Who discovered special relativity?
Germany
Notable German physicists before the 20th century include Hermann von Helmholtz, Joseph von Fraunhofer and Gabriel Daniel Fahrenheit, among others. Albert Einstein introduced the special relativity and general relativity theories for light and gravity in 1905 and 1915 respectively. Along with Max Planck, he was instrumental in the introduction of quantum mechanics, in which Werner Heisenberg and Max Born later made major contributions. Wilhelm Röntgen discovered X-rays. Otto Hahn was a pioneer in the fields of radiochemistry and discovered nuclear fission, while Ferdinand Cohn and Robert Koch were founders of microbiology. Numerous mathematicians were born in Germany, including Carl Friedrich Gauss, David Hilbert, Bernhard Riemann, Gottfried Leibniz, Karl Weierstrass, Hermann Weyl, Felix Klein and Emmy Noether.
History of special relativity
Some claim that Poincaré and Lorentz, not Einstein, are the true founders of special relativity. For more see the article on relativity priority dispute.
Achilles Papapetrou
Achille Papapetrou (; February 2, 1907 – August 12, 1997) was a Greek theoretical physicist, who contributed to the general theory of relativity. He is known for the Mathisson–Papapetrou–Dixon equations, the Majumdar–Papapetrou solution, and the Weyl−Lewis−Papapetrou coordinates of gravity theory.
Spacetime
Other physicists and mathematicians at the turn of the century came close to arriving at what is currently known as spacetime. Einstein himself noted, that with so many people unraveling separate pieces of the puzzle, "the special theory of relativity, if we regard its development in retrospect, was ripe for discovery in 1905."
An important example is Henri Poincaré, who in 1898 argued that the simultaneity of two events is a matter of convention. In 1900, he recognized that Lorentz's "local time" is actually what is indicated by moving clocks by applying an explicitly "operational definition" of clock synchronization assuming constant light speed. In 1900 and 1904, he suggested the inherent undetectability of the aether by emphasizing the validity of what he called the principle of relativity, and in 1905/1906 he mathematically perfected Lorentz's theory of electrons in order to bring it into accordance with the postulate of relativity. While discussing various hypotheses on Lorentz invariant gravitation, he introduced the innovative concept of a 4-dimensional space-time by defining various four vectors, namely four-position, four-velocity, and four-force. He did not pursue the 4-dimensional formalism in subsequent papers, however, stating that this line of research seemed to "entail great pain for limited profit", ultimately concluding "that three-dimensional language seems the best suited to the description of our world". Furthermore, even as late as 1909, Poincaré continued to believe in the dynamical interpretation of the Lorentz transform. For these and other reasons, most historians of science argue that Poincaré did not invent what is now called special relativity.
History of special relativity
Other physicists besides Lorentz and Larmor also tried to develop a consistent model of electrodynamics. For example, Emil Cohn (1900, 1901) 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 inconsistencies within his theory, like different light speeds in different directions, it was superseded by Lorentz's and Einstein's.Janssen/Stachel (2004), 31–32
Hendrik Lorentz
In 1905, Einstein would use many of the concepts, mathematical tools and results Lorentz discussed to write his paper entitled "On the Electrodynamics of Moving Bodies", known today as the theory of special relativity. Because Lorentz laid the fundamentals for the work by Einstein, this theory was originally called the "Lorentz-Einstein theory".
Introduction to general relativity
General relativity is a theory of gravitation that was developed by Albert Einstein between 1907 and 1915. According to general relativity, the observed gravitational effect between masses results from their warping of spacetime.
Absolute rotation
French physicist Georges Sagnac in 1913 conducted an experiment that was similar to the Michelson–Morley experiment, but was intended to observe the effects of rotation. Sagnac set up this experiment to prove the existence of the luminiferous aether that Einstein's 1905 theory of special relativity had discarded.
C. K. Raju
Raju built on E.T. Whittaker's beliefs that Albert Einstein's theories of special and general relativity built on the earlier work of Henri Poincaré. Raju claims that they were "remarkably similar", and every aspect of special relativity was published by Poincaré in papers between 1898 and 1905. Raju goes further, saying that Einstein made a mistake that much of physics has been built on; he proposes corrections to the equations, and says that physics needs to go through a major reformulation. He proposed that modern physics must be reformulated using functional differential equations.
Affine geometry
In 1912, Edwin B. Wilson and Gilbert N. Lewis developed an affine geometry to express the special theory of relativity.
Strong gravitational lensing
The strong lensing was predicted by Albert Einstein's general theory of relativity and observationally discovered by Dennis Walsh, Bob Carswell, and Ray Weymann in 1979. They determined that the Twin Quasar Q0957+561A comprises two images of the same object.
History of special relativity
Like Poincaré, Alfred Bucherer (1903) believed in the validity of the relativity principle within the domain of electrodynamics, but contrary to Poincaré, Bucherer even assumed that this implies the nonexistence of the aether. However, the theory that was created by him later in 1906 was incorrect and not self-consistent, and the Lorentz transformation was absent within his theory as well.
Roman Ulrich Sexl
Roman Ulrich Sexl (19 October 1939 – 10 July 1986) was one of the leading Austrian theoretical physicists. He is famous for his textbooks on Special relativity.
Special relativity
where
Relativity priority dispute
In a 1965 series of articles tracing the history of relativity, Keswani claimed that Poincaré and Lorentz should have the main credit for special relativity - claiming that Poincaré pointedly credited Lorentz multiple times, while Lorentz credited Poincaré and Einstein, refusing to take credit for himself. He also downplayed the theory of general relativity, saying "Einstein's general theory of relativity is only a theory of gravitation and of modifications in the laws of physics in gravitational fields". This would leave the special theory of relativity as the unique theory of relativity. Keswani cited also Vladimir Fock for this same opinion.
History of special relativity
In a September 1904 lecture in St. Louis named , Poincaré drew some consequences from Lorentz's theory and 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.
History of special relativity
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. Cayley's matrix calculus notation was used by Minkowski (1908) in formulating relativistic electrodynamics, even though it was later replaced by Sommerfeld using vector notation. According to a recent source the Lorentz transformations are equivalent to hyperbolic rotations. However Varicak (1910) had shown that the standard Lorentz transformation is a translation in hyperbolic space.
Special relativity
Special relativity is mathematically self-consistent, and it is an organic part of all modern physical theories, most notably quantum field theory, string theory, and general relativity (in the limiting case of negligible gravitational fields).
Fizeau interferometer
Over half a century passed before a satisfactory explanation of Fizeau's unexpected measurement was developed with the advent of Einstein's theory of special relativity.
Albert Einstein
General relativity (GR) is a theory of gravitation that was developed by Einstein between 1907 and 1915. According to general relativity, the observed gravitational attraction between masses results from the warping of space and time by those masses. General relativity has developed into an essential tool in modern astrophysics. It provides the foundation for the current understanding of black holes, regions of space where gravitational attraction is so strong that not even light can escape.
History of physics
In 1905 a young, 26-year-old German physicist (then a Bern patent clerk) named Albert Einstein (1879–1955), showed how measurements of time and space are affected by motion between an observer and what is being observed. To say that Einstein's radical theory of relativity revolutionized science is no exaggeration. Although Einstein made many other important contributions to science, the theory of relativity alone represents one of the greatest intellectual achievements of all time. Although the concept of relativity was not introduced by Einstein, his major contribution was the recognition that the speed of light in a vacuum is constant, i.e. the same for all observers, and an absolute physical boundary for motion. This does not impact a person's day-to-day life since most objects travel at speeds much slower than light speed. For objects travelling near light speed, however, the theory of relativity shows that clocks associated with those objects will run more slowly and that the objects shorten in length according to measurements of an observer on Earth. Einstein also derived the famous equation, "E" = "mc", which expresses the equivalence of mass and energy.
Paul Harzer
Paul Harzer (1857–1932) was a mathematician and astronomer best known for his papers arguing with Albert Einstein regarding the Sagnac effect and its relationship to Special Relativity. Harzer was Professor of Astronomy at the University of Kiel and Director of its observatory. His published article on the experiment of Franz Harress drew two reply articles from Einstein.
Louis Essen
Louis Essen FRS O.B.E. (6 September 1908 – 24 August 1997) was an English physicist whose most notable achievements were in the precise measurement of time and the determination of the speed of light. He was a critic of Albert Einstein's theory of relativity, particularly as it related to time dilation.
Born in Nottingham, Essen earned his degree in physics from the University of London in 1928, having studied at University College Nottingham. He started work at the National Physical Laboratory (NPL) the following year, under D. W. Dye, investigating the potential of tuning forks and quartz crystal oscillators for precise time measurement. His research led to his development of the quartz ring clock in 1938, the clock soon becoming a standard for time measurement at observatories throughout the world.
Electromagnetism
The theoretical implications of electromagnetism, particularly the establishment of the speed of light based on properties of the "medium" of propagation (permeability and permittivity), led to the development of special relativity by Albert Einstein in 1905.
Jean Metzinger
There was, after all, little to prevent the Cubists from developing their own pictorial variants on the topological space in parallel to (or independently of) relativistic considerations. Though the concept of observing a subject from different points in space and time simultaneously (multiple or mobile perspective) developed by Metzinger and Gleizes was not derived directly from Albert Einstein's theory of relativity, it was certainly influenced in a similar way, through the work of Jules Henri Poincaré (particularly "Science and Hypothesis"), the French mathematician, theoretical physicist and philosopher of science, who made many fundamental contributions to algebraic topology, celestial mechanics, quantum theory and made an important step in the formulation of the theory of special relativity.
History of special relativity
As was explained above, already in 1895 Lorentz succeeded in deriving Fresnel's dragging coefficient (to first order of v/c) and the Fizeau experiment by using the electromagnetic theory and the concept of local time. After first attempts by Jakob Laub (1907) to create a relativistic "optics of moving bodies", it was Max von Laue (1907) who derived the coefficient for terms of all orders by using the colinear case of the relativistic velocity addition law. In addition, Laue's calculation was much simpler than the complicated methods used by Lorentz.
List of Dutch discoveries
In physics, the Lorentz transformation (or Lorentz transformations) is named after the Dutch physicist Hendrik Lorentz. It was the result of attempts by Lorentz and others to explain how the speed of light was observed to be independent of the reference frame, and to understand the symmetries of the laws of electromagnetism. The Lorentz transformation is in accordance with special relativity, but was derived before special relativity. Early approximations of the transformation were published by Lorentz in 1895. In 1905, Poincaré was the first to recognize that the transformation has the properties of a mathematical group, and named it after Lorentz.
Acceleration (special relativity)
1905: Albert Einstein derived the equations of motions on the basis of his special theory of relativity, which represent the relation between equally valid inertial frames without the action of a mechanical aether. Einstein concluded, that in a momentary inertial frame formula_127 the equations of motion retain their Newtonian form:
Special relativity
or simply
Theory of relativity
Relativity is a falsifiable theory: It makes predictions that can be tested by experiment. In the case of special relativity, these include the principle of relativity, the constancy of the speed of light, and time dilation. The predictions of special relativity have been confirmed in numerous tests since Einstein published his paper in 1905, but three experiments conducted between 1881 and 1938 were critical to its validation. These are the Michelson–Morley experiment, the Kennedy–Thorndike experiment, and the Ives–Stilwell experiment. Einstein derived the Lorentz transformations from first principles in 1905, but these three experiments allow the transformations to be induced from experimental evidence.
Aberration of light
Aberration is historically significant because of its role in the development of the theories of light, electromagnetism and, ultimately, the theory of special relativity. It was first observed in the late 1600s by astronomers searching for stellar parallax in order to confirm the heliocentric model of the Solar System. However, it was not understood at the time to be a different phenomenon.
In 1727, James Bradley provided a classical explanation for it in terms of the finite speed of light relative to the motion of the Earth in its orbit around the Sun, 
which he used to make one of the earliest measurements of the speed of light. However, Bradley's theory was incompatible with 19th century theories of light, and aberration became a major motivation for the aether drag theories of Augustin Fresnel (in 1818) and G. G. Stokes (in 1845), and for Hendrik Lorentz's aether theory of electromagnetism in 1892. The aberration of light, together with Lorentz's elaboration of Maxwell's electrodynamics, the moving magnet and conductor problem, the negative aether drift experiments, as well as the Fizeau experiment, led Albert Einstein to develop the theory of special relativity in 1905, which presents a general form of the equation for aberration in terms of such theory.
Ricardo Carezani
Ricardo Libertario Carezani (Córdoba, Argentina; 11 April 1921) is an Argentine theoretical physicist. Carezani is best known for proposing the theory of Autodynamics (AD), which aimed to formulate a mathematical basis of Einstein's theories of special and general relativity.
Special relativity
In physics, special relativity (SR, also known as the special theory of relativity or STR) is the generally accepted and experimentally well-confirmed physical theory regarding the relationship between space and time. In Albert Einstein's original pedagogical treatment, it is based on two postulates:It was originally proposed by Albert Einstein in a paper published 26 September 1905 titled "On the Electrodynamics of Moving Bodies". The inconsistency of Newtonian mechanics with Maxwell's equations of electromagnetism and the lack of experimental confirmation for a hypothesized luminiferous aether led to the development of special relativity, which corrects mechanics to handle situations involving motions at a significant fraction of the speed of light (known as ""). As of today, special relativity is the most accurate model of motion at any speed when gravitational effects are negligible. Even so, the Newtonian mechanics model is still useful as an approximation at small velocities relative to the speed of light, due to its simplicity and high accuracy within its scope.
Relativity priority dispute
Roger Cerf (2006) gave priority to Einstein for developing special relativity, and criticized the assertions of Leveugle and others concerning the priority of Poincaré. While Cerf agreed that Poincaré made important contributions to relativity, he argued (following Pais) that Poincaré ""stopped short before the crucial step"" because he handled length contraction as a "third hypothesis", therefore Poincaré lacked a complete understanding of the basic principles of relativity. ""Einstein's crucial step was that he abandoned the mechanistic ether in favor of a new kinematics."" He also denies the idea, that Poincaré invented E=mc² in its modern relativistic sense, because he did not realize the implications of this relationship. Cerf considers Leveugle's Hilbert-Planck-Einstein connection an implausible conspiracy theory.
Doubly special relativity
First attempts to modify special relativity by introducing an observer-independent length were made by Pavlopoulos (1967), who estimated this length at about .
In the context of quantum gravity, Giovanni Amelino-Camelia (2000) introduced what now is called doubly special relativity, by proposing a specific realization of preserving invariance of the Planck length .
This was reformulated by Kowalski-Glikman (2001) in terms of an observer-independent Planck mass.
A different model, inspired by that of Amelino-Camelia, was proposed in 2001 by João Magueijo and Lee Smolin, who also focused on the invariance of Planck energy.
Alfred Robb
He is known for his four books on special relativity (1911, 1914, 1921, 1936) where he gave a spacetime derivation of the theory in an axiomatic-geometric way. Robb therefore was sometimes called the "Euclid of relativity". In the first of these works he used a hyperbolic angle ω to introduce the concept of rapidity and showed that the kinematic space of velocities is hyperbolic, so that "instead of a Euclidean triangle of velocities, we get a Lobachevski triangle of rapidities". 
However, contrary to the scientific mainstream, he believed that the works of Joseph Larmor and Hendrik Lorentz were more important for relativity than the works of Albert Einstein and Hermann Minkowski.
Spacetime
Einstein, for his part, was initially dismissive of Minkowski's geometric interpretation of special relativity, regarding it as "überflüssige Gelehrsamkeit" (superfluous learnedness). However, in order to complete his search for general relativity that started in 1907, the geometric interpretation of relativity proved to be vital, and in 1916, Einstein fully acknowledged his indebtedness to Minkowski, whose interpretation greatly facilitated the transition to general relativity. Since there are other types of spacetime, such as the curved spacetime of general relativity, the spacetime of special relativity is today known as "Minkowski spacetime."
Classical electromagnetism and special relativity
where
Elastic collision
According to special relativity,
Special relativity
Galileo Galilei had already postulated that there is no absolute and well-defined state of rest (no privileged reference frames), a principle now called Galileo's principle of relativity. Einstein extended this principle so that it accounted for the constant speed of light, a phenomenon that had been recently observed in the Michelson–Morley experiment. He also postulated that it holds for all the laws of physics, including both the laws of mechanics and of electrodynamics.
Special relativity
so
Two-body problem in general relativity
Around 1904–1905, the works of Hendrik Lorentz, Henri Poincaré and finally Albert Einstein's special theory of relativity, exclude the possibility of propagation of any effects faster than the speed of light. It followed that Newton's law of gravitation would have to be replaced with another law, compatible with the principle of relativity, while still obtaining the newtonian limit for circumstances where relativistic effects are negligible. Such attempts were made by Henri Poincaré (1905), Hermann Minkowski (1907) and Arnold Sommerfeld (1910). In 1907 Einstein came to the conclusion that to achieve this a successor to special relativity was needed. From 1907 to 1915, Einstein worked towards a new theory, using his equivalence principle as a key concept to guide his way. According to this principle, a uniform gravitational field acts equally on everything within it and, therefore, cannot be detected by a free-falling observer. Conversely, all local gravitational effects should be reproducible in a linearly accelerating reference frame, and vice versa. Thus, gravity acts like a fictitious force such as the centrifugal force or the Coriolis force, which result from being in an accelerated reference frame; all fictitious forces are proportional to the inertial mass, just as gravity is. To effect the reconciliation of gravity and special relativity and to incorporate the equivalence principle, something had to be sacrificed; that something was the long-held classical assumption that our space obeys the laws of Euclidean geometry, e.g., that the Pythagorean theorem is true experimentally. Einstein used a more general geometry, pseudo-Riemannian geometry, to allow for the curvature of space and time that was necessary for the reconciliation; after eight years of work (1907–1915), he succeeded in discovering the precise way in which space-time should be curved in order to reproduce the physical laws observed in Nature, particularly gravitation. Gravity is distinct from the fictitious forces centrifugal force and coriolis force in the sense that the curvature of spacetime is regarded as physically real, whereas the fictitious forces are not regarded as forces. The very first solutions of his field equations explained the anomalous precession of Mercury and predicted an unusual bending of light, which was confirmed "after" his theory was published. These solutions are explained below.
Lorentz ether theory
Einstein's 1905 presentation of special relativity was soon supplemented, in 1907, by Hermann Minkowski, who showed that the relations had a very natural interpretation in terms of a unified four-dimensional "spacetime" in which absolute intervals are seen to be given by an extension of the Pythagorean theorem. (Already in 1906 Poincaré anticipated some of Minkowski's ideas, see the section "Lorentz-transformation"). The utility and naturalness of the representations by Einstein and Minkowski contributed to the rapid acceptance of special relativity, and to the corresponding loss of interest in Lorentz's ether theory.
Criticism of the theory of relativity
As was shown by Einstein, the only form of accelerated motion that cannot be described is the one due to gravitation, since special relativity is not compatible with the Equivalence principle. Einstein was also unsatisfied with the fact that inertial frames are preferred over accelerated frames. Thus over the course of several years (1908–1915), Einstein developed general relativity. This theory includes the replacement of Euclidean geometry by non-Euclidean geometry, and the resultant curvature of the path of light led Einstein (1912) to the conclusion that (like in accelerated frames) the speed of light is not constant in extended gravitational fields. Therefore, Abraham (1912) argued that Einstein had given special relativity a coup de grâce. Einstein responded that within its area of application (in areas where gravitational influences can be neglected) special relativity is still applicable with high precision, so one cannot speak of a coup de grâce at all.
Laurent Nottale
Laurent Nottale (born 29 July 1952) is an astrophysicist, a director of research at CNRS, and a researcher at the Paris Observatory. He is the author and inventor of the theory of Scale Relativity which aims to unify quantum physics and relativity theory.
Special relativity
Einstein discerned two fundamental propositions that seemed to be the most assured, regardless of the exact validity of the (then) known laws of either mechanics or electrodynamics. These propositions were the constancy of the speed of light and the independence of physical laws (especially the constancy of the speed of light) from the choice of inertial system. In his initial presentation of special relativity in 1905 he expressed these postulates as:
Arthur Eddington
He is famous for his work concerning the theory of relativity. Eddington wrote a number of articles that announced and explained Einstein's theory of general relativity to the English-speaking world. World War I severed many lines of scientific communication and new developments in German science were not well known in England. He also conducted an expedition to observe the solar eclipse of 29 May 1919 that provided one of the earliest confirmations of general relativity, and he became known for his popular expositions and interpretations of the theory.
Joshua N. Goldberg
Joshua N. Goldberg (born May 30, 1925 in Rochester, New York) is an American physicist and educator. He is particularly noted for his research on general relativity.
Giovanni Amelino-Camelia
He is the first proposer of doubly special relativity that is the idea of introducing the Planck length in physics as an observer-independent quantity, obtaining a relativistic theory (like Galileian relativity and Einstein's special relativity). The principles of doubly special relativity probably imply the loss of the notion of classical (Riemannian) spacetime; this led Amelino-Camelia to the study of non-commutative geometry as a feasible theory of quantum spacetime.
Amelino-Camelia is the initiator of "quantum-gravity phenomenology", for being the first to show that with some experiments under reach of current technology sensitivity to Planck-scale effects is feasible (see Fermi Gamma-ray Space Telescope).
Theory of relativity
Albert Einstein published the theory of special relativity in 1905, building on many theoretical results and empirical findings obtained by Albert A. Michelson, Hendrik Lorentz, Henri Poincaré and others. Max Planck, Hermann Minkowski and others did subsequent work.
History of Lorentz transformations
On June 30, 1905 (published September 1905) Einstein published what is now called special relativity and gave a new derivation of the transformation, which was based only on the principle on relativity and the principle of the constancy of the speed of light. While Lorentz considered "local time" to be a mathematical stipulation device for explaining the Michelson-Morley experiment, Einstein showed that the coordinates given by the Lorentz transformation were in fact the inertial coordinates of relatively moving frames of reference. For quantities of first order in "v/c" this was also done by Poincaré in 1900, while Einstein derived the complete transformation by this method. Unlike Lorentz and Poincaré who still distinguished between real time in the aether and apparent time for moving observers, Einstein showed that the transformations concern the nature of space and time.
List of scientific publications by Albert Einstein
Albert Einstein (1879–1955) was a renowned theoretical physicist of the 20th century, best known for his theories of special relativity and general relativity. He also made important contributions to statistical mechanics, especially his treatment of Brownian motion, his resolution of the paradox of specific heats, and his connection of fluctuations and dissipation. Despite his reservations about its interpretation, Einstein also made seminal contributions to quantum mechanics and, indirectly, quantum field theory, primarily through his theoretical studies of the photon.
Quantum field theory
In the same year as his paper on the photoelectric effect, Einstein published his theory of special relativity, built on Maxwell's electromagnetism. New rules, called Lorentz transformation, were given for the way time and space coordinates of an event change under changes in the observer's velocity, and the distinction between time and space was blurred. It was proposed that all physical laws must be the same for observers at different velocities, "i.e." that physical laws be invariant under Lorentz transformations.
Einstein Prize (APS)
Since 2003, the Einstein Prize is a biennial prize awarded by the American Physical Society. The recipients are chosen for their outstanding accomplishments in the field of gravitational physics. The prize is named after Albert Einstein (1879-1955), who authored the theories of special and general relativity. The prize was established by the Topical Group on Gravitation at the beginning of 1999. As of 2013, the prize is valued at $10,000.
Vladimir Ignatowski
Ignatowski wrote some papers on special relativity. In 1910 he was to first who tried to derive the Lorentz transformation by group theory only using the relativity principle, and without the postulate of the constancy of the speed of light (1910b, 1911b, 1911c, 1911h). Although he derived the correct transformation, the invariant limiting speed remained undefined. Ignatowski had to resort to length contraction of moving electrostatic fields in order to identify this limiting velocity with the velocity of light in vacuum. While some said that this approach was insufficient and the second postulate is still needed, others continued the attempts to derive special relativity without the light postulate (see Postulates of special relativity). Ignatowski also investigated the status of rigid bodies within special relativity (1910a, 1911a). He concluded that velocities greater than the speed of light are possible, even though he showed that those are not signal velocities and therefore are not in conflict with relativity (1910b, 1911g). He also formulated a relativistic theory of hydrodynamics (1911f).
History of special relativity
In 1962 J. G. Fox pointed out that all previous experimental tests of the constancy of the speed of light were conducted using light which had passed through stationary material: glass, air, or the incomplete vacuum of deep space. As a result, all were thus subject to the effects of the extinction theorem. This implied that the light being measured would have had a velocity different from that of the original source. He concluded that there was likely as yet no acceptable proof of the second postulate of special relativity. This surprising gap in the experimental record was quickly closed in the ensuing years, by experiments by Fox, and by Alvager et al., which used gamma rays sourced from high energy mesons. The high energy levels of the measured photons, along with very careful accounting for extinction effects, eliminated any significant doubt from their results.
Hermann Minkowski
By 1907 Minkowski realized that the special theory of relativity, introduced by his former student Albert Einstein in 1905 and based on the previous work of Lorentz and Poincaré, could best be understood in a four-dimensional space, since known as the "Minkowski spacetime", in which time and space are not separated entities but intermingled in a four-dimensional space–time, and in which the Lorentz geometry of special relativity can be effectively represented using the invariant interval formula_1 (see History of special relativity).
Acceleration (special relativity)
with
Special relativity (alternative formulations)
Euclidean relativity
Special relativity
The principle of relativity, which states that physical laws have the same form in each inertial reference frame, dates back to Galileo, and was incorporated into Newtonian physics. However, in the late 19th century, the existence of electromagnetic waves led physicists to suggest that the universe was filled with a substance that they called "aether", which would act as the medium through which these waves, or vibrations travelled. The aether was thought to constitute an absolute reference frame against which speeds could be measured, and could be considered fixed and motionless. Aether supposedly possessed some wonderful properties: it was sufficiently elastic to support electromagnetic waves, and those waves could interact with matter, yet it offered no resistance to bodies passing through it. The results of various experiments, including the Michelson–Morley experiment, led to the theory of special relativity, by showing that there was no aether. Einstein's solution was to discard the notion of an aether and the absolute state of rest. In relativity, any reference frame moving with uniform motion will observe the same laws of physics. In particular, the speed of light in vacuum is always measured to be "c", even when measured by multiple systems that are moving at different (but constant) velocities.
Spherical wave transformation
In 1905 both Poincaré and Einstein pointed out that the Lorentz transformation of special relativity (setting formula_76)
Jakob Laub
In 1905 he investigated cathode rays together with Wilhelm Wien. Afterwards he investigated some topics on special relativity and wrote in 1907 an important work on the optics of moving bodies. In 1908 he wrote several works together with Einstein on the basic electromagnetic equations, which was aimed to replace the four-dimensional formulation of the electrodynamics by Minkowski by a simpler, classical formulation. Both Laub and Einstein discounted the spacetime formalism as too complicated. However, it turned out that Minkowski's spacetime formalism was fundamental for the further development of special relativity. Laub also published some papers on relativistic effects within gases and in 1910 he wrote one of the first survey articles on relativity. Also in the following years Laub still wrote many scientific papers on different topics.
Walter Kaufmann (physicist)
Walter Kaufmann (June 5, 1871 – January 1, 1947) was a German physicist. He is best known for the first experimental proof of the velocity dependence of mass, which was an important contribution to the development of modern physics, including special relativity.
Relativity priority dispute
Albert Einstein presented the theories of special relativity and general relativity in publications that either contained no formal references to previous literature, or referred only to a small number of his predecessors for fundamental results on which he based his theories, most notably to the work of Hendrik Lorentz for special relativity, and to the work of Carl F. Gauss, Bernhard Riemann, and Ernst Mach for general relativity. Subsequently, claims have been put forward about both theories, asserting that they were formulated, either wholly or in part, by others before Einstein. At issue is the extent to which Einstein and various other individuals should be credited for the formulation of these theories, based on priority considerations.
History of special relativity
Max Abraham (1902–1904), who was a supporter of the electromagnetic world view, quickly offered an explanation for Kaufmann's experiments by deriving expressions for the electromagnetic mass. Together with this concept, Abraham introduced (like Poincaré in 1900) the notion of "Electromagnetic Momentum" which is proportional to formula_16. But unlike the fictitious quantities introduced by Poincaré, he considered it as a "real" physical entity. Abraham also noted (like Lorentz in 1899) that this mass also depends on the direction and coined the names "Longitudinal" and "Transverse" Mass. In contrast to Lorentz, he didn't incorporate the Contraction Hypothesis into his theory, and therefore his mass terms differed from those of Lorentz.
Theory of relativity
The defining feature of special relativity is the replacement of the Galilean transformations of classical mechanics by the Lorentz transformations. (See Maxwell's equations of electromagnetism).
Postulates of special relativity
Historically, Hendrik Lorentz and Henri Poincaré (1892–1905) derived the Lorentz transformation from Maxwell's equations, which served to explain the negative result of all aether drift measurements. By that the luminiferous aether becomes undetectable in agreement with what Poincaré called the principle of relativity (see History of Lorentz transformations and Lorentz ether theory). A more modern example of deriving the Lorentz transformation from electrodynamics (without using the historical aether concept at all), was given by Richard Feynman.
Lorentz transformation
In 1905, Poincaré was the first to recognize that the transformation has the properties of a mathematical group,
and named it after Lorentz.
Later in the same year Albert Einstein published what is now called special relativity, by deriving the Lorentz transformation under the assumptions of the principle of relativity and the constancy of the speed of light in any inertial reference frame, and by abandoning the mechanistic aether as unnecessary.
Nathan Rosen
At the beginning of the 20th century science was progressing quickly and the inner workings of the atom were just beginning to be discovered. In 1900, Max Planck proposed the quantum theory, the idea that all energy moves in discrete amounts called quanta. In 1905, Albert Einstein published his theory of special relativity, which would be instrumental in the progression of physics and the understanding of the universe. Around 1927, Niels Bohr and Werner Heisenberg, collaborating with many other physicists, developed the Copenhagen interpretation of quantum theory, determining the probabilities of the movement of particles. These breakthroughs provided the model for the structure and workings of the atom and drove the revolution that would sweep up Nathan Rosen.
George Francis FitzGerald
The Lorentz–FitzGerald contraction (or FitzGerald–Lorentz contraction) hypothesis became an essential part of the Special Theory of Relativity, as Albert Einstein published it in 1905. He demonstrated the kinematic nature of this effect, by deriving it from the principle of relativity and the constancy of the speed of light.
Principle of relativity
General relativity was developed by Einstein in the years 1907 - 1915. General relativity postulates that the global Lorentz covariance of special relativity becomes a local Lorentz covariance in the presence of matter. The presence of matter "curves" spacetime, and this curvature affects the path of free particles (and even the path of light). General relativity uses the mathematics of differential geometry and tensors in order to describe gravitation as an effect of the geometry of spacetime. Einstein based this new theory on the general principle of relativity, and he named the theory after the underlying principle.See the special relativity references and the general relativity references.
Velocity-addition formula
The aberration of light, of which the easiest explanation is the relativistic velocity addition formula, together with Fizeau's result, triggered the development of theories like Lorentz aether theory of electromagnetism in 1892. In 1905 Albert Einstein, with the advent of special relativity, derived the standard configuration formula ( in the ) for the addition of relativistic velocities. The issues involving aether were, gradually over the years, settled in favor of special relativity.
Hendrik Lorentz
Hendrik Antoon Lorentz (; 18 July 1853 – 4 February 1928) was a Dutch physicist who shared the 1902 Nobel Prize in Physics with Pieter Zeeman for the discovery and theoretical explanation of the Zeeman effect. He also derived the transformation equations underpinning Albert Einstein's theory of special relativity.
Spacetime
In 1905, Einstein introduced special relativity (even though without using the techniques of the spacetime formalism) in its modern understanding as a theory of space and time. While his results are mathematically equivalent to those of Lorentz and Poincaré, it was Einstein who showed that the Lorentz transformations are not the result of interactions between matter and aether, but rather concern the nature of space and time itself. He obtained all of his results by recognizing that the entire theory can be built upon two postulates: The principle of relativity and the principle of the constancy of light speed.
Numerical relativity
Albert Einstein published his theory of general relativity in 1915. It, like his earlier theory of special relativity, described space and time as a unified spacetime subject to what are now known as the Einstein field equations. These form a set of coupled nonlinear partial differential equations (PDEs). After more than 100 years since the first publication of the theory, relatively few closed-form solutions are known for the field equations, and, of those, most are cosmological solutions that assume special symmetry to reduce the complexity of the equations.
Special relativity
Einstein consistently based the derivation of Lorentz invariance (the essential core of special relativity) on just the two basic principles of relativity and light-speed invariance. He wrote:
Thus many modern treatments of special relativity base it on the single postulate of universal Lorentz covariance, or, equivalently, on the single postulate of Minkowski spacetime.
Motion (physics)
Classical mechanics was further enhanced by Albert Einstein's special relativity and general relativity. Special relativity is concerned with the motion of objects with a high velocity, approaching the speed of light; general relativity is employed to handle gravitational motion at a deeper level.
Postulates of special relativity
The two-postulate basis for special relativity is the one historically used by Einstein, and it remains the starting point today. As Einstein himself later acknowledged, the derivation of the Lorentz transformation tacitly makes use of some additional assumptions, including spatial homogeneity, isotropy, and memorylessness. Also Hermann Minkowski implicitly used both postulates when he introduced the Minkowski space formulation, even though he showed that "c" can be seen as a space-time constant, and the identification with the speed of light is derived from optics.
History of special relativity
Einstein (1908) tried – as a preliminary in the framework of special relativity – also to include accelerated frames within the relativity principle. In the course of this attempt he recognized that for any single moment of acceleration of a body one can define an inertial reference frame in which the accelerated body is temporarily at rest. It follows that in accelerated frames defined in this way, the application of the constancy of the speed of light to define simultaneity is restricted to small localities. However, the equivalence principle that was used by Einstein in the course of that investigation, which expresses the equality of inertial and gravitational mass and the equivalence of accelerated frames and homogeneous gravitational fields, transcended the limits of special relativity and resulted in the formulation of general relativity.
E. T. Whittaker
In 1951 (Vol. 1) and 1953 (Vol. 2), he published an extended and revised edition of his book in two volumes. The second volume contains some interesting historical remarks. For example, it contains a chapter named "The Relativity Theory of Poincaré and Lorentz", where Whittaker credited Henri Poincaré and Lorentz for developing special relativity, and especially alluded to Lorentz's 1904 paper (dated by Whittaker as 1903), Poincaré's St. Louis speech () of September 1904, and Poincaré's June 1905 paper. He attributed to Einstein's special relativity paper only little importance, which he said "set forth the relativity theory of Poincaré and Lorentz with some amplifications, and which attracted much attention”, and he credited Einstein only with being the first to publish the correct relativistic formulas for relativistic aberration and the Doppler effect. He also attributed the formula formula_1 to Poincaré. In 1984 Clifford Truesdell wrote that Whittaker "aroused colossal antagonism by trying to set the record straight on the basis of print and record rather than recollection and folklore and professional propaganda..." On the other hand, Abraham Pais wrote that "Whittaker's treatment of special relativity shows how well the author's lack of physical insight matches his ignorance of the literature". According to Roberto Torretti, "Whittaker's views on the origin of special relativity have been rejected by the great majority of scholars", and he cites Max Born (1956), Gerald Holton (1960,1964), Schribner (1964), Goldberg (1967), Zahar (1973), Hirosige (1976), Schaffner (1976), and Arthur I. Miller (1981).
Dirac equation
In particle physics, the Dirac equation is a relativistic wave equation derived by British physicist Paul Dirac in 1928. In its free form, or including electromagnetic interactions, it describes all spin- massive particles such as electrons and quarks for which parity is a symmetry. It is consistent with both the principles of quantum mechanics and the theory of special relativity, and was the first theory to account fully for special relativity in the context of quantum mechanics. It was validated by accounting for the fine details of the hydrogen spectrum in a completely rigorous way.
History of special relativity
Important early experiments confirming special relativity as mentioned above were the Fizeau experiment, the Michelson–Morley experiment, the Kaufmann–Bucherer–Neumann experiments, the Trouton–Noble experiment, the experiments of Rayleigh and Brace, and the Trouton–Rankine experiment.
Herbert Dingle
Initially Dingle argued that, contrary to the usual understanding of the famous twin paradox, special relativity did not predict unequal aging of twins, one of whom makes a high-speed voyage and returns to Earth, but he then came to realize and acknowledge that his understanding had been mistaken. He then began to argue that special relativity was empirically wrong in its predictions, although experimental evidence showed he was mistaken about this. Ultimately Dingle re-focused his criticism to claim that special relativity was logically inconsistent: "The theory [special relativity] unavoidably requires that A works more slowly than B and B more slowly than A --which it requires no super-intelligence to see is impossible." Hence he asserted that the well-known reciprocity of the Lorentz transformation is self-evidently impossible. As Whitrow explained in his obituary for Dingle, this is not correct, as it rests on Dingle's mistaken assumption that the conflicting ratios of event times used by Dingle are invariants.
Special relativity (alternative formulations)
Test theories of special relativity are flat space-time theories which differ from special relativity by having a different postulate about light concerning one-way speed of light vs two-way speed of light. Different postulates on light result in different notions of time simultaneity. There is Robertson's test theory (1949) which predicts different experimental results from Einstein's special relativity, and then there is Edward's theory (1963) which cannot be called a test theory because it is physically equivalent to special relativity, and then there is the Mansouri-Sexl theory (1977) which is equivalent to Robertson's theory.
History of special relativity
After Heinrich Hertz in 1887 demonstrated the existence of electromagnetic waves, Maxwell's theory was widely accepted. In addition, Oliver 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, and Heaviside's notation is still used today. Other important contributions to Maxwell's theory were made by George FitzGerald, Joseph John Thomson, John Henry Poynting, Hendrik Lorentz, and Joseph Larmor.
Light cone
This view of special relativity was first proposed by Albert Einstein's former professor Hermann Minkowski and is known as Minkowski space. The purpose was to create an invariant spacetime for all observers. To uphold causality, Minkowski restricted spacetime to non-Euclidean hyperbolic geometry.
Bondi k-calculus
Bondi "k"-calculus is a method of teaching special relativity popularised by Professor Sir Hermann Bondi, and now common in university and college-level physics classes.
Michelson–Morley experiment
Albert Einstein formulated the theory of special relativity by 1905, deriving the Lorentz transformation and thus length contraction and time dilation from the relativity postulate and the constancy of the speed of light, thus removing the "ad hoc" character from the contraction hypothesis. Einstein emphasized the kinematic foundation of the theory and the modification of the notion of space and time, with the stationary aether no longer playing any role in his theory. He also pointed out the group character of the transformation. Einstein was motivated by Maxwell's theory of electromagnetism (in the form as it was given by Lorentz in 1895) and the lack of evidence for the luminiferous aether.
Modern history
Albert Einstein is known for his theories of special relativity and general relativity. He also made important contributions to statistical mechanics, especially his mathematical treatment of Brownian motion, his resolution of the paradox of specific heats, and his connection of fluctuations and dissipation. Despite his reservations about its interpretation, Einstein also made contributions to quantum mechanics and, indirectly, quantum field theory, primarily through his theoretical studies of the photon.
Criticism of the theory of relativity
It was also claimed that special relativity cannot handle acceleration, which would lead to contradictions in some situations. However, this assessment is not correct, since acceleration actually can be described in the framework of special relativity (see Acceleration (special relativity), Proper reference frame (flat spacetime), Hyperbolic motion, Rindler coordinates, Born coordinates). Paradoxes relying on insufficient understanding of these facts were discovered in the early years of relativity. For example, Max Born (1909) tried to combine the concept of rigid bodies with special relativity. That this model was insufficient was shown by Paul Ehrenfest (1909), who demonstrated that a rotating rigid body would, according to Born's definition, undergo a contraction of the circumference without contraction of the radius, which is impossible (Ehrenfest paradox). Max von Laue (1911) showed that rigid bodies cannot exist in special relativity, since the propagation of signals cannot exceed the speed of light, so an accelerating and rotating body will undergo deformations.
Einstein's thought experiments
The topic of how Einstein arrived at special relativity has been a fascinating one to many scholars: A lowly, twenty-six year old patent officer (third class), largely self-taught in physics and completely divorced from mainstream research, nevertheless in the year 1905 produced four extraordinary works ("Annus Mirabilis" papers), only one of which (his paper on Brownian motion) appeared related to anything that he had ever published before.
History of special relativity
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 (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, 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. In 1908, Einstein and Laub rejected the four-dimensional electrodynamics of Minkowski as overly complicated "learned superfluousness" and published a "more elementary", non-four-dimensional derivation of the basic-equations for moving bodies. But it was Minkowski's geometric model that (a) showed that the special relativity is a complete and internally self-consistent theory, (b) added the Lorentz invariant proper time interval (which accounts for the actual readings shown by moving clocks), and (c) served as a basis for further development of relativity. Eventually, Einstein (1912) recognized the importance of Minkowski's geometric spacetime model and used it as the basis for his work on the foundations of general relativity.
History of special relativity
with the following consequences for the speed of light and the theories known at that time:In order to make the principle of relativity as required by Poincaré an exact law of nature in the immobile aether theory of Lorentz, the introduction of a variety ad hoc hypotheses was required, such as the contraction hypothesis, local time, the Poincaré stresses, etc.. This method was criticized by many scholars, since the assumption of a conspiracy of effects which completely prevent the discovery of the aether drift is considered to be very improbable, and it would violate Occam's razor as well. Einstein is considered the first who completely dispensed with such auxiliary hypotheses and drew the direct conclusions from the facts stated above: that the relativity principle is correct and the directly observed speed of light is the same in all inertial reference frames. Based on his axiomatic approach, Einstein was able to derive "all results" obtained by his predecessors – and in addition the formulas for the relativistic Doppler effect and relativistic aberration – in a few pages, while prior to 1905 his competitors had devoted years of long, complicated work to arrive at the same mathematical formalism. Before 1905 Lorentz and Poincaré had adopted these same principles, as necessary to achieve their final results, but didn't recognize that they were also sufficient in the sense that there was no immediate logical need to assume the existence of a stationary aether in order to arrive at the Lorentz transformations. Another reason for Einstein's early rejection of the aether in any form (which he later partially retracted) may have been related to his work on quantum physics. Einstein discovered that light can also be described (at least heuristically) as a kind of particle, so the aether as the medium for electromagnetic "waves" (which was highly important for Lorentz and Poincaré) no longer fitted into his conceptual scheme.
Édouard Guillaume
Édouard Guillaume (1881–1959) was a Swiss physicist and patent examiner, notorious for his published papers attacking Einstein's theory of special relativity. He is also noteworthy for his work on mathematical economics.
De Sitter double star experiment
The de Sitter effect was described by Willem de Sitter in 1913 (as well as by Daniel Frost Comstock in 1910) and used to support the special theory of relativity against a competing 1908 emission theory by Walther Ritz that postulated a variable speed of light. De Sitter showed that Ritz's theory predicted that the orbits of binary stars would appear more eccentric than consistent with experiment and with the laws of mechanics, however, the experimental result was negative. This was confirmed by Brecher in 1977 by observing the x-rays spectrum. For other experiments related to special relativity, see tests of special relativity.
Special relativity
We can write
Albert Einstein
Einstein originally framed special relativity in terms of kinematics (the study of moving bodies). In 1908, Hermann Minkowski reinterpreted special relativity in geometric terms as a theory of spacetime. Einstein adopted Minkowski's formalism in his 1915 general theory of relativity.
Hermann Minkowski
Minkowski is perhaps best known for his work in relativity, in which he showed in 1907 that his former student Albert Einstein's special theory of relativity (1905) could be understood geometrically as a theory of four-dimensional space–time, since known as the "Minkowski spacetime".
Special relativity
A defining feature of special relativity is the replacement of the Galilean transformations of Newtonian mechanics with the Lorentz transformations. Time and space cannot be defined separately from each other. Rather, space and time are interwoven into a single continuum known as spacetime. Events that occur at the same time for one observer can occur at different times for another.
Aaron Bernstein
A story in volume 16 of Bernstein's "Naturwissenschaftliche Volksbücher" about riding along with the electricity travelling through a telegraph wire is often credited with inspiring the 16-year-old Albert Einstein to think about travelling along with a beam of light and seeing it stationary. Such thought experiments eventually led to his famous theory of special relativity.
Ludwik Silberstein
Ludwik Silberstein (1872 – 1948) was a Polish-American physicist who helped make special relativity and general relativity staples of university coursework. His textbook "The Theory of Relativity" was published by Macmillan in 1914 with a second edition, expanded to include general relativity, in 1924.