einstein, New York: Oxford University Press, ISBN 0-19-520438-7 
  • Schaffner, Kenneth F. (1972), Nineteenth-century aether theories, Oxford: Pergamon Press, pp. 99–117 und 255–273, ISBN 0-08-015674-6 
  • Stachel, John (2002), Einstein from "B" to "Z", Boston: Birkhäuser, ISBN 0-8176-4143-2 
  • Whittaker, Edmund Taylor (1951), A History of the theories of aether and electricity Vol. 1: The classical theories (2. ed.), London: Nelson 
  • Whittaker, Edmund Taylor (1953), A History of the theories of aether and electricity Vol. 2: The modern theories 1900-1926 (2. ed.), London: Nelson 
  • Zahar, Elie (1988/2003), Einstein's Revolution: A Study in Heuristic, Chicago: Open Court Publishing Company, ISBN 0812690672 
Non-mainstream

[edit] Notes

  1. ^ Whittaker (1951), 128ff
  2. ^ Whittaker (1951), 240ff
  3. ^ Whittaker (1951), 306ff; (1953) 51f
  4. ^ Miller (1981), 46
  5. ^ Miller (1981), 99-100
  6. ^ Whittaker (1951), 319ff
  7. ^ Janssen/Stachel (2004), 20
  8. ^ Miller (1981), 46
  9. ^ Whittaker (1951), 107ff
  10. ^ Whittaker (1951), 386f
  11. ^ Janssen/Stachel (2004), 4-15
  12. ^ Whittaker (1951), 390f
  13. ^ Whittaker (1951), 386ff
  14. ^ Janssen/Stachel (2004), 18-19
  15. ^ Janssen/Stachel (2004), 19-20
  16. ^ Miller (1981), 114-115
  17. ^ a b Pais (1982), Chap. 6b
  18. ^ Brown (2001)
  19. ^ Miller (1981), 27–29
  20. ^ Janssen (1995), Chap. 3.3
  21. ^ Janssen (1995), Ch. 3.3
  22. ^ Janssen (1995), Ch. 3.1
  23. ^ Macrossan (1986)
  24. ^ Janssen (1995), Ch. 3.4
  25. ^ Miller (1981), 46, 103
  26. ^ Darrigol (2005), 18-21
  27. ^ Janssen/Stachel (2004), 31-32
  28. ^ Miller (1981), 47-54
  29. ^ Miller (1981), 61-67
  30. ^ Lange (1886)
  31. ^ Giulini (2001), Ch. 4
  32. ^ DiSalle (2002)
  33. ^ Goenner (2008)
  34. ^ Archibald (1914)
  35. ^ Boyce Gibson (1928)
  36. ^ Hentschel (1990), 153f.
  37. ^ Galison (2003)
  38. ^ Katzir (2005), 272-275
  39. ^ Darrigol (2005), 10-11
  40. ^ Galison (2002), Ch. 4 - Etherial Time
  41. ^ Darrigol (2000), 369-372
  42. ^ Janssen (1995), Ch. 3.3, 3.4
  43. ^ Miller (1981), Chap. 1, Footnote 57
  44. ^ Miller (1981), 75ff
  45. ^ Katzir (2005), 275-277
  46. ^ Janssen/Stachel (2004), 31-32
  47. ^ Miller (1981), 359-360
  48. ^ Miller (1981), 79-86
  49. ^ Katzir (2005), 280-288
  50. ^ a b Walter (2007), Ch. 1
  51. ^ Katzir (2005)
  52. ^ Darrigol (2005), 15-18
  53. ^ Janssen (1995), Ch. 4
  54. ^ Holton (1988)
  55. ^ Miller (1981)
  56. ^ a b Stachel (1982)
  57. ^ Darrigol (2004), 624
  58. ^ Miller (1981), 86-92
  59. ^ a b Born (1956), 193
  60. ^ Darrigol (2005), 18-21
  61. ^ Miller (1981), 334-352
  62. ^ Miller (1981), 88
  63. ^ Miller (1981), 334-352
  64. ^ Miller (1981), 329-330
  65. ^ Pauli (1921), 634-636
  66. ^ Darrigol (2005), 18-21
  67. ^ Miller (1981), 359-367
  68. ^ Janssen (1995), Ch. 3.1
  69. ^ Miller (1981), 245-253
  70. ^ Norton (2004)
  71. ^ Pauli (1921), 549-553
  72. ^ Bjerknes (2002)
  73. ^ Klein (1910)
  74. ^ Miller (1981), Ch. 7.4.6
  75. ^ a b c Walter (1999b), Ch. 3
  76. ^ Walter (1999a), 49
  77. ^ Miller (1981), Ch. 12.5.8
  78. ^ Janssen/Mecklenburg (2007)
  79. ^ Miller (1981), 257-264
  80. ^ Pauli (1921), 690-691
  81. ^ Pauli (1921), 556-557
  82. ^ Pauli (1921), 555-556
  83. ^ Miller (1981), 218-219
  84. ^ a b Walter (1999b)
  85. ^ Pais (1982), Ch. 12b
  86. ^ Roman Ulrich Sexl, Helmuth Kurt Urbantke, (2001), "Relativity, Groups, Particles: Special Relativity and Relativistic Symmetry in Field and Particle Physics", pages 141-142, Springer, ISBN 9783211834435
  87. ^ Abraham A. Ungar (2005), "Analytic Hyperbolic Geometry: Mathematical Foundations and Applications", Published by World Scientific, ISBN 9789812564573
  88. ^ Pais (1982), 11a
  89. ^ Miller (1981), Ch. 7.4.12
  90. ^ CosmosMagazine: Was Einstein a fake?

[edit] See also

[edit] External links

Retrieved from "http://en.wikipedia.org/wiki/History_of_special_relativity"
Personal tools
Visit joltnews for the latest headlines
Visit bloit.com for company information
Geed Media does computer consulting on long island.
This page viewed times. See Logs