History of the special theory of relativity
The history of the special theory of relativity describes the development of empirical and conceptual proposals and findings within theoretical physics , which led to a new understanding of space and time. After a series of theoretical and experimental preparatory work by various authors in the 19th century, this development was initiated in the years around 1900, in particular by Hendrik Antoon Lorentz and Henri Poincaré , and culminated in 1905 in the elaboration of the special theory of relativity by Albert Einstein . The theory was subsequently expanded, especially by Hermann Minkowski .
overview
Isaac Newton's Principia, published in 1687, assumed an absolute space and an absolute time . At the same time, Galileo Galilei's principle of relativity also applied in his theory , according to which all observers who are uniformly moved relative to one another cannot determine their absolute state of motion. Their perspectives are therefore equal and subject to the Galileo transformation ; there is no privileged frame of reference. At the end of the 19th century, various physicists emphasized that, strictly speaking, this leads to a multiplication of “absolute spaces” - for example Ludwig Lange , who introduced the operationally justified term inertial system in 1885 . Ernst Mach saw the absoluteness of space and time not being adequately phenomenologically and empirically founded.
The counterpart to the “absolute space” of mechanics was the ether in electrodynamics . This concept is based on the assumption, which was not questioned until the beginning of the 20th century, that waves need a medium to propagate. In analogy to sound, which needs air to propagate, the “ether” was postulated for light, which was also presented as material. James Clerk Maxwell formulated this requirement in such a way that all optical and electrical phenomena propagate in one medium. Under these assumptions, the speed of light has the value given by Maxwell's equations only relative to the ether. As a result of the then widespread assumption that the aether was resting and not being carried along by the earth, it would be possible to determine the state of motion of the earth relative to the aether and to use it as an excellent reference system. However, all attempts to determine the relative motion of the earth to him failed.
From 1892 this led to the development of Maxwell-Lorentzian electrodynamics by Hendrik Antoon Lorentz , which was based on an absolutely stationary ether. Its undetectability was explained by the assumption that bodies moving in the ether are shortened ( length contraction ), and processes in bodies moving in the ether are slowed down ( time dilation ). The basis for this, however, was that the Galileo transformation was replaced by the Lorentz transformation . In his subsequent work from 1904, Lorentz was only able to partially fulfill the principle of relativity. In 1904, Henri Poincaré recognized that the impossibility of exceeding the speed of light was the main characteristic of the “new mechanics” (that is, of Lorentz's theory) for all observers. In 1905 he succeeded in a complete physical generalization and mathematically elegant formalization of Lorentzian electrodynamics, whereby he established the principle of relativity as a universally valid law of nature including electrodynamics and gravity - however, he continued to adhere to the existence of an ether and the distinction between "true" and "apparent" Fixed lengths and times.
Albert Einstein finally succeeded in 1905 with the special theory of relativity (SRT) by changing the concepts of space and time and by abolishing the aether, a complete reinterpretation of Lorentzian electrodynamics. Einstein derived these results exclusively from the principle of relativity and the principle of the constancy of the speed of light, which he based his theory on as postulates. With the abolition of the conception of an ether there was no longer any reason to differentiate between “true” and “apparent” coordinates, as was the case with Poincaré and Lorentz. All of this paved the way for relativistic field theories and the development of general relativity (GTR). According to Einstein, the investigations into SRT were continued by Hermann Minkowski , among others , who in 1907 developed the formal basis for today's concept of four-dimensional space - time .
Ether and electrodynamics of moving bodies
Ether models and Maxwell's equations
In the 19th century, mainly through the work of Thomas Young (1804) and Augustin Jean Fresnel (1816), one came to the conviction that light propagates as a transverse wave in a medium (“ light ether ”) which many consider to be elastic Solid was understood. However, a distinction was still made between optical phenomena on the one hand and electrodynamic phenomena on the other. That means, separate ether variants had to be constructed for each of these phenomena. Attempts to unite these ether variants and to present a completely valid mechanical description of the ether failed, however.
After preliminary work by physicists such as Michael Faraday , Lord Kelvin and others, James Clerk Maxwell (1864) developed basic equations for electricity and magnetism , the so-called Maxwell's equations . He designed a model in which the phenomena of optics and electrodynamics can be traced back to a single, electromagnetic ether, and defined light as an electromagnetic wave that spreads constantly with the speed of light in relation to the ether. As a further important consequence of the theory, Maxwell (1873) derived the existence of electrostatic and magnetic "tensions" which can exert pressure on bodies - a direct consequence of this is the radiation pressure exerted by light . Adolfo Bartoli (1876) deduced the existence of the same pressure from thermodynamic considerations.
After Heinrich Hertz (1887) had demonstrated the existence of electromagnetic waves, Maxwell's theory was finally widely accepted. Oliver Heaviside (1889) and Hertz (1890 a, b) introduced modernized versions of Maxwell's equations, which formed an important basis for the further development of electrodynamics ("Maxwell-Hertz" and "Heaviside-Hertz" equations). In the end, it was the form given by Heaviside which generally prevailed. In early 1900, however, Hertz's theory was experimentally refuted and had to be abandoned. Hertz himself was one of the last supporters of the “mechanistic worldview”, according to which all electromagnetic processes should be traced back to mechanical impact and contact effects in the ether.
The ether cannot be found
As for the state of motion of the aether relative to matter, two possibilities were considered in principle, which were already discussed before Maxwell's work:
- Fresnel (1816) and later Hendrik Antoon Lorentz (1892a) put forward the idea of an ether that is at rest or only partially carried along with a certain coefficient, and
- that by George Gabriel Stokes (1845) and later by Hertz (1890b) assumed complete entrainment of the ether through matter.
Fresnel's theory was preferred because his theory could explain the aberration of light and many optical phenomena and because his drag coefficient was measured very precisely by Hippolyte Fizeau (1851) using the Fizeau experiment . On the other hand, Stokes' theory could not prevail because it contradicted both the aberration and the result of the Fizeau experiment - the auxiliary hypotheses introduced as a result were not convincing or contradicting at all.
Albert A. Michelson (1881) tried to directly measure the relative movement of earth and ether ("ether wind"), which according to Fresnel's theory should have occurred. However, with his interferometer arrangement he could not determine the result he expected and interpreted the result as evidence for the thesis of Stokes (complete ether entrainment through the earth) and thus against the theory of Fresnel. Lorentz (1886) demonstrated, however, that Michelson had made a calculation error in the calculations, from which it emerged that the experiment was too imprecise to even produce a positive measurement result within the scope of the measurement accuracy, which Michelson himself admitted. Since the Fresnel theory did not seem refuted after all, Michelson and Edward W. Morley (1886) carried out an experiment in which Fizeau's measurements of the Fresnel drag coefficient were to be checked. In fact, the confirmation was successful and, contrary to his statement from 1881, Michelson was of the opinion this time that Fresnel's dormant ether was confirmed. However, this required a repetition of the Michelson experiment from 1881, whereby, to the great surprise of Michelson and Morley, this now famous Michelson-Morley experiment once again failed to deliver the expected positive result. Again, the experiment seemed to confirm the Stokes' ether, which had actually already been refuted, and was in stark contrast to the experiment of 1886, which spoke for the Fresnel ether.
Woldemar Voigt developed (1887) on the basis of an elastic ether model ( i.e. not Maxwell's electromagnetic model) and in the course of investigations into the Doppler effect, a coordinate transformation between a system resting in the ether and a moving system. The equations of the Voigt transformation left the wave equation unchanged, were identical to the later Lorentz transformation except for a different scale factor and could explain the Michelson-Morley experiment. They included the expression for the y and z coordinates, later known as the “Lorentz factor”, and a new time variable later called local time . However, they were not symmetrical and consequently violated the principle of relativity.
Yet another possibility of an explanation emerged: Heaviside (1889) and George Frederick Charles Searle (1897) found that electrostatic fields were contracted in the direction of movement (Heaviside ellipsoid). Following Heaviside's work, George FitzGerald (1889) introduced the ad hoc hypothesis that material bodies also contract in the direction of movement, which leads to length contraction and could explain the Michelson-Morley experiment - in contrast to Voigt's equations, the x -Coordinate changed. FitzGerald justified this with the fact that the intermolecular forces are possibly of electrical origin. However, his idea was initially not noticed and only became known through a publication by Oliver Lodge (1892). Independently of FitzGerald, Lorentz (1892b) also proposed the same hypothesis ("FitzGerald-Lorentz contraction hypothesis"). For reasons of plausibility, like FitzGerald, he referred to the analogy to the contraction of electrostatic fields, although he himself admitted that this was not a compelling reason.
Lorentz's 1895 theory
Hendrik Antoon Lorentz laid the foundations of (Maxwell) Lorentz's electrodynamics or ether or electron theory in 1892 and above all in 1895 by assuming, like others before him, the existence of electrons in addition to ether. He assumed that the aether was completely at rest and not carried along by the electrons. This resulted in the important consequence that the speed of light is completely independent of the speed of the light source and consequently it is constant under all circumstances relative to a coordinate system in which the aether rests. Instead of making any statements about the mechanical nature of the ether and the electromagnetic processes, he tried, conversely, to trace many mechanical processes back to electromagnetic ones. As part of his theory, Lorentz (like Heaviside) calculated the contraction of the electrostatic fields and, independently of Voigt, introduced local time as a mathematical auxiliary variable. Thus he had a preliminary form of the equations later known as the Lorentz transformation , which served to explain all negative aether drift experiments for quantities of the first order of v / c. He used (1895) the term "theorem of the corresponding states", i. H. the Lorentz covariance of the electromagnetic equations for relatively low speeds. From this it follows that the form of the electromagnetic equations of a "real" system - resting in the ether - corresponds to the form of a "fictitious" system - moving in the ether. However, Lorentz recognized that his theory violated the principle of actio and reactio , because although the aether had an effect on the matter, the matter could not react on the aether.
Joseph Larmor (1897, 1900) designed a very similar model to Lorentz, but he went one step further and brought the Lorentz transformation into an algebraically equivalent form, as it is used to this day. He saw that not only the length contraction can be deduced from it, but he also calculated a kind of time dilation , according to which rotations of electrons moving in the ether proceed more slowly than electrons at rest. Larmor was only able to show that this transformation is valid for quantities of the second order, but not for all orders. Lorentz (1899) also extended his transformation for quantities of the second order (with an, however, indefinite factor) and, like Larmor before, noted a kind of time dilation. It is not known to what extent Lorentz and Larmor influenced each other; that is, it is not clear whether Larmor (1897) took over the local time from Lorentz and, conversely, whether Lorentz (1899) took over the complete transformations from Larmor. Although both cite the other's works and were in contact by letter, they did not discuss the Lorentz transformation.
However, there were also alternative models to the theories of Lorentz and Larmor. Emil Cohn (1900) designed electrodynamics in which he was one of the first to reject the existence of the ether (at least in its previous form) and instead, like Ernst Mach , used the fixed stars as reference bodies. In this way he was able to explain the Michelson-Morley experiment, since the earth is at rest relative to the fixed stars, but according to his theory the speed of light in media could be exceeded simultaneously in different directions. Because of this and other discrepancies, the theory (also by Cohn himself) was later rejected. In addition, he also discussed Lorentz's theory and used the term "Lorentz's transformation".
Electromagnetic mass
Joseph John Thomson (1881) recognized during his further development of Maxwell's electrodynamics that electrostatic fields behave as if they were adding an "electromagnetic mass" to the body in addition to the mechanical one. At that time this was interpreted as the result of a self-induction of the convection currents in the ether. He also recognized that this mass increases with moving bodies (by a factor that is the same for all positive speeds). Above all, George FitzGerald , Oliver Heaviside , and George Frederick Charles Searle corrected some errors and continued Thomson's work - using the formula (in modern notation) as the expression for the electromagnetic mass . Heaviside (1888) also recognized that the increase in electromagnetic mass in moving bodies is by no means constant, but rather increases with greater speed. Searle (1897) concluded from this that this makes it impossible to exceed the speed of light, since an infinite amount of energy would be required. This connection was also integrated into his theory by Lorentz in 1899. He noted that these due to the Lorentz transformation varies not only with the speed, but also with the direction and led the later of Max Abraham became known as longitudinal and transverse mass Terme one - with only the transverse mass of the later than relativistic mass designated Term corresponded.
Wilhelm Wien (1900) (and before him Larmor and Emil Wiechert ) took the view, based on Lorentz's theory, that - contrary to Hertz's “mechanistic worldview” - all forces of nature can be explained electromagnetically (“electromagnetic worldview”). Accordingly, he assumed that the entire mass was of electromagnetic origin. This means that for Vienna the formula - which Thomson (in it Heaviside and Searle followed) used - applied to the entire mass of matter. He also noted that gravity must be proportional to electromagnetic energy if it could also be traced back to electromagnetic energy. And in the same journal, Henri Poincaré (1900b) derived the electromagnetic impulse from the Maxwellian stresses mentioned and the theory of Lorentz and concluded, in connection with the reaction principle , that the electromagnetic energy corresponded to a "fictitious" mass of or - Poincaré using these terms regarded as mathematical fictions. In the process, however, he came across a radiation paradox that was only later resolved satisfactorily by Einstein.
Walter Kaufmann (1901–1903) was the first to experimentally confirm the speed dependence of the electromagnetic mass. A cathode beam of electrons was generated from metals so that the relationships between charge, speed and mass could be determined. Since it was already known that the charge of an electron is independent of its speed, the result of a decrease in the charge-to-mass ratio for speeds close to the speed of light, shown experimentally by Kaufmann, could only be attributed to an increase in the mass of the investigated electrons. Kaufmann believed that his measurements had proven that the entire mass of matter was of electromagnetic origin.
Max Abraham (1902–1903), who like Vienna was a staunch supporter of the electromagnetic worldview, presented an explanation and continued the theory started by Lorentz. He was the first to present a field theoretical concept of electrons. In contrast to Lorentz, however, he defined the electron as a rigid, spherical structure and rejected its contraction, which is why his mass terms also differed from those used by Lorentz (Abraham was the first to coined the terms longitudinal and transversal mass). In addition, following Poincaré, he introduced the term “electromagnetic pulse”, which is proportional to . In contrast to Poincaré and Lorentz, however, he understood this as a real physical entity. Abraham's theory became the main competitor to Lorentz's theory over the next few years. Kaufmann's experiments, however, were too imprecise to allow a decision between the theories.
Finally, Friedrich Hasenöhrl (1904) combined energy with indolence in a script that, in his own words, was very similar to Abraham's. Hasenöhrl assumed that part of the mass of a body (the "apparent mass") can be understood as radiation in a hollow body. The inertia of this radiation is proportional to its energy according to the formula . He noticed the close connection between mechanical work, temperature and apparent mass, since radiation and thus additional inertia arise with every heating. However, Hasenöhrl restricted this energy-apparent-mass relationship to radiating bodies; For Hasenöhrl, this means when a body has a temperature that is greater than 0 Kelvin. However, he published (1905) the summary of a letter that Abraham had written to him, in which Abraham criticized the result and gave it as the corrected value for the apparent mass, i.e. the same value as for the already known electromagnetic mass. Hasenöhrl checked his own calculations and confirmed Abraham's result.
Absolute space and absolute time
Newton's definition of absolute space and absolute time has now been questioned by some authors. For example, instead of any absolute quantities , Carl Gottfried Neumann (1870) introduced a "body alpha" which is supposed to represent a rigid and fixed reference body to which the inertial movement can be related. Ernst Mach (1883) argued that terms such as absolute space and time are meaningless and that only reference to relative movement is meaningful. He also said that even accelerated movement such as rotation can be relativized by referring to “distant masses” without having to assume an absolute space. Neumann's argument was continued by Heinrich Streintz (1883). If measurements by gyroscopes show no rotation, one could, according to Streintz, speak of an inertial movement in relation to a “fundamental body” or a “fundamental coordinate system ”. After all, Ludwig Lange (1885) was the first to introduce the term inertial system based on similar lines of thought in order to remove absolute quantities from kinematics. He defines this as " a system of the nature that with reference to it the converging, continuously described paths of three points projected at the same time from the same spatial points and immediately left to one another (but which should not lie in a straight line) are all straight ". Furthermore, Poincaré (1902) published the philosophical and popular science book "Wissenschaft und Hypothese", which u. a. Contained: Philosophy about the relativity of space, time and simultaneity; the terms "principle of relative motion" and " principle of relativity "; the opinion that the ether can never be discovered, d. H. the validity of the principle of relativity; the possible non-existence of the ether - but also arguments for the ether; detailed descriptions of non-Euclidean geometry .
There has also been speculation about time as a fourth dimension . For example, Jean d'Alembert did this in the Encyclopédie as early as 1754 , as did some authors in the 19th century such as HG Wells in his novel The Time Machine (1895). And Menyhért Palágyi (1901) developed a philosophical model according to which space and time are merely linguistic terms for a "space-time form" that is actually uniform. He uses time as the fourth dimension for his “spacetime theory”, which he already had in the form of it ( i denotes the imaginary unit ). However, in Palágyi's philosophy there was no connection to Lorentz's local time, because with him the time dimension is not dependent on the speed of light. He also rejected any connection with the already existing constructions of n-dimensional spaces and non-Euclidean geometry. Significantly, Palágyi later (1915) also rejected the space-time constructions of Minkowski and Einstein - this is why Palágyi's criticism is viewed as unfounded and it is judged that his theory has little to do with the theory of relativity.
Principle of relative movement and clock synchronization
In the second half of the 19th century one was intensely busy with building a worldwide clock network synchronized with electrical signals, whereby the finiteness of the speed of light was already taken into account. Henri Poincaré (1898) drew far-reaching consequences for philosophy and physics from this. He noted that synchronization with light signals impact on the definition of simultaneity in different places to be had, and therefore the definition of simultaneity is a pure, based on convenience Convention. He argued that the assumption of a constant speed of light in all directions (e.g. for astronomical purposes) as a " postulate " would be advantageous in order to give laws such as Newton's law of gravity as simple as possible. In further works Poincaré (1895, 1900a) declared that he did not believe in an absolute movement or the discovery of a movement in relation to the ether, and called this view the "principle of relative movement". In the same year (1900b) Poincaré recognized that one can define Lorentz local time by two observers synchronizing their clocks with light signals (Poincaré- Einstein synchronization ). If, based on the principle of relativity, they assume that they are at rest, they conclude that light is traveling at the same speed in both directions. However, if they were moved towards the aether, they would make a mistake and the clocks could not be synchronous ( relativity of simultaneity ). Thus Poincaré defined local time as something that can be physically interpreted and displayed with clocks - in clear contrast to the purely mathematical interpretation of Lorentz.
Alfred Bucherer (1903) explained, like Poincaré, that only relative movements of the bodies to one another, but not to the ether, can be determined. In contrast to Poincaré, however, he drew the conclusion that the concept of light ether should then be rejected at all. The theory that Bucherer constructed in the following was, however, unusable for experimental reasons as well as for content-related reasons - and Bucherer did not draw any conclusions with regard to the relativity of space and time, despite the rejection of the ether concept.
The 1904 theory by Lorentz
Influenced by Poincaré's demand that an absolute motion be undetectable, Lorentz (1904b) finally came very close to completing his theorem of the corresponding states. Like Abraham, he developed a field-theoretical concept of electrons, which, in contrast to Abraham, tried to take into account the contraction of electrons and thus the principle of relativity. This enabled him to explain the negative result of the Trouton Noble experiment (1903), in which a torque due to the ether wind was expected , using the electromagnetic pulse . The negative results of the experiments by Rayleigh and Brace (1902, 1904) on birefringence could also be explained. Another important step was that he extended the validity of the Lorentz transformation to non-electrical forces (if they exist). However, Lorentz failed to show the full Lorentz covariance of the electromagnetic equations.
Around the same time as Lorentz was drafting his theory, Wien (1904a), like Searle (1897) before him, determined that, due to the speed dependence of mass, exceeding the speed of light requires an infinite amount of energy and is therefore impossible. And after he had the final version of Lorentz's theory, he (1904b) concluded the same from the contraction of length, since at faster than light the length of a body would assume an imaginary value.
Abraham (1904), however, showed a fundamental flaw in Lorentz's theory. On the one hand, this theory was constructed in such a way that the principle of relativity is fulfilled, but the electromagnetic origin of all forces should also be shown. Abraham showed that both assumptions are incompatible, since in Lorentz's theory the contracted electrons require a non-electrical binding energy that guarantees the stability of matter. In Abraham's rigid electron theory, such energy was not necessary. The question now arose whether the electromagnetic worldview (compatible with Abraham's theory) or the principle of relativity (compatible with Lorentz's theory) was correct.
Already taking into account the new theory of Lorentz, Poincaré (1904) defined in a speech in September in St. Louis (by combining the Galilean principle of relativity with the Lorentz theorem of the corresponding states) the “principle of relativity” as a requirement that the laws of nature for all observers must be the same, regardless of whether they are moving or not and therefore their absolute state of motion must remain unknown. He specified his clock synchronization method through light and thus his physical interpretation of the local time and explained that a “new method” or “new mechanics” might come, which would be based on the impossibility of exceeding the speed of light (also for observers moving relative to the ether). However, he noted critically that both the relativity principle, Newton's actio and reactio , the law of conservation of mass and the law of conservation of energy are by no means certain.
In November (1904) Cohn showed possibilities for a physical interpretation of Lorentz's theory (which he compared with his own). He referred to the close connection with the measurement by measuring rods and clocks. If these rest in the Lorentzian ether, they show the "true" lengths and times, and if they are moved, they show contracted or dilated values. Like Poincaré, Cohn made the important observation that local time comes about when light propagates on earth as a spherical wave, that is, the propagation of light on earth is assumed to be isotropic. In contrast to Lorentz and Poincaré, Cohn found that the distinction between “true” and “apparent” coordinates in Lorentz's theory seems very artificial, since no experiment can show the true state of motion and all coordinates are equal. On the other hand, Cohn believed that all of this was only valid for the field of optics, whereas mechanical clocks could show the "true" time.
Lorentz 'article from 1904 was summarized in the spring of 1905 by Richard Gans in issue No. 4 of the bi-weekly supplement to the annals of physics (with mention of the Lorentz transformation ), for which Albert Einstein also summarized at the same time used to contribute important international essays. It is noteworthy that Einstein later stated that he did not know Lorentz's 1904 work, although 14 days later he himself published a whole series of summaries in the same journal, in issue no. 5, signed with the abbreviation "AE" are.
Poincaré's dynamics of the electron
On June 5, 1905, Poincaré finally presented the summary of a work that formally closed the existing gaps in Lorentz's work. Although this document contained many results, it did not contain the derivations of his observations, with essential parts of which were already contained in two letters which Poincaré wrote to Lorentz around May 1905. He spoke of the postulate of the total impossibility of discovering an absolute motion, which is apparently a law of nature. He recognized the group character of the Lorentz transformation he called the first, he gave it the modern symmetrical shape and using the relativistic speed addition, he corrected Lorentz's terms for charge density and speed and thus achieved the full Lorentz covariance. Following Lorentz, he explained that the Lorentz transformation (and thus the Lorentz invariance) must be applied to all forces of nature. But, unlike Lorentz, he also dealt with gravity and claimed the possibility of a Lorentz-invariant gravity model and mentioned the existence of gravitational waves . In order to refute Abraham's criticism, Poincaré introduced a non-electrical pressure (the “Poincaré tensions”), which is supposed to guarantee the stability of the electron and possibly also to dynamically justify the length contraction. With this, however, Poincaré gave up the electromagnetic worldview in favor of the principle of relativity.
Finally, Poincaré (presented on July 23, printed on December 14, published in January 1906) independently of Einstein submitted his work, known as the Palermo Work, which was a significantly expanded version of Poincaré's first 1905 work. He spoke of the "postulate of relativity"; he showed that the transformations are a consequence of the principle of least effect , and he demonstrated in more detail than before their group property, where he coined the name Lorentz group ("Le groupe de Lorentz"). He dealt in detail with the properties of the Poincaré tensions. In connection with his conception of gravity (which, however, turned out to be insufficient) Poincaré showed that the combination is invariant and introduced the expression ict (in contrast to Palágyi, i.e. with the speed of light) as the fourth coordinate of a four-dimensional space - he used a kind of Four-vector . However, Poincaré noted in 1907 that a reformulation of physics into a four-dimensional language is possible, but too cumbersome and therefore of little use, which is why he did not pursue his approaches in this regard - this was only done later by Minkowski. And in contrast to Einstein, Poincaré continued to stick to the concept of the ether.
Special theory of relativity
Einstein 1905
Special theory of relativity
Albert Einstein published in his work On the Electrodynamics of Moving Bodies (transmitted on June 30th, published on September 26th, 1905) with the special theory of relativity, a completely new approach to solve this problem. He not only succeeded in deriving the relevant parts of Lorentz's electrodynamics, but the theory also contained the "abolition of the ether" and the change in the fundamentals of space and time. This was based solely on the assumption of two principles, namely the principle of relativity and the constancy of the speed of light in all uniformly moving frames of reference. In order to understand Einstein's step, the initial situation should be summarized here once again, especially with a view to the theoretical and experimental prerequisites (whereby it must be noted that Einstein, according to his own statement, did indeed use the 1895 theory of Lorentz and "Science and Hypothesis" (1902) von Poincaré knew, but not their work from 1904 to 1905):
- Maxwell-Lorentz's electrodynamics of 1895, which was by far the most successful theory. According to this theory the speed of light is constant in all directions in the aether and independent of the speed of the light source.
- The inability to find an absolute state of motion as a consequence of the negative outcome of all ether drift experiments as well as the fact that the effects of electromagnetic induction are only dependent on the relative motion.
- The Fizeau experiment .
- The existence of the aberration of light .
This has the following consequences for the speed of light and the theories discussed at the time:
- The measured speed of light is not additively composed of the vacuum speed of light and the speed of a preferred reference system, because of 2. This is in contradiction to the theory of the static or partially entrained ether.
- The measured speed of light is not an additive combination of the speed of light in a vacuum and the speed of the light source, because of 1 and 3. This is in contradiction to the emission theory .
- The measured speed of light is not additively composed of the vacuum speed of light and the speed of an entrained medium within or near the matter, because of 1, 3 and 4. This is in contradiction to the theory of complete aether entrainment.
- The measured speed of light in moving media is not composed directly of the speed of light in the medium at rest and the speed of the medium, but rather follows Fresnel's entrainment coefficient, because of 3.
Although it is always possible to introduce various ad hoc hypotheses in order to save a particular theory, in science such “conspiracies” of effects that prevent certain discoveries are classified as very unlikely. If, like Einstein, one dispenses with auxiliary hypotheses and unobservable properties, the above list (and a large number of other experiments that have been carried out to date) immediately shows the validity of the principle of relativity and the constancy of the speed of light in all inertial systems. Poincaré and Lorentz partly used the same principles as Einstein, they also taught the complete mathematical equality of the reference systems and recognized that different spatial and time coordinates are actually measured. But they continued to attribute the effects of the Lorentz transformation to dynamic interactions with the ether, differentiated between the "true" time in the stationary ether system and the "apparent" time in relatively moving systems and mentioned the ether until the end in their writings. Specifically, this means that they wanted to modify Newtonian mechanics, but not fundamentally change them. As a result, the fundamental asymmetry in Lorentz's ether theory, namely the mutually exclusive terms such as “resting ether” and the principle of relativity, continued to exist side by side in the conception of the theory, linked only by a system of auxiliary hypotheses. The solution to this problem, namely the fundamental re-evaluation of space and time in the context of a scientific theory, was left to Einstein. This turning away from the ether was easier for him than many of his contemporaries because he already recognized, based on his work on quantum theory , that light can be described as a particle. The classic idea that electromagnetic waves need an ether as a carrier medium was no longer as important for Einstein as it was for Lorentz, for example.
In just a few pages, Einstein was able to derive results based on his axiomatic method that others had only encountered before him in years of complicated work. Einstein explained that the apparent contradiction between the two principles (which he based his theory on as postulates) could be resolved by examining the properties of space, time and simultaneity and the introduction of an ether became superfluous. From the synchronization of clocks with light signals and the related relativity of simultaneity in §§ 1–2, he derived the Lorentz transformation in § 3 from purely kinematic considerations. From this transformation he was able to derive the length contraction, time dilation and the relativistic speed addition theorem in §§ 4-5 as secondary consequences of the theory. In §§ 6-10 he now transferred the results of his kinematic investigations to electrodynamics. He derived the relativistic Doppler effect and the relativistic aberration from the transformations, showed the Lorentz covariance of the electromagnetic equations and calculated the relativistic expressions for the radiation pressure . Finally, he derived the longitudinal and transverse mass of the electrons (the latter, however, with a wrong value).
Equivalence of mass and energy
Already in his work on electrodynamics (§10) Einstein specified the kinetic energy of an electron with:
- .
For the time being, however, it remained open whether this relationship, as in classical mechanics, is only relevant for moving bodies, or whether bodies at rest are also included. In his work “ Does the inertia of a body depend on its energy content? “From September (published November) showed Einstein using a radiation paradox, as it was formulated in a similar form by Poincaré (1900) but could not be resolved, that even bodies at rest can lose and gain mass through the transfer of energy , which is the real thing Equivalence of mass and energy according to leads. Similar formulas for “electromagnetic mass” had already been established by Thomson, Poincaré, Hasenöhrl, etc., as explained above, but they did not fully recognize the meaning of the formula. Einstein, on the other hand, was able to show the deep connection between equivalence and the principle of relativity, and its derivation was completely independent of the question of whether the mass is of electromagnetic origin or not.
Early reception
First assessments
Walter Kaufmann (1905, 1906) was probably the first to refer to Einstein's work. He compared the theories of Lorentz and Einstein, and although he indicated that Einstein's method was preferable, he found the observational equivalence of the two theories. That is why he spoke of the principle of relativity as the "Lorentz-Einsteinian" assumption. Even Max Planck - who played a key role in spreading the theory of relativity and his students Max von Laue and Kurd of Mosengeil won for this theory - said in his first work (1906a) for the SRT from the "Lorentz-Einstein theory" because the principle of relativity was introduced by Lorentz and in an even more “general version” by Einstein. (The name Poincarés can only be found in a few works in the early history of the SRT.) Planck was also the first to use the term “relative theory” derived from the relativity principle for the term “Lorentz-Einstein theory” in a further work (1906b). introduced - in contrast to the "ball theory" of Abraham. In the subsequent discussion of the work, Alfred Bucherer changed this term to (Einstein's) “theory of relativity”. Many (including Einstein) often only used the expression "principle of relativity" for the new method. All of these terms were used alternately by different physicists over the next few years. And Einstein described in an important review article on the principle of relativity (1908a) the content of the SRT as a “union of the Lorentzian theory with the relativity principle” and the main finding that the Lorentzian local time is in reality a real, equal time.
Kaufmann-Bucherer experiments
Kaufmann (1905, 1906) now announced the results of his new experiments. In his opinion, these represent a clear refutation of the relativity principle and the Lorentz-Einstein theory, but the data are very compatible with Abraham's theory. For a few years, Kaufmann's experiments represented a weighty objection to the principle of relativity, but Planck and Adolf Bestelmeyer (1906) questioned the significance of the experiments. Alfred Bucherer finally carried out new experiments in 1908 , which were intended to verify Kaufmann's measurements. This time, however, the result was interpreted by Bucherer as confirmation of the “Lorentz-Einstein theory” and the principle of relativity. However, doubts remained open here too. Further experiments by Neumann (1914) and others also spoke in favor of the theory of relativity, so that one generally came to the conclusion that the matter was decided. However, later research showed that the Kaufmann-Bucherer-Neumann experiments were basically all not accurate enough to allow a decision between the competing theories. In such experiments it was not until 1940 that the Lorentz-Einstein formula was finally confirmed. However, this problem only existed for this type of experiment. When investigating the fine structure of the hydrogen lines , a much more precise confirmation of the Lorentz-Einstein formula, and thus the refutation of Abraham's theory, could be produced as early as 1917.
Relativistic mass and momentum
Planck (1906a) corrected the error in Einstein's definition of transversal relativistic mass and showed that the correct spelling was equivalent to that of Lorentz (1899). He also defined the relativistic impulse . Following Planck's work on relativistic momentum, Gilbert Newton Lewis (1908) and Richard C. Tolman (1912) developed the concept of relativistic mass by defining mass as the ratio of momentum and speed and not as the ratio of force and acceleration ( temporal momentum - or speed change ). This made the old definition for the longitudinal and transverse mass superfluous.
Mass-energy equivalence
Einstein (1906) established that the inertia of energy (mass-energy equivalence) is a necessary and sufficient condition for maintaining the movement of the center of gravity . He referred to Poincaré (1900b) and explained that the content of his work largely coincides with his own. And Kurd von Mosengeil (1907) developed Hasenöhrl's approach for calculating black body radiation in a hollow body, taking Einstein's theory into account, and laid an important foundation stone for relativistic thermodynamics - he received the same value for the mass of electromagnetic radiation as Hasenöhrl. Based on Mosengeil's work, Planck (1907) was also able to derive the mass-energy equivalence from the approach of cavity radiation, and he also took into account the binding forces in matter. He recognized the priority of Einstein's 1905 work on equivalence, but Planck considered his own derivation to be more general.
Experiments by Fizeau and Sagnac
As mentioned above, Lorentz (1895) had already been able to explain the Fresnel entrainment coefficient for quantities of the first order and thus the result of the Fizeau experiment from electromagnetic light theory using local time. After Jakob Laub's first attempts to create an “optics of moving bodies”, it was Max von Laue (1907) who derived this effect for sizes of all orders through a very simple application of the relativistic velocity addition theorem - in contrast to the comparatively complicated method of Lorentz . This result is therefore not only confirmation, but also an example of the efficiency and simplicity of the SRT.
Max von Laue (1911) discussed a possible experiment in which light rays are emitted in opposite directions with a rotating experimental set-up and then return to the starting point. His calculation for the view of a non-rotating inertial system showed that there would have to be a shift of the interference fringes, since according to the theory of relativity the speed of light is independent of the speed of the source and thus the paths of the two rays are different relative to the moving starting point. That means there is no inertial system in which the path of the two light rays would be the same length. An experiment of this kind was carried out by Georges Sagnac (1913), who actually found the corresponding shift ( Sagnac effect ). While Sagnac himself believed to have proven the existence of a dormant light ether, Max von Laue's previous calculation shows that this effect is also in agreement with the SRT - because in both theories the speed of light is independent of the state of motion of the source. On the other hand, an observer rotating with the test arrangement attributes the different light transit times to the acceleration during rotation, whereby the Sagnac effect can be seen as the optical counterpart to rotational mechanical effects, such as e.g. B. Foucault's pendulum . The description from the point of view of a rotating reference system was carried out by Paul Langevin (1937), whereby it should be noted that in accelerated reference systems the speed of light is no longer constant (see section Acceleration ).
A similar experiment was carried out by Franz Harress between 1909 and 1911, which can be viewed as a synthesis of the Fizeau and Sagnac experiments. He tried to measure the entrainment coefficient in glass, but he used a rotating test arrangement, which is very similar to that later used by Sagnac. The displacements he found were not interpreted correctly by Harress, but Laue was able to show that the result found by Harress corresponded to the Sagnac effect. Finally, in the Michelson-Gale experiment (1925, a variation of the Sagnac experiment), the rotation of the earth in accordance with the SRT and a dormant light ether could be demonstrated.
Relativity of simultaneity
The first derivations of the relativity of simultaneity through synchronization with light signals by Poincaré and Einstein have now also been simplified. Daniel Frost Comstock (1910) suggested placing a transmitter in the middle between two clocks at A and B, which sends a signal to both clocks, which in turn are started when the signal arrives. In the system in which A and B rest, the clocks begin to run synchronously. However, from the point of view of a system in which A and B move with v, clock B is set in motion first and then clock A - so the clocks are not synchronized. Einstein also designed a model in 1917 with a moving receiver in the middle between A and B. He also didn't start the signal from the middle, but instead sent two signals from A to B to the receiver. From the point of view of the system in which A and B are at rest, the signals are sent simultaneously - here, however, the receiver approaches the signal from B and runs away from the signal from A, so the signals do not arrive at the same time. From the point of view of the system in which the receiver is at rest, however, this non- simultaneous arrival is interpreted to mean that the signals were not sent simultaneously from A and B from the start .
Emission theory
As an alternative to the theory of relativity, Walter Ritz (1908) and others developed an emission theory based on Newton's corpuscular theory , according to which the speed of light in all reference systems is only constant relative to the emission source (and not to an ether) and where instead of the Lorentz transformation, the Galileo Transformation is used (that is, in systems where the source moves with ± v, the light does not propagate with velocity c, but with c ± v). This theory violates the constancy of light, but still satisfies the principle of relativity and can explain the Michelson-Morley experiment. Even Albert Einstein moved before 1905 such a hypothesis briefly consider what the reason was that he was indeed still unused in his later writings, the Michelson-Morley experiment to confirm the principle of relativity but as confirmation of light consistency. However, an emission theory would require a complete reformulation of electrodynamics, which the great success of Maxwell's theory argued against. And finally, the emission theory has been disproved since the discovery of the Sagnac effect and the experiments of Willem de Sitter (1913), since with such a theory the orbits observed in binary stars would appear to contradict Kepler's laws, which, however, was not observed. More recent experiments with high-frequency light confirm this result, and experiments in particle accelerators have not been able to demonstrate any source dependence of the speed of light.
Spacetime physics
Minkowski's spacetime
Poincaré's four-dimensional approach was decisively further developed by Hermann Minkowski (1907, 1908). This geometry of the Lorentz transformation was based, for example, on mathematical achievements such as group theory , invariant theory and projective geometry , as developed in the 19th century by mathematicians such as Arthur Cayley . In a lecture from 1907, Minkowski introduced space- time as a “four-dimensional non-Euclidean manifold”. He succeeded in reformulating the entire electrodynamics by introducing a four-dimensional formalism in the so-called Minkowski space , which enabled a much clearer and more coherent interpretation of the SRT. He introduced important terms such as proper time, Lorentz invariance and used four-vector vectors , which he called differently. However, his attempt to set up a Lorentz-invariant law of gravity turned out to be just as ineffective as Poincaré's model. In his famous lecture Raum und Zeit (1909), where he announced the end of the previous conceptions of space and time, he conceived the Minkowski diagram to illustrate space-time.
Minkowski himself named in 1907 as his forerunners in working out the principle of relativity: Lorentz, Einstein, Poincaré and Planck. In contrast, in his famous lecture Raum und Zeit , he only mentioned Voigt, Lorentz and Einstein. He criticized Lorentz for the artificiality of his contraction hypothesis, whereas he saw his own geometrical interpretation as much more natural. He praised Einstein above all for his complete relativization of time, but he complained that both Lorentz and Einstein had not fully taken into account the relativity of space. Minkowski's claims of priority in relation to the completion of the theory of relativity are rejected in this context by the historians of science. This is because Minkowski (like Wien and Abraham) continued to be a representative of the electromagnetic world view and apparently had not fully recognized the difference between Lorentz's electron theory and Einstein's kinematics.
For the time being, however, Einstein and Laub rejected a four-dimensional formulation of the theory of relativity as being too complex and published a non-four-dimensional derivation of the basic equations for moving bodies. Nevertheless, it was precisely Minkowski's formalism that was decisive for the spread and acceptance of the SRT from 1909 onwards.
Vector notation and closed systems
The fact that Minkowski's concept was formally considerably refined and modernized was particularly significant. For example, Arnold Sommerfeld (1910) replaced Minkowski's matrix notation with a more elegant vector notation and for the first time used terms such as “four-vector” or “six-vector”. He also introduced a trigonometric derivation of speed addition, which in his opinion removed much of the strangeness of this concept. Other important contributions were made by Laue. He expanded Minkowski's expressions to include non-electromagnetic processes and thus deepened the concept of mass-energy equivalence. Laue also showed that non-electrical forces are required so that all forces in the electron are correctly subjected to the Lorentz transformation, and so that the electron remains stable - that is, he showed that the Poincaré voltage is a natural consequence of the SRT, so that the electron forms a closed system.
Lorentz transformation without postulate of light
Attempts have now been made to derive the Lorentz transformation without including the postulate of the constancy of the speed of light. Vladimir Sergeyevich Ignatovsky (1910) z. B. used for this purpose a) the principle of relativity, b) isotropy and homogeneity of space, c) the requirement of reciprocity. Philipp Frank and Hermann Rothe (1910) now showed that this derivation is incomplete and was based on other additional assumptions which Ignatowski did not list. Their own derivation was based on the assumptions that a) the Lorentz transformation should form a single-parameter, homogeneous linear group, b) that when the reference system changes, the relative speed only changes the sign , c) that the length contraction depends exclusively on the relative speed. According to Pauli and Miller, however, both Ignatowski and Frank / Rothe were not able to identify the invariant speed with the speed of light in the transformations obtained, since Ignatowski, for example, had to resort to electrodynamics to obtain the speed of light. Pauli was therefore of the opinion that both postulates are necessary for the derivation of the Lorentz transformation. Similar attempts to derive the transformations without using the light postulate have been made by a number of other authors.
Non-Euclidean Reformulations of Theory
Minkowski found in 1907 that the spacetime formalism is closely related to non-Euclidean geometry . However, he continued to use an imaginary time coordinate as the fourth dimension. Likewise, from Born's work (1909) on the acceleration of rigid bodies, analogies to Riemann's geometry became clear, with the Ehrenfest paradox being an important clue for Einstein's development of the theory of gravity. Various mathematicians and physicists have now undertaken further systematic attempts to reformulate the entire SRT on the basis of a non-Euclidean geometry, i.e. H. these space-time models operated with a real time coordinate as the fourth dimension. The knowledge gained thereby enabled an elegant formulation of various expressions of the theory. Nevertheless, as far as the physical content is concerned, these models did not go beyond the statements of the SRT. Vladimir Varičak (1910, 1912) noticed the analogy to hyperbolic geometry and tried to reformulate the SRT with it. Alfred Robb (1911) introduced the term rapidity as a hyperbolic function to describe the system speed . Edwin Bidwell Wilson and Gilbert Newton Lewis (1912) used a non-Euclidean vector calculation. Émile Borel (1913) made an important discovery , who laid the kinematic basis of the Thomas precession on the basis of a hyperbolic geometry . However, Minkowski's original spacetime formalism continued to be preferred and it was not until the development of general relativity that non-Euclidean geometry played an important role in physics. And in most of the modern work on RT, the non-Euclidean representation with a real time coordinate is preferred.
Time dilation and the twin paradox
Einstein (1907a) showed that the transverse Doppler effect (which is a consequence of time dilation) revealed the possibility of experimentally verifying the existence of time dilation. In 1938 Herbert E. Ives (although he was a bitter opponent of the SRT) and GR Stilwell actually succeeded in demonstrating this effect and thus the time dilation experimentally ( Ives-Stilwell experiment ).
And Lewis and Tolman (1909) illustrated the reciprocity of time dilation required by Einstein by using two light clocks A and B, which move at a certain relative speed to each other. The clocks consist of two mirrors, between which a light signal is sent back and forth. For an observer resting in the same inertial frame as A, the path of the signal is simply the distance between them through the speed of light. However, if you look at clock B, you will notice that the running time is longer there, because the light beam has to spread at an incline in order to reach its destination - A goes faster than B. However, an observer who is resting at B sees it exactly the other way round: B is at rest here , and A is moving, and hence B is the faster running clock. And in a lecture between 1910 and 1912, Lorentz also discussed the reciprocity of time dilation and, related to it, an apparent clock paradox. Lorentz shows that the statement that everyone perceives the other's clock more slowly is not a paradox. It must be borne in mind that only one clock is used to measure in one system, but two clocks are required in the other - in this case the relativity of simultaneity must also be taken into account.
Furthermore, Paul Langevin (1911) created a similar situation with the famous twin paradox by replacing the clocks with people (although he did not speak literally of twins, his representation contains all the other features of the paradox). Langevin resolved the paradox by pointing out the asymmetry of the two observers, according to which a body changes direction caused by acceleration. Langevin himself saw this, however, as an indication of an "absolute movement" in an ether. Although this explanation has been retained in principle to this day, its conclusions regarding the aether are rejected. For example, Max von Laue (1913) pointed out that the acceleration in relation to the inertial movement can be made arbitrarily small. This enabled Laue to show that it is of far more important importance that the traveling twin is in two inertial systems during its journey on the outward and return flight , while the remaining twin remains in a single one. Laue was also the first to illustrate this with Minkowski diagrams and to determine how the world lines of inertially moving observers maximize the proper time between two events.
acceleration
Einstein (1908) tried (for the time being still in the context of the SRT) to also capture accelerated movements with the principle of relativity. He realized that an inertial system can be defined for each individual acceleration section, in which the accelerated body is at rest. The result is that the speed of light is no longer constant in accelerated reference systems defined in this way, since the principle of the constancy of the speed of light can only be used to determine simultaneity for small light paths. The equivalence principle established by Einstein in this context , according to which heavy and inert mass are equivalent, and processes in an accelerated frame of reference are equivalent to processes in a homogeneous gravitational field, however, went beyond the limits of the SRT and gave birth to the general theory of relativity .
Almost simultaneously with Einstein, Minkowski (1908) also discussed the special case of uniform acceleration within the framework of his spacetime formalism, and recognized that the resulting world line corresponds to a hyperbola. This was continued by Born (1909) and Sommerfeld (1910b), where Born coined the term hyperbolic movement . He realized that the uniform acceleration can be used as an approximation for the description of different accelerations in the SRT. Furthermore, Harry Bateman and Ebenezer Cunningham (1910) were able to show that Maxwell's equations remained invariant not only under the Lorentz group but also under a more general group of spherical wave transformations (or conformal transformations ), and thus accelerated their validity for a number of Kept movements. A general covariant formulation of electrodynamics was finally given by Friedrich Kottler (1912), whereby this is also valid within the framework of the general theory of relativity developed later. As regards the further elaboration of the description of accelerations in the context of the SRT, a. to mention the work of Paul Langevin for rotating reference systems, and above all of Wolfgang Rindler .
Rigid bodies and the reality of contraction in length
Einstein (1907b) discussed the question of whether in rigid bodies , or at all, the speed of information could be greater than the speed of light and explained that under these circumstances information could be sent into the past and causality would be violated. However, since this radically violates any experience, faster than light speed is excluded. He added that a dynamic of the rigid body had to be created in the SRT (with which Einstein, like Planck and Bucherer, also used the expression "theory of relativity"). When Born (1909) tried to extend the SRT to accelerated motion, he used the concept of the rigid body. However, this model ended in a conceptual dead end, because Paul Ehrenfest (1909) published a short work in which he showed, using the Ehrenfest paradox named after him , that a rigid body cannot be set in rotation within the framework of the SRT, because of the Lorentz contraction the circumference of a rotating disk (viewed as a rigid body) would be shortened if the radius remained the same. These investigations were u. a. continued by Gustav Herglotz and Fritz Noether , who developed a relativistic theory of elasticity, but had to restrict the use of "rigid bodies" considerably. Finally, Max von Laue (1911b) recognized that in the SRT a body has an infinite number of degrees of freedom , that is, there are no “rigid” bodies at all. So while Born's definition of rigid bodies was incompatible, it was quite useful for describing rigid body movements . In any case, a similar thought experiment became an important clue for Einstein in his developing theory of gravity, because he recognized that the geometry in a co-rotating reference system is non-Euclidean. The description of non-Euclidean geometry in a rotating frame of reference, which is still relevant today, was given by Langevin (1935), although various variations and expansions of this solution have been published to this day due to the complexity of the relationships (and often also due to lack of knowledge of the existing solutions).
In connection with the Ehrenfest paradox, Vladimir Varičak (1911) discussed the question of whether the length contraction is “real” or “apparent”. However, it was more a question of a dispute about words, because as Einstein explained in his answer to Varičak, the kinematic length contraction is "apparent" insofar as it does not exist for a moving observer, but it is very much for a non-moving observer probably "real" and their consequences are measurable. As far as the measurement results are concerned, the same applies to Lorentz's contraction hypothesis: Here, too, the contraction can only be measured for an observer who is not moving, but not for someone who is moving. The fundamental difference lies in the interpretation - while according to Einstein the contraction is a consequence of kinematic effects such as the (in) simultaneous measurement of the endpoints of a distance, Lorentz is a dynamic-mechanical effect caused by forces transmitted in the ether .
Acceptance of the theory
The essential interpretative and philosophical difference between the theories of Lorentz and Einstein now finally crystallized out. The term "Lorentz-Einstein theory" was no longer used and hardly anyone (with the exception of Lorentz, Poincaré, Langevin and a few others) still acknowledged the existence of an ether in any form. As early as 1909, Planck compared the effects of the modern principle of relativity - especially with a view to Einstein's relativity of time - with the upheavals caused by the Copernican world system . The fact that Minkowski's space-time concept was formally considerably refined and modernized was also particularly significant, which from 1911 onwards helped the SRT to achieve widespread acceptance, especially among mathematicians and theoretical physicists. In that year Laue published the first monograph on SRT, Sommerfeld already declared SRT to be a secure basis for physics, and in 1912 Vienna proposed Lorentz and Einstein jointly for the Nobel Prize for their achievements in working out the principle of relativity. At this time Einstein was already intensively working on the general theory of relativity, showing (see above) that the SRT was not sufficient to develop a theory of gravity that was consistent with the observations. Finally, in 1915, he first used the expression “special theory of relativity” to differentiate between the theories.
Relativistic theories
Gravity
The first attempt to formulate a relativistic theory of gravity was made by Poincaré (1905). His endeavor was to modify Newton's law of gravitation so that the resulting law takes a Lorentz covariant form. He noticed himself that his solution was not clear and that different solutions were possible. However, he was able to refute an objection made by Pierre-Simon Laplace around 1800 , according to which the speed of propagation of gravity must be much faster than that of light due to the aberration of gravity . Poincaré, on the other hand, showed that in a Lorentz covariant theory, propagation occurs at the speed of light, and stable orbits are still possible. Similar models were presented following Poincaré by Minkowski (1907b) and Sommerfeld (1910). But in 1914 Abraham was able to show that practically all older “mechanical” models such as Le Sage gravitation but also the theories of Poincaré and Minkowski belonged to the class of “vector theories” of gravitation. These had the fundamental error that the energy of the gravitational field would have to assume a negative value and a violation of the conservation of energy could not be avoided. As an alternative, Abraham (1912) and Gustav Mie (1914) proposed various “scalar theories”. While Mie was never able to formulate his theory completely consistently, Abraham (who was an opponent of the theory of relativity all his life) later developed a theory in which the speed of light was no longer even locally constant and was therefore no longer compatible with the basic principles of the theory of relativity .
In addition, all of these theories violated a condition proposed by Einstein in 1907: namely, the equivalence of inert and heavy mass. Einstein now believed that it was impossible to develop a theory that was both Lorentz covariant and fulfilled the principle of equivalence. But Gunnar Nordström (1912, 1913) succeeded in developing a scalar theory of gravitation in which both conditions are met. He could achieve this by making both inert and heavy mass dependent on the gravitational potential. His theory is also remarkable because in it (as Einstein and Adriaan Daniël Fokker showed in 1914) for the first time the gravitational effects could be represented completely by the geometry of a curved spacetime. Even though Nordström's theory was free of contradictions, it had a fundamental problem from Einstein's point of view: It did not meet the general covariance that he considered to be particularly important, since preferred reference systems could still be defined in Nordström's theory. In contrast to these “scalar theories”, which correspond to the special theory of relativity, Einstein (1911–1915) therefore drafted a “tensor theory” of gravitation, which both fulfill the principle of equivalence and contain the description of various movements (including accelerations) in a generally covariant way should. It turned out that such a theory (which Einstein called general relativity theory in 1915 ) went beyond the limits of special relativity theory and Lorentz covariance, because the principle of constancy of light is only locally valid. The decision between the Lorentz covariant theories and Einstein's general RT only provided the explanation of a phenomenon that was mentioned in most of the works on gravitation, but was not initially considered to be decisive: namely, the perihelion of Mercury, which can only be fully explained with Einstein's theory could be. In addition, only the ART (in contrast to the Lorentz covariant theories) provided the correct value for the deflection of light by the sun.
Quantum field theory
The need to combine the SRT with quantum mechanics was one of the main motivations in the development of quantum field theory . Pascual Jordan and Wolfgang Pauli showed in 1928 that quantum theory can be formulated relativistically. Paul Dirac derived the Dirac equation for electrons and predicted the existence of antimatter. Many other areas of physics, such as thermodynamics , statistical mechanics , hydrodynamics , quantum chemistry, etc., can also be reformulated relativistically.
Experiments
As explained above, the following experiments in particular prepared the development of the SRT before 1905: The Fizeau experiment , the Michelson-Morley experiment , the Kaufmann-Bucherer-Neumann experiments , the Trouton-Noble experiment , the experiments by Rayleigh and Brace , plus experiments on the aberration of light .
From the 1920s the Michelson-Morley experiment was repeated many times, with modern experiments being carried out with optical resonators . In 1932, with the Kennedy Thorndike experiment and its modern repetitions, the independence of the speed of light from the speed of the experimental set-ups with respect to a preferred reference system was demonstrated. The contribution of time dilation to the relativistic Doppler effect was confirmed from 1938 with the Ives-Stilwell experiment and repetitions, and the time dilation of moving particles from 1940. Many tests of the relativistic energy-momentum relationship were also carried out. These relativistic effects have to be taken into account when designing particle accelerators . In addition, many modern tests of Lorentz invariance are performed to test possible theories of quantum gravity .
criticism
Some scientists, philosophers, and lay people opposed (and reject) the SRT. For more details see the article → Critique of the Theory of Relativity .
priority
Edmund Taylor Whittaker spoke of the theory of relativity as the creation of Poincaré and Lorentz in the second edition of his well-known History of the theories of aether and electricity in 1953, and gave Einstein's contributions only secondary importance. However, this is not the opinion of the vast majority of the professional world. Science historians such as Gerald Holton , Arthur I. Miller, Abraham Pais , and John Stachel recognize the achievements of Poincaré, but it is emphasized that Einstein was the first to teach the complete relativization of space and time per se, and to ban (classical) ether from physics , and only then paved the way for a fundamentally new theory. Other historians of science go a little further and call Poincaré's theory a kind of “relativistic physics” (Katzir) or “relativity theory” (Walter) - although not the same as Einstein's SRT. On the other hand, the opinion that Poincaré (and Lorentz), and not Einstein, are the real founders of the SRT taught today, is only represented outside the scientific mainstream (e.g. Logunov).
Lorentz
Although Lorentz continued to adhere to the etheric idea, he spoke in his main work The theory of electrons (1909) with full appreciation about "Einstein's principle of relativity" and his remarks on clocks, scales and synchronization. Einstein's great achievement was to replace Lorentz's cumbersome formulation with a much more transparent and simpler one by completely equating the different inertial systems (especially the time variable). It is remarkable that neither here nor in the new edition (1916) is the name of Poincaré mentioned in this context.
On the other hand, Lorentz paid tribute to Poincaré for his work from 1905/1906 in a work written in 1914 but not published until 1921. He referred to this as the first to recognize the formal equivalence of local time with "normal" time, while he himself had viewed it as a mathematical trick. That is why he was unable to specify the correct application of the transformation himself - this was done first by Poincaré and later by Einstein and Minkowski. Poincaré also recognized the fundamental importance of the principle of relativity for electrodynamics before him and was the first to use the terms “postulate of relativity” and “principle of relativity”. Finally, he referred to the fundamental findings made by Poincaré (described in the section “Lorentz Transformation”).
Aside from this exception, Lorentz continued to only mention Einstein in this context. For example, Michelson (1928) suggested that Lorentz was the originator of the theory of relativity. Lorentz replied that at the time Einstein was creating the SRT, he was only looking at his time transformation as a heuristic working hypothesis. The theory of relativity was therefore really Einstein's work alone - there could be no doubt that Einstein discovered it, even if the work of his predecessors in this area had not been done at all.
Poincaré
Poincaré, on the other hand, always presented the new theories as Lorentz's creation and saw no reason to even mention Einstein and Minkowski in this context. In 1912, shortly before his death, he wrote about the question of whether "Lorentzian mechanics" will continue to exist after the development of quantum physics :
“In all the points in which Lorentz's mechanics deviate from Newton's, it rightly remains. It is still believed that a moving body can under no circumstances ever assume a speed greater than that of light, that the mass of a body is not an immutable quantity, but depends on its speed and on the angle this speed makes with the This includes the force acting on the body, further that no attempt will ever be able to decide whether a body, taken absolutely, is in a state of rest or in that of movement, be it in relation to space as such, be it itself in Relation to the ether. "
Although Poincaré emphasized the relativity of time in his philosophical writings, he continued to refer in his physical works (1900b, 1904, 1906, 1908b) to an (impossible to discover) ether and subdivided coordinates or phenomena into local / apparently for moving observers, and true / real for observers resting in the ether. Therefore (with a few exceptions) it is assumed by most historians that Poincaré's theory does not correspond to what is still referred to as special relativity theory to this day, although it is admitted that he anticipated essential methods and contents of the theory.
Einstein
Einstein's work on electrodynamics (1905) contains no references to other works. Therefore, the Einstein biographers Abraham Pais and Albrecht Fölsing refer to the following Einstein quote in connection with his literary reception:
“It seems to me to be in the nature of things that the following should already be clarified in part by other authors. In view of the fact that the questions in question are treated from a new point of view, I believed that I should be able to refrain from a very laborious survey of the literature, especially since it is to be hoped that this gap will be filled by other authors, as has already happened in a thankful way in my first work on the principle of relativity by Mr. Planck and Mr. Kaufmann. "
In a letter to Stark from 1907, Einstein also wrote that, due to his work in the patent office, he hardly had the opportunity to study relevant specialist literature in the libraries. However, this does not mean that Einstein was generally not informed about the state of the art in science, but that he was well informed in certain areas. And so some historians of science try to list the sources used by Einstein.
In philosophical terms, Einstein claimed to have been influenced by the empirical philosophers David Hume and Ernst Mach . Einstein may also have knowledge of the important works by Wien, Cohn, Abraham, Bucherer, or Hasenöhrl in the Annals of Physics , since he himself published several articles in this journal from 1901 onwards. Following Abraham, for example, he used the expression “Maxwell-Hertz equations” and “based on the usual approach” the terms transverse and longitudinal mass. Finally, in § 9, he mentions the “Lorentz theory of electrodynamics”. In addition, Einstein published twenty-one reviews of mainly thermodynamic work in supplements to the annals of physics in 1905 alone . Jürgen Renn , Director of the MPIWG , wrote:
"The Annalen also served as a source of modest additional income for Einstein, who wrote more than twenty reports for its Beiblätter - mainly on the theory of heat - thus demonstrating an impressive mastery of the contemporary literature. This activity started in 1905 and probably resulted from his earlier publications in the Annalen in this field. Going by his publications between 1900 and early 1905, one would conclude that Einstein's specialty was thermodynamics. "
“ The annals also served as a source of modest extra income for Einstein, who wrote more than twenty reports for its supplements - mostly on the theory of warmth - demonstrating an impressive mastery of contemporary literature. This activity began in 1905 and probably resulted from his previous annals publications in the field. Based on his publications between 1900 and early 1905, one could conclude that Einstein's specialty was thermodynamics. "
An important source was August Föppl's textbook on electrodynamics (1894), which contained Maxwell's theory in the formulation of Heaviside and Hertz and a variant of the "moving magnet and conductor" problem that was important for Einstein in connection with the principle of relativity. In addition, Einstein worked as a patent examiner, where he possibly had to do with various patents for clock synchronization on an electrical basis. He was also familiar with Lorentz's work from 1895, where he described local time, length contraction, and the Michelson-Morley experiment. As he explained in 1909, Einstein therefore also derived the principle of light constancy from the Lorentzian ether (or the “Maxwell-Lorentzian” equations). In 1912 he summed it up as follows:
“It is generally known that a theory of the laws of transformation of space and time cannot be based on the principle of relativity alone. As is well known, this has to do with the relativity of the terms “simultaneity” and “shape of moving bodies”. In order to fill this gap, I introduced the principle of the constancy of the speed of light, borrowed from HA Lorentz's theory of the quiescent light ether, which, like the principle of relativity, contains a physical presupposition that appeared to be justified only by relevant experience (experiments by Fizeau, Rowland, etc.) . "
Einstein came to the conclusion that the local time was a real, equal time indication and not just a mathematical trick. And in contrast to Poincaré and Lorentz, he recognized that it was precisely the equality of the reference systems and thus the undetectability of the aether that made the concept of aether meaningless.
It is also known that before 1905 he read with Maurice Solovine and Conrad Habicht in the Olympia Academy Poincaré's book Science and Hypothesis , which “captivated and fascinated them for weeks”. It remains unclear whether Einstein read any of Poincaré's other works before 1905. In his scientific writings after 1905 Einstein only refers to Poincaré in connection with the inertia of energy (1906) and non-Euclidean geometry (1921), but not to his achievements in the formulation of the Lorentz transformation, the connection between clock synchronization and simultaneity, or the Relativity Principle. It was not until 1953, on the occasion of the 50th anniversary of the SRT, that he mentioned Poincaré for the first time - perhaps because Abraham Pais had given Einstein a copy of Poincaré's Palermo work around 1950. He wrote:
"Hopefully it will be ensured that the services of HA Lorentz and H. Poincaré will also be properly recognized on this occasion."
And in 1955 he wrote to Carl Seelig :
“There is no doubt that the special theory of relativity, if we look back at its development, was ripe for discovery in 1905. Lorentz had already recognized that the transformation, which was later named after him, was essential for the analysis of Maxwell's equations, and Poincaré deepened this knowledge. As far as I am concerned, I only knew Lorentz's important work from 1895 La theorie electromagnetique de Maxwell and attempt at a theory of electrical and optical phenomena in motion , but not Lorentz's later works, nor the subsequent study by Poincaré. In this sense, my work from 1905 was independent. […] What was new was the realization that the meaning of the Lorentz transformation went beyond the connection with Maxwell's equations and concerned the nature of space and time in general. The insight was also new that the “Lorentz invariance” is a general condition for every physical theory. This was of particular importance to me because I had already recognized earlier that Maxwell's theory does not represent the microstructure of radiation and is therefore not generally tenable. "
See also
literature
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Individual references and secondary sources
In the text, the year numbers in brackets next to the names refer to the publication date of the primary source of the respective author. The individual references given in the footnotes, however, refer to the following secondary sources from the historians of science, which form the substantive basis of the article.
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Web links
- Albert Einstein in Annals of Physics
- O'Connor, John J. & Robertson, Edmund F., “ Special relativity, ” MacTutor History of Mathematics archive
- Mathpages: Who Invented Relativity? , Poincaré Contemplates Copernicus , Corresponding States , The End of My Latin ,