Search Results for relativity
Biographies
- Kerr Roy biography
- One of his lecturers at Canterbury College was Walter Warwick Sawyer who had specialised in relativity and quantum theory when studying at St John's College, Cambridge.
- He undertook research in relativity, although he was assigned a thesis advisor with no interest in that topic [7]:-
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- My nominal supervisor was a particle physicist who had no interest in general relativity.
- He submitted his doctoral thesis Equations of Motion in General Relativity in 1958 and published the results of the thesis in three papers entitled The Lorentz-covariant approximation method in general relativity in Nuovo Cimento in 1959.
- Before he left, Josh and I became interested in the new methods that were entering general relativity from differential geometry at that time.
- He had just persuaded the Texas state legislators to finance a Center for Relativity at the University of Texas, and had arranged for an outstanding group of relativists to join.
- In 1963, Roy Kerr, a New Zealander, found a set of solutions of the equations of general relativity that described rotating black holes.
- In my entire scientific life, extending over forty-five years, the most shattering experience has been the realization that an exact solution of Einstein's equations of general relativity, discovered by the New Zealand mathematician, Roy Kerr, provides the absolutely exact representation of untold numbers of massive black holes that populate the universe.
- Everybody who tried to solve the problem was going at it from the front, but I was trying to solve the equation from a different point of view - there were a number of new mathematical methods coming into relativity at the time and Josh [Goldberg] and I had had some success with these.
- Teddy Newman and Roger Penrose were working on a similar set of methods, but Teddy had come out with this as-yet unpublished theorem that basically 'proved' that my solution couldn't exist! Luckily, my neighbour, who was playing around with relativity, too, got hold of a preprint and I just scanned through it (I'm a lazy reader) and hit the crucial part which proved to me that my solution could exist! After that, I kept working like mad and found the solution in a few weeks.
- The Hughes Medal is awarded to Professor R P Kerr in recognition of his distinguished work on relativity, especially for his discovery of the so-called Kerr black hole.
- Professor Kerr has made other significant contributions to general relativity theory, but the discovery of the Kerr black hole was so remarkable as to compare with the discovery in physics of a new elementary particle.
- for his contribution to relativity through the Kerr metric.
- The Kerr Fest, a Symposium on Black Holes in Astrophysics, General Relativity and Quantum Gravity, was held 26 - 28, August 2004 at the University of Canterbury, Christchurch, to mark Roy Kerr's 70th birthday.
- for his fundamental contribution to Einstein's theory of general relativity: "The gravitational field of a spinning mass as an example of algebraically special metrics."
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- Einstein biography
- Einstein's second 1905 paper proposed what is today called the special theory of relativity.
- He based his new theory on a reinterpretation of the classical principle of relativity, namely that the laws of physics had to have the same form in any frame of reference.
- Einstein was not the first to propose all the components of special theory of relativity.
- He made important contributions to quantum theory, but he sought to extend the special theory of relativity to phenomena involving acceleration.
- Einstein called his new work the general theory of relativity.
- Just before publishing this work he lectured on general relativity at Gottingen and he wrote:-
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- In fact Hilbert submitted for publication, a week before Einstein completed his work, a paper which contains the correct field equations of general relativity.
- However he received the Barnard Medal during his visit and lectured several times on relativity.
- Einstein received the Nobel Prize in 1921 but not for relativity rather for his 1905 work on the photoelectric effect.
- In 1944 he made a contribution to the war effort by hand writing his 1905 paper on special relativity and putting it up for auction.
- Ether and Relativity
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- History Topics: Special relativity
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- History Topics: General relativity
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- History Topics: Light through the ages: Relativity and quantum era
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- Carmichael biography
- Carmichael was promoted to Associate Professor at Indiana in 1912 and in the autumn of that year he delivered a short course on the theory of relativity.
- He published On the Theory of Relativity: Analysis of the Postulates in the Physical Review in September 1912.
- This analysis of the postulates of relativity was undertaken in order to ascertain on just which of the postulates certain fundamental conclusions of the theory depend.
- Some of the conclusions of relativity have been attacked by those who admit just the parts of the postulates from which the conclusions objected to can be derived by purely logical processes.
- In November 1912 he submitted another article On the Theory of Relativity: Philosophical Aspects to the Physical Review which was published in March 1913.
- Based on these papers and his lecture course, Carmichael published a 74-page book The theory of relativity in 1913.
- It is now more than eight years since the theory of relativity was expounded by Einstein, and, although the literature of the subject is already considerable, this is practically the first presentation in book form which has been offered to English readers.
- Of course this work was on what is now called the special theory of relativity and after Einstein published the general theory of relativity, Carmichael brought out a second edition of his book in 1920.
- The theory of relativity has now reached its furthest conceivable generalisation in the direction of the covariance of the laws of nature under transformations of coordinates.
- The older theory of relativity remains valid as a special case of the general theory and may well serve as an introduction to its more far-reaching aspects.
- In May 1926 a debate on the theory of relativity was held at Indiana University and Carmichael both participated in the debate and edited the resulting volume A Debate on the Theory of Relativity (1927).
- Carmeli biography
- The significance of the "tail" and the relation to other equations of motion (1965), Motion of a charge in a gravitational field (1965), The equations of motion of slowly moving particles in the general theory of relativity (1965), and Equations of motion without infinite self-action terms in general relativity (1965).
- He carried out his research in general relativity and gravitation, and lectured in Lehigh University, Temple University and then in the University of Maryland.
- Carmeli's field included gravitation and gauge field theory, the theory of spinors as applied to physics, Einstein special and general relativity, and astrophysics.
- He developed his own cosmological relativity theory, both special and general, in which the age of Universe is postulated as constant, just as the speed of light is in Einstein's theory, and the velocity of receding galaxies is considered as a new independent variable.
- Group theory and general relativity : Representations of the Lorentz group and their applications to the gravitational field (1977):-
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- the first book to found the theory of general relativity on the principle of gauge invariance;
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- Classical fields : general relativity and gauge theory (1982):-
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- devoted to the formulation of Einstein's theory of general relativity as a gauge theory with the SL(2, C) group as the gauge group;
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- Cosmological special relativity : The large scale structure of space, time and velocity (1997):-
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- which gives an introduction to the theory of spinors for the general physicist, not only for workers in general relativity.
- Re-envisioning Einstein's theories of Special and General Relativity and building on the work of Edwin Hubble, Dr Carmeli has suggested that the universe's expansion must be constantly accelerating, and that time is therefore relative; in other words, it can only be measured relative to the position and velocity of the measurer.
- Eddington biography
- Eddington made important contributions to the theory of general relativity.
- He lectured on relativity at the British Association meeting in 1916 and produced a major report on the topic for the Physical Society in 1918.
- Its aim was to verify the bending of light passing close to the sun which was predicted by relativity theory.
- Eddington lectured on relativity at Cambridge, giving a beautiful mathematical treatment of the topic.
- He used these lectures as a basis for his book Mathematical Theory of Relativity which was published in 1923.
- In addition to his work in relativity theory Eddington also did important work on the internal structure of stars.
- In [Eddington\'s search for a fundamental theory : a key to the universe (Cambridge, 1994).',9)">9] Kilmister delves deeply into the ideas which led Eddington to the theories he put forward in Fundamental Theory in attempting to unite quantum mechanics and general relativity.
- It was Dirac's 1928 paper on the wave equation of the electron which had first set Eddington on the path of seeking ways to unify quantum mechanics and general relativity.
- Mathematical Theory of Relativity Preface
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- Mathematical Theory of Relativity Introduction
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- History Topics: Light through the ages: Relativity and quantum era
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- Lichnerowicz biography
- Chapter I (Axiomatique de la theorie de la gravitation) [gives] relevant results on the initial value problem associated with the field equations of general relativity; most important for the sequel are those which deal with the continuation of an "interior field," in a region containing matter, across a boundary into an "exterior field" in regions free of matter.
- He had continued to work on relativity theory during the war and he spoke in [22] about a particular problem from that time:-
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- With the German occupation, very few scientific papers were available; I realized that if one wanted relativity to work well, there was a fundamental question which arose.
- The first course he gave there in the academic year 1952-53 was on the general theory of relativity.
- that general relativity, now nearly forty years old, has passed from theoretical into mathematical physics and should be treated with mathematical rigour like the theory of potential.
- In this spirit he presents relativity axiomatically, with much more attention to mathematical precision than has been customary and much less attention to its physical aspects.
- Relativite generale et theories unitaires which gives a rigorous mathematical treatment of more advanced topics in general relativity.
- We have already said a little about Lichnerowicz's work on Einstein's theory of general relativity.
- The papers are divided into three sections: relativity theory, differential geometry, and infinite-dimensional Lie algebras.
- Fock biography
- Fock had strong views on general relativity which he interpreted somewhat differently from Einstein.
- First, it is a text-book for the use of graduate students in theoretical physics, giving a complete exposition of the theories of special and general relativity.
- He objects to the use of the name "general relativity" for Einstein's theory of gravitation.
- He defines "relativity" to mean an invariance in the description of nature as viewed from different physical observation-points (not coordinate-systems).
- In this sense the gravitation theory contains less relativity than what is usually called "special relativity", and not more.
- So he vehemently insists that we call "special relativity" "relativity", and "general relativity" "gravitation theory." ..
- Chazy biography
- Having done brilliant work on differential equations, Chazy's interests now turned towards the theory of relativity.
- Albert Einstein's general theory of relativity was, at this time, very new only having been published near the end of 1915.
- An important paper on relativity he published in 1924 is Sur le champ de gravitation de deux masses fixes dans la theorie de la relativite.
- He published the two-volume treatise The Theory of Relativity and Celestial Mechanics (1928, 1930).
- The purpose of this book, which is the development of a course taught at the Faculty of Sciences of Paris in 1927, is to expose as clearly as possible the theory of relativity in dealing with celestial mechanics, taking as a starting point the knowledge of a student who has attended a few lessons on differential and integral calculus, and mechanics.
- It discusses the principles of relativity, the equations of gravitation, the determination of ds2, Schwarzschild equations of motion, the n-body problem and finally cosmogonic hypotheses related to the ds2 of the universe.
- (3) The law of gravitation of the theory of relativity and the classical theory of perturbations;
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- (7) Birth of the Theory of Relativity.
- While penetrating in an original and profound way the field of research opened by the relativity revolution, Chazy nevertheless remained a classically trained mathematician.
- Hawking biography
- From Oxford, Hawking moved to Cambridge to take up research in general relativity and cosmology, a difficult area for someone with only a little mathematical background.
- Between 1965 and 1970 Hawking worked on singularities in the theory of general relativity devising new mathematical techniques to study this area of cosmology.
- Using quantum theory and general relativity he was able to show that black holes can emit radiation.
- His success with proving this made him work from that time on combining the theory of general relativity with quantum theory.
- These mini black holes have large gravitational attraction governed by general relativity, while the laws of quantum mechanics would apply to objects that small.
- This book, which he edited, contains reprints of nearly complete editions of: Copernicus, On the revolution of the heavenly spheres (1543); Galileo, Dialogues concerning two new sciences (1638); Kepler, Harmony of the world (Book Five) (1618); Newton, Principia (1687); and seven papers on relativity by Einstein.
- Although his work on black hole thermodynamics is perhaps the most well known, Hawking has also made major contributions to the study of singularity theorems in general relativity, black hole uniqueness, quantum fields in curved spacetimes, Euclidean quantum gravity, the wave function of the universe and many other areas as well.
- In the same year Black holes and the information paradox was published, being the transcript of the famous talk Hawking gave at the 17th International Conference on General Relativity and Gravitation in Dublin in 2004.
- Grossmann biography
- He was struggling to extend his special theory of relativity to include gravitation and immediately began collaborating with his old friend Grossmann.
- It was Grossmann who pointed out to him the relevance to general relativity of the tensor calculus which had been proposed by Elwin Bruno Christoffel in 1864, and developed by Gregorio Ricci-Curbastro and Tullio Levi-Civita around 1901.
- Compared with this problem, the original theory of relativity is child's play.
- The collaboration between Grossmann and Einstein led to the first paper on the general theory of relativity in 1913.
- Finally we should mention the honour given to Marcel Grossmann by naming the series of conferences, the Marcel Grossmann Meetings (on Recent Developments in Theoretical and Experimental General Relativity, Gravitation, and Relativistic Field Theories).
- These conferences, begun in 1975, are international meetings held every three years, which provide opportunities for discussing recent advances in gravitation, general relativity and relativistic field theories.
- History Topics: General relativity
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- Synge biography
- The origin of the name "Synge" is described in the introduction to General relativity : papers in honour of J L Synge :-
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- Professor Synge made outstanding contributions to widely varied fields: classical mechanics, geometrical mechanics and geometrical optics, gas dynamics, hydrodynamics, elasticity, electrical networks, mathematical methods, differential geometry and, above all, Einstein's theory of relativity.
- He felt just as much at home in the ordinary three dimensional Euclidean space as in the four dimensional space-time of relativity.
- Synge retired in 1972 and during his time at the Dublin Institute for Advanced Studies about 12% of all workers in relativity theory studied there.
- Synge's classic, written in 1956, had a large influence [General relativity : papers in honour of J L Synge (Oxford, 1972), 257-265.',1)">1]:-
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- It is a remarkable fact that hardly a single space-time diagram is to be found in the standard texts on relativity before Synge's own presentation in 1956.
- Here was a royal road to relativity which did not involve precarious juggling with factors of √(1 - v2/c2).
- Freundlich biography
- At this time Einstein was working on the general theory of relativity and, although he did not have the details of the theory worked out, he was beginning to understand some of its consequences.
- Freundlich worked with Einstein in 1911 attempting to make the measurements of Mercury's orbit required to confirm the general theory of relativity.
- Freundlich was interested in measuring the deflection in a light ray passing close to the sun since again Einstein's incomplete theory of relativity suggested that this test could be used to check the validity of the theory and show that Newton's theory was incorrect.
- He made other tests of general relativity based on gravitational redshift but these were inconclusive.
- He wrote his first book in 1916 following Einstein's publication of the general theory of relativity.
- Freundlich's book Grundlagen der Einsteinschen Gravitationstheorie discussed the ways that the general theory of relativity could be tested by astronomical observations.
- History Topics: General relativity
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- Sitter biography
- De Sitter corresponded with Paul Ehrenfest in 1916, and he proposed that a four-dimensional space-time would fit in with cosmological models based on general relativity.
- He published a series of papers (1916-17) on the astronomical consequences of Einstein's general theory of relativity.
- De Sitter, unlike Einstein, maintained that relativity actually implied that the universe was expanding, theoretical results which were later verified observationally and only then accepted by Einstein.
- This is a particularly simple solution of the field equations of general relativity for an expanding universe.
- Although de Sitter is best known for this work on relativity, he made many other contributions of great significance.
- The privilege accorded me involves a task of unusual difficulty, for the major part of de Sitter's work is in intricate, speculative, and mathematical fields dealing with the perturbations of the motions of bodies of the solar system according to classical celestial mechanics, and with the theory of relativity from a purely speculative point of view as well as in relation to perturbations observed, but not explained, and relativistic theoretical perturbations not perceived or as yet perceivable by observation.
- for his theoretical investigations on the orbits of the satellites of Jupiter, and for his contribution to the Theory of Relativity.
- McCrea biography
- His first research topic involved applying advanced mathematical methods to the study of quantum theory and relativity.
- In 1935 McCrea published Relativity Physics, a little book of less than 100 pages.
- provide an accessible account of the deduction of results of relativity theory which find common application in physics.
- The book studies results all taken from the theory of special relativity which are described in terms of three-dimensional vector notation.
- We have mentioned his text on relativity, but he also published many papers on the topic.
- In particular he wrote on the 'twin paradox' of relativity which states that the space-travelling member of a pair of twins would age less than the twin who remained on the earth.
- was one of the few people to take seriously the steady-state theory developed by Hermann Bondi, Thomas Gold and Fred Hoyle, and he showed how to treat the theory within the framework of general relativity.
- Reichenbach biography
- He was sent back to Berlin where by 1917 he was one of only five people who attended Einstein's first course on relativity.
- There he taught a wide variety of topics showing both the breadth of his interests and his background: relativity, philosophy of science, history of philosophy, surveying, and radio techniques.
- In the year he took up this position he published his first major text on relativity Relativitatstheorie und Erkenntnis apriori (The theory of relativity and a priori knowledge) which attacked Kant's synthetic a priori theory of space and time, and of physics.
- This was followed by papers such as Bericht uber eine Axiomatik der Einsteinschen Raum-Zeit-Lehre (1921) and Der gegenwartige Stand der Relativitatsdiskussion (The present state of the discussion on relativity) (1922) before his second major book Axiomatik der relativistischen Raum-Zeit-Lehre (Axiomatisation of the theory of relativity) was published in 1924.
- This work again examined the philosophical meaning of the theory of relativity.
- Abraham Max biography
- During this time Abraham and Einstein disagreed strongly about the theory of relativity in a correspondence discussed in [Einstein and the history of general relativity (Boston, MA, 1989), 160-174.',3)">3] and [Italian mathematics between the two world wars (Bologna, 1987), 143-159.',4)">4].
- Einstein also argued about relativity in a correspondence with Levi-Civita and Abraham played a role in this argument too, see for example [Italian mathematics between the two world wars (Bologna, 1987), 143-159.',4)">4].
- Abraham was opposed to relativity all his life.
- At first he objected both to the postulates on which relativity was based and also to the fact that he felt that the experimental evidence did not support the theory.
- By 1912 Abraham, who despite his objections was one of those who best understood relativity theory, was prepared to accept that the theory was logically sound.
- He hoped that further astronomical data would support the aether theory and show that relativity was not in fact a good description of the real world.
- Choquet-Bruhat biography
- She dedicated the book General Relativity and the Einstein Equations (2009) she wrote many years later to:-
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- Her research has created new mathematical methods that have provided a solid foundation for the study of several physical theories: the theory of general relativity, relativistic hydrodynamics, non-Abelian gauge theory, the theory of supergravity, etc.
- She introduced some new formulations of Einstein's theory of gravitation which has led to spectacular recent progress in numerical relativity, including the calculation of gravitational waves emitted during the collapse and merger of two black holes.
- Global Solutions of the Problem of Constraints on a Closed Manifold, published in 1973, shows that the existence of global solutions of the constraint equations of general relativity on a closed manifold depend on subtle properties of the manifold.
- Her latest book, General relativity and the Einstein equations was published in 2009.
- This massive book covers in detail the areas of classical mathematical relativity theory to which the author has made major contributions during her long and active research career.
- But the inclusion of some introductory chapters on Lorentzian manifolds, special relativity and kinetic theory makes it an up-to-date reference work or even a textbook for an advanced graduate course.
- Penrose biography
- One was a course by Hermann Bondi on general relativity which was fascinating ..
- The first was The apparent shape of a relativistically moving sphere while in 1960 he published A spinor approach to general relativity.
- Basically under these conditions space-time cannot be continued and classical general relativity breaks down.
- Penrose looked for a unified theory combining relativity and quantum theory since quantum effects become dominant at the singularity.
- One of Penrose's major breakthroughs was his introduction of twistor theory in an attempt to unite relativity and quantum theory.
- His deep work on General Relativity has been a major factor in our understanding of black holes.
- Sir Roger, Emeritus Rouse Ball Professor of Mathematics at the University of Oxford, has made outstanding contributions to general relativity theory and cosmology, most notably for his work on black holes and the Big Bang.
- Pauli biography
- He was certainly not a typical pupil for he read Einstein's papers on relativity while he was still at the Gymnasium.
- Within two months of leaving school he had submitted his first paper on the theory of relativity.
- While still an undergraduate at Munich he wrote two further articles on the theory of relativity.
- Sommerfeld asked Pauli to write a review article on relativity for the Encyclopadie der mathematischen Wissenschaften when he had only been two years at university, a mark of the high regard in which he held Pauli.
- Two months after the award of his doctorate Pauli's survey of the theory of relativity appeared, by this time having grown into a work of 237 pages.
- His genius was immediately recognised by Einstein who, after reading Pauli's monograph on relativity, wrote a review [The genius of science (Oxford, 2000), 210-262.',21)">21]:-
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- Yano biography
- Everyone in Japan was saying that the theory of relativity was so difficult that only twelve people in the world could understand it.
- I do not know how difficult the theory of relativity is to understand, but it was not created by God, it was created by a human being called Albert Einstein.
- So Kentaro! I am sure that if you study hard you may someday understand what the theory of relativity is.
- This stuck with Kentaro so when he was in secondary school and discovered that his physics textbook had an appendix on the theory of relativity, he tried to read it.
- Not finding it too difficult he spoke to his physics teacher who explained to him that what he had read was the special theory of relativity.
- To understand the general theory of relativity one had to study differential geometry.
- Lorentz biography
- Lorentz transformations, which he introduced in 1904, form the basis of Einstein's special theory of relativity.
- They embodied the first systematic appearance of the electrodynamic principle of relativity, and in 1920 he brought out "The Einstein Theory of Relativity: A Concise Statement".
- History Topics: General relativity
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- History Topics: Special relativity
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- History Topics: Light through the ages: Relativity and quantum era
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- Milne biography
- He developed a new form of relativity called kinematic relativity, an alternative to Einstein's general theory of relativity, which also met with considerable opposition.
- Milne's books include Thermodynamics of the Stars (1930) which contains material relating to his Smith's Prize essay discussed above, Relativity, Gravitation and World-Structure (1935), and Kinematic Relativity (1948).
- for his researches on the atmosphere of the Earth and the sun, on the internal constitution of the stars, and on the theory of relativity.
- Infeld biography
- Feeling the need for wider academic contacts, he spent the year 1920 - 21 in Berlin, where he met Einstein and produced his first paper entitled "Light waves in the theory of relativity."
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- Other papers he published around this time include (with P R Wallace, one of his doctoral students) The equations of motion in electrodynamics (1940), On the Theory of Brownian Motion (1940), On a new treatment of some eigenvalue problems (1941), A generalization of the factorization method for solving eigenvalue problems (1942), and Clocks, rigid rods and relativity theory (1943).
- The years 1950 - 68 were full of scientific activity as evidenced by the publication of more than forty papers and the book with J Plebanski 'Motion and relativity' in 1960.
- The important book Motion and relativity referred to in this quote is an important monograph.
- In it are collected "final results" of the study, begun by Infeld with Einstein and Hoffmann in Princeton in 1938, and carried on by him with his students in Warsaw during the last decade, of the problem of motion in the general relativity theory of gravitation.
- It will have permanent value, in any serious library of the subject, as a definitive, detailed account of this part of general relativity theory.
- Vagner biography
- He was particularly attracted by the theory of relativity and he now asked Igor Tamm, a professor in Moscow, if he would supervise his doctoral studies in that topic.
- Although Tamm was very interested in the theory of relativity, he was not allowed to have students in this field.
- Of course, this was a political decision by the Soviet government who had decided that relativity was not a proper science.
- Tamm had to supervise students on the physics of metals but after having discussions with Vagner he clearly saw how the young student had his heart set on studying relativity.
- The very spirit of modern geometry is close to that of relativity.
- Vagner started his research activity at the time when differential geometry was rapidly developing and providing a part of mathematical apparatus for general relativity.
- Bondi biography
- For the extrapolative theories, such as the theory of relativity, this "principle" is merely an aid to the formulation of a problem which is to be attacked within the framework of the extrapolated physical laws; for the deductive theories, such as Milne's kinematical relativity, it is an a priori requirement, a sort of categorical imperative, to which physical experience must conform.
- It would certainly be a mistake to think that this represents the most important part of Bondi's scientific work, however, for he was a leading expert on many topics in applied mathematics, in particular in relativity theory.
- Also with co-authors, he wrote a series of papers Gravitational waves in general relativity.
- In the same year he wrote the survey Relativity and cosmology and then published The contraction of gravitating sphere two years later which a referee described as an:-
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- Also in 1964 he published Massive spheres in general relativity which he describes as follows:-
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- Weyl biography
- In his first academic year in this new post he was a colleague of Einstein who was at this time working out the details of the theory of general relativity.
- In 1917 Weyl gave another course presenting an innovative approach to relativity through differential geometry.
- He attempted to incorporate electromagnetism into the geometric formalism of general relativity.
- More recently attempts to incorporate electromagnetism into general relativity have been made by Wheeler.
- [In the fourth lecture he] shows how the special theory of relativity is essentially the study of the inherent symmetry of the four-dimensional space-time continuum, where the symmetry operations are the Lorentz transformations; and how the symmetry operations of an atom, according to quantum mechanics, include the permutations of its peripheral electrons.
- History Topics: General relativity
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- Schouten biography
- Schouten was, as were so many mathematicians at that time, deeply interested in the theory of relativity.
- I was never so much interested in quantum mechanics as in the theory of relativity, because the Delft is vectors and tensor, and so those things had become very familiar.
- Of course, working on tensor analysis put Schouten in the exciting area of developments associated with the theory of relativity.
- He produced 180 papers and 6 books on tensor analysis, applying tensor analysis to Lie groups, general relativity, unified field theory, and differential equations.
- He also acknowledged the ideas that came about through discussions with others, for example writing in his paper Uber die Einordnung der Affingeometrie in die Theorie der hoheren Ubertragungen (1923) (see for example [On the History of Unified Field Theories (Living Reviews Relativity, 2004).',2)">2]):-
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- This text contains an excellent treatment of tensor analysis and applications to linear elasticity theory, dynamics, relativity, and quantum mechanics.
- Minkowski biography
- Einstein was a student in several of the courses he gave and the two would later become interested in similar problems in relativity theory.
- Minkowski developed a new view of space and time and laid the mathematical foundation of the theory of relativity.
- This space-time continuum provided a framework for all later mathematical work in relativity.
- These ideas were used by Einstein in developing the general theory of relativity.
- History Topics: Special relativity
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- Lemaitre biography
- Einstein was at the conference and he spoke to Lemaitre in Brussels telling him that the ideas in his 1927 paper had been presented by Friedmann in 1922, but he also said that although he thought Lemaitre's solutions of the equations of general relativity were mathematically correct, they presented a solution which was not feasible physically.
- In 1949 he returned to his study of an expanding universe in Cosmological application of relativity.
- The paper opens with a rapid expository review of the general relativity theory of gravitation, including discussion of kinematics, conservation laws, spherical symmetry, and the solutions of Schwarzschild and de Sitter in terms of comoving coordinates.
- We end this biography by quoting from a review by R N Tiwari of [Studies in the history of general relativity, Luminy, 1988, Einstein Stud.
- He joined the army and, to quote from the author's statement, "after 53 months of war ordeals and military camps, he lost interest in a professional career and decided to become a priest"; this ultimately resulted in a change from engineering to the mathematical sciences, particularly to general relativity, which marked a very notable turning point in Lemaitre's life.
- Poincare biography
- He made contributions to numerous branches of mathematics, celestial mechanics, fluid mechanics, the special theory of relativity and the philosophy of science.
- In applied mathematics he studied optics, electricity, telegraphy, capillarity, elasticity, thermodynamics, potential theory, quantum theory, theory of relativity and cosmology.
- He is acknowledged as a co-discoverer, with Albert Einstein and Hendrik Lorentz, of the special theory of relativity.
- History Topics: General relativity
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- History Topics: Special relativity
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- Durell biography
- Among the books he wrote around this time were: Readable relativity (1926), A Concise Geometry (1928), Matriculation Algebra (1929), Arithmetic (1929), Advanced Trigonometry (1930), A shorter geometry (1931), The Teaching of Elementary Algebra (1931), Elementary Calculus (1934), A School Mechanics (1935), and General Arithmetic (1936).
- First let us look more closely at Readable Relativity.
- It is worth noting that the first text in English on relativity was by Eddington in 1923 so Durell's text came very early.
- Precise, brief, and practical, this text is the work of a highly respected teacher with years of classroom experience, who sketches the mathematical background essential to a clear understanding of the fundamentals of relativity theory.
- The best layman's introduction to relativity that has ever been written by anybody.
- Segal biography
- CC assumes special relativity (SR) as a local theory inasmuch as this can be identified with M'.
- Otherwise CC does not assume general relativity (GR) but is compatible with it.
- The papers which he wrote developing this theory include A variant of special relativity and long-distance astronomy (1974) and Theoretical foundations of the chronometric cosmology (1976).
- Segal's theory, which is a variant of special relativity, is based on the idea that there are two kinds of time.
- I do not agree with comments made by Segal about general relativity and its degree of experimental verification.
- Levi-Civita biography
- He is best known, however, for his work on the absolute differential calculus and with its applications to the theory of relativity.
- Levi-Civita's work was of extreme importance in the theory of relativity, and he produced a series of papers elegantly treating the problem of a static gravitational field.
- This excellent monograph on the n-body problem in the general theory of relativity was prepared about ten years ago, but its appearance now is none the less timely for those who have worried themselves with one or another aspect of the problem.
- History Topics: General relativity
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- Chandrasekhar biography
- During most of the 1960s he studied the equilibrium and the stability of ellipsoidal figures of equilibrium but during this period he also began work on topics from general relativity, the radiation reaction process, and the stability of relativistic stars.
- Eddington, who was a leading expert on relativity at this time, argued that:-
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- one of the ways in which one may explore the physical content of the general theory of relativity is to allow one's sensibility to its aesthetic base guide in the formulation of problems with conviction in the harmonious coherence of its mathematical structure.
- in recognition of his distinguished work on theoretical physics, including stellar structure, theory of radiation, hydrodynamic stability and relativity.
- Noether Emmy biography
- The reason for this was that Hilbert was working on physics, in particular on ideas on the theory of relativity close to those of Albert Einstein.
- The second problem Emmy investigated was a problem from special relativity.
- This basic result in the theory of relativity was praised by Einstein in a letter to Hilbert when he referred to Noether's penetrating mathematical thinking.
- History Topics: General relativity
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- Dirac biography
- Dirac had been hoping to have his research supervised by Ebenezer Cunningham, for by this time Dirac had become fascinated in the general theory of relativity and wanted to undertake research on this topic.
- Also in 1928 he found a connection between relativity and quantum mechanics, his famous spin-1/2 Dirac equation.
- Dirac unified the theories of quantum mechanics and relativity theory, but he also is remembered for his outstanding work on the magnetic monopole, fundamental length, antimatter, the d-function, bra-kets, etc.
- we vividly see everywhere the brilliant imprints of Dirac, unifier of quantum mechanics and relativity theory.
- Heisenberg biography
- He also took courses in experimental physics, which were compulsory, and he began to plan to undertake research in relativity.
- However Pauli, who was at that time working on his major survey of the theory of relativity, advised him against doing research in that topic.
- Relativity and quantum theory were classed as "Jewish" and as a consequence Heisenberg's appointment to Munich was blocked.
- History Topics: Light through the ages: Relativity and quantum era
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- Eisenhart biography
- The second stage started after 1921 when Eisenhart, prompted by Einstein's general theory of relativity and the related geometries, studied generalisations of Riemannian geometry.
- In fact he published 21 papers between 1951 and 1963, for example: Generalized Riemann spaces and general relativity (1953); A unified theory of general relativity of gravitation and electromagnetism (1956); The cosmology problem in general relativity (1960); and The Einstein generalized Riemannian geometry (1963).
- Schrodinger biography
- Schrodinger published his revolutionary work relating to wave mechanics and the general theory of relativity in a series of six papers in 1926.
- There he studied electromagnetic theory and relativity and began to publish on a unified field theory.
- During his last few years Schrodinger remained interested in mathematical physics and continued to work on general relativity, unified field theory and meson physics.
- History Topics: Light through the ages: Relativity and quantum era
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- FitzGerald biography
- George FitzGerald was a brilliant mathematical physicist who today is known by most scientists as one of the proposers of the FitzGerald-Lorentz contraction in the theory of relativity.
- The FitzGerald-Lorentz contraction now plays an important role in relativity.
- History Topics: Special relativity
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- History Topics: Light through the ages: Relativity and quantum era
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- Lanczos biography
- His physics teacher was Eotvos who first interested Lanczos in relativity.
- He worked on relativity theory and after writing his dissertation Relation of Maxwell's Aether Equations to Functional Theory he sent a copy to Einstein.
- Lanczos continued to work on his first love of relativity and corresponded with Einstein both on a scientific level and as a friend.
- A very special, and in some ways the most beautiful, period of his life started there when he returned again to his 'first love' in science, devoting himself primarily to the study of the theory of relativity.
- Friedmann biography
- This group discussed quantum theory, relativity and statistical mechanics.
- Einstein's general theory of relativity, although published in 1915, was not known in Russia due to World War I and the Civil War.
- I have been working on the axiomatics of the relativity principle, proceeding from two underlying propositions:
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- In Gottingen he talked to Prandtl and Hilbert, talking to Hilbert about his work in relativity.
- Robertson biography
- However he did make outstanding contributions to differential geometry, quantum theory, the theory of general relativity, and cosmology [H P Robertson : January 27, 1903-August 26, 1961.
- Before we move on to discuss the area for which Robertson is rightly most famed, namely for his work on general relativity and cosmology, we complete the description of his academic career.
- Around this time he built on de Sitter's solution of the equations of general relativity in an empty universe and developed what are now called Robertson-Walker spaces [Biographical Memoirs National Academy of Sciences 51 (1980), 343-361.',2)">2]:-
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- The Poynting-Robertson effect is so named for Robertson's paper Dynamical effects of radiation in the solar system in which he studied the behaviour of a moving body, subject to the laws of general relativity, which is absorbing and re-emitting solar radiation.
- Wien biography
- They had to adopt a policy towards the new discoveries of relativity which were changing the face of physics so they sought to publish papers that illuminated the physical meaning or concepts of relativity; they left manuscripts that stressed mathematical interpretations to their mathematician colleagues in Gottingen.
- History Topics: Light through the ages: Relativity and quantum era
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- History Topics: Special relativity
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- Cunningham biography
- While at Cambridge, he had read Larmor's famous book Aether and Matter and then, in 1905, after reading Einstein's paper on special relativity, he began to work on that topic.
- Cunningham published The Principle of Relativity in 1914, the first English book on the topic.
- Many papers on relativity followed.
- Of course during this period he found it hard to keep in touch with developments in relativity theory which took place in Germany.
- Schwarzschild biography
- While in Russia he wrote two papers on Einstein's relativity theory and one on Planck's quantum theory.
- Schwarzschild's relativity papers give the first exact solution of Einstein's general gravitational equations, giving an understanding of the geometry of space near a point mass.
- History Topics: General relativity
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- Schiffer biography
- Teaching these courses led to him being a joint author of the textbook Introduction to general relativity (1965) written jointly with Ronald Adler and Maurice Bazin.
- The principal science topics covered are the lever and inclined plane, population growth, geometric optics and special relativity.
- Matrices and the associated linear transformations of the plane are introduced, enabling the authors to take advantage of these tools in the discussion of relativity theory, which occupies the last third of the book.
- Burali-Forti biography
- However this collaboration ended when they differed in their views on relativity.
- Burali-Forti never understood the theory of relativity and, together with Boggio, he wrote a book which claimed to prove that the theory of relativity was impossible.
- Larmor biography
- Larmor's contributions came at a time when there were major revolutions in physics with the passing of classical physics to be replaced by quantum theory and relativity.
- In the end he rejected, not only the curvature of space, but even the standpoint of the earlier special theory of relativity.
- History Topics: Special relativity
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- Birkhoff biography
- The foundations of relativity and quantum mechanics were also topics which Birkhoff studied.
- Jointly with R E Langer, he published the monograph Relativity and Modern Physics in 1923.
- Among his works, some of which we have already mentioned above, are Relativity and Modern Physics (1923), Dynamical Systems (1928), Aesthetic Measure (1933), and Basic Geometry (1941).
- Adams Edwin biography
- His greatest fame came in 1921 when Einstein first visited Princeton to deliver five Stafford Little lectures on the theory of relativity and to accept an honorary degree.
- Each lecture, which Einstein delivered in German, was followed with a resume in English by Princeton physicist Edwin P Adams, who was, the Daily Princetonian noted, among the leading American expositors of the relativity theory, along with his Princeton colleagues mathematician Luther P Eisenhart and astrophysicist Henry Norris Russell.
- The Meaning of Relativity has been republished in five editions and is still in print.
- Klein Oskar biography
- His first work in this new arena was a philosophical paper that was a refutation of an objection to relativity theory by Swedish philosophers.
- In the 1940s Klein worked on a wide variety of subjects including superconductivity (with Jens Lindhard in 1945), biochemistry, universal p-decay, general relativity, and stellar evolution.
- In the 1950s and 1960s Klein remained active, addressing the 11th Solvay Conference in 1958, developing a new model for cosmology in conjunction with Hannes Alfven in 1963, and tackling Einstein's General Relativity in a paper published in Astrophisica Norvegica in 1964.
- Ehrenfest biography
- Ehrenfest's arguments were based both on Newton's celestial mechanics and also on Einstein's relativity theory.
- Ehrenfest's graduate lectures consisted of a two-year course: Maxwell theory, ending with the theory of electrons and some relativity, one year; and statistical mechanics, ending with atomic structure and quantum theory the other.
- History Topics: General relativity
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- Maxwell biography
- History Topics: General relativity
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- History Topics: Special relativity
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- History Topics: Light through the ages: Relativity and quantum era
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- Darmois biography
- He was promoted to professor at Nancy in 1921, and he became interested in both the theory of relativity and in applications of probability theory.
- He wrote many excellent papers on relativity beginning with Sur l'integration locale des equations d'Einstein (1923).
- Although he continued his interest in relativity, he began to become seriously interested in statistics from around 1923.
- Pars biography
- Part 1 was Geometrical Vector Theory and the Restricted Principle of Relativity and Part 2 was On the General Theory of Relativity.
- Pars's first publications, influenced by Larmor and Eddington, were on relativity and were part of his prize essay.
- Jeffery biography
- Jeffery also worked on general relativity and produced exact solutions to Einstein's field equations in certain special cases.
- He wrote only one book and this was a teaching book on relativity Relativity for physics students (1924).
- Bose biography
- This university was a research institution for postgraduate studies and here Bose was able to study recent European texts on quantum theory and relativity which, before the opening of the new institution, had not been readily available in India.
- He also studied Einstein's papers on relativity and obtained Einstein's permission to translate them for publication in India.
- History Topics: Light through the ages: Relativity and quantum era
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- Schoen biography
- [A] watershed for the mathematical development of relativity is the celebrated work of Rick Schoen and S-T Yau from the late seventies on the 'Positive Mass Theorem'.
- Schoen's ideas have been applied to a wide range of mathematical problems, from general relativity to questions about rigidity for lattice subgroups of algebraic groups.
- His research has fundamentally shaped geometric analysis, and his results form many cornerstones within geometry, partial differential equations and general relativity.
- Planck biography
- History Topics: General relativity
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- History Topics: Special relativity
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- History Topics: Light through the ages: Relativity and quantum era
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- Hilbert biography
- Many have claimed that in 1915 Hilbert discovered the correct field equations for general relativity before Einstein but never claimed priority.
- In the printed version of his paper, Hilbert added a reference to Einstein's conclusive paper and a concession to the latter's priority: "The differential equations of gravitation that result are, as it seems to me, in agreement with the magnificent theory of general relativity established by Einstein in his later papers".
- History Topics: General relativity
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- Veblen biography
- Soon after Einstein's theory of general relativity appeared Veblen turned his attention to differential geometry.
- This work led to important applications in relativity theory, and much of his work also found application in atomic physics.
- In Projective relativity theory (1933) he gave a new treatment of spinors, used to represent electron spin.
- Le Verrier biography
- Now the advance of the perihelion of Mercury by more than Newtonian theory predicted was to become important evidence for Einstein's general theory of relativity, but of course none of this could be known to Le Verrier who, in a paper presented to the Academy of Sciences on 12 September 1859, attributed it to an undiscovered planet, which he called Vulcan, closer to the Sun than Mercury or to a second asteroid belt so close to the Sun as to be invisible.
- It was long after Le Verrier's death, in 1915, that Einstein's general theory of relativity explained the orbit of Mercury without the need for perturbing bodies.
- History Topics: General relativity
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- Newton biography
- History Topics: General relativity
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- History Topics: Special relativity
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- Riemann biography
- The general theory of relativity splendidly justified his work.
- History Topics: General relativity
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- Nash biography
- Soon, however, his growing interest in mathematics had him take courses on tensor calculus and relativity.
- There he came in contact with John Synge who had recently been appointed as Head of the Mathematics Department and taught the relativity course.
- Geiser biography
- His teaching did, however, make an important contribution to general relativity in an indirect fashion.
- In this course Geiser taught the Gaussian theory of surfaces and, in 1912, Einstein had what he described as "the decisive idea" of an analogy between general relativity and Gaussian surfaces.
- Temple biography
- Whitehead had been the main reason for Temple's move to Imperial as he had been interested in papers in relativity which Temple had published.
- Relativity theory, aerodynamics and quantum mechanics have been mentioned above but he also worked on analysis contributing to the study of the Lebesgue integral.
- Whitehead biography
- This interest arose out of the attempt to explain the relation of formal mathematical theories in physics to their basis in experience, and was sparked by the revolution brought on by Einstein's general theory of relativity.
- In The Principle of Relativity (1922), Whitehead presented an alternative to Einstein's views.
- Witten biography
- His mother was Lorraine W Witten while his father, Louis Witten, was a theoretical physicist specializing in gravitation and general relativity.
- It used to be that when one thought of geometry in physics, one thought chiefly of classical physics - and in particular general relativity - rather than quantum physics.
- Feigenbaum biography
- He entered MIT with the intention of researching in electrical engineering for his doctorate but after only one term he changed to physics and began to study general relativity.
- Now again general relativity was a topic which he studied on his own, reading the book Course of Theoretical Physics by Lev Landau and Evgenii Lifshitz.
- Cercignani biography
- Before the age of eighteen I had learned the basics of analysis through consulting encyclopaedias and by constructing missing proofs on my own (some quite correct, others only fanciful) in the Calculus of Variations, in Rational Mechanics, in Tensor Calculus, and I thoroughly read articles on Einstein's special and general theory of relativity.
- After the first year of university I studied (in the summer) Pauli's contributions to the theory of relativity, seen by many as very difficult.
- Cosserat Francois biography
- The bearing of this original and coherent conception was diminished in importance because at the time it was proposed, fundamental ideas were already being called into question by both the theory of relativity and progress in physical theory.
- Relativity Theory and Quantum Physics overtook this period in science and the work of E and F Cosserat was almost rediscovered after 1950 because of the use of liquid crystals.
- Piaggio biography
- Here list a few articles which Piaggio published in The Mathematical Gazette: Relativity rhymes with a mathematical commentary (January 1922); Geometry and relativity (July 1922); Mathematics for evening technical students (July 1924); Mathematical physics in university and school (October 1924); Probability and its applications (July 1931); Three Sadleirian professors: A R Forsyth, E W Hobson and G H Hardy (October 1931); Mathematics and psychology (February 1933); Lagrange's equation (May 1935); Fallacies concerning averages (December 1937); and The incompleteness of "complete" primitives of differential equations (February 1939).
- Whittaker biography
- On the applied side of mathematics he was interested in relativity theory for many years, publishing at least five articles on the topic.
- He also worked on electromagnetic theory giving a general solution of Maxwell's equation, and it was through this topic that his interest in relativity arose.
- Uhlenbeck biography
- Ehrenfest's graduate lectures consisted of a two-year course: Maxwell theory, ending with the theory of electrons and some relativity, one year; and statistical mechanics, ending with atomic structure and quantum theory the other.
- The two quickly became friends and exchanged ideas, particularly on Klein's ideas about five dimensional relativity.
- Yau biography
- Yau was awarded a Fields Medal in 1982 for his contributions to partial differential equations, to the Calabi conjecture in algebraic geometry, to the positive mass conjecture of general relativity theory, and to real and complex Monge-Ampere equations.
- His work has had, and will continue to have, a great impact on areas of mathematics and physics as diverse as topology, algebraic geometry, representation theory, and general relativity as well as differential geometry and partial differential equations.
- Bianchi biography
- His work on non-euclidean geometries was used by Einstein in his general theory of relativity.
- History Topics: General relativity
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- Born biography
- Around this time Born read Einstein's 1905 papers on relativity and was immediately captivated.
- History Topics: Light through the ages: Relativity and quantum era
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- Turing biography
- He read Einstein's papers on relativity and he also read about quantum mechanics in Eddington's The nature of the physical world.
- Not only did he press forward with further study of morphogenesis, but he also worked on new ideas in quantum theory, on the representation of elementary particles by spinors, and on relativity theory.
- Feynman biography
- He read Eddington's Mathematical Theory of Relativity while in his first year of studies and felt that this was what he wanted from mathematics.
- History Topics: Light through the ages: Relativity and quantum era
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- Szekeres biography
- Another prominent topic in George's career is general relativity; George is perhaps best known for his role in developing the mathematical theory underlying the study of black holes.
- He continued to publish on relativity with work such as Kinematic geometry: An axiomatic system for Minkowski space-time (1968).
- Daniell biography
- It is highly likely that Daniell attended these (and other courses) and certainly he undertook research on a problem in the theory of relativity which Hilbert discussed in his course Theory of the Electron.
- His other 1915 paper was The rotation of elastic bodies and the principle of relativity and it followed the theme of research he had conducted while studying at Gottingen.
- Ricci-Curbastro biography
- Ricci-Curbastro's absolute differential calculus became the foundation of tensor analysis and was used by Einstein in his theory of general relativity.
- History Topics: General relativity
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- Ingarden biography
- For example his early work includes Equations of motion and field equations in five-dimensional unified relativity theory (Russian) (1953) in which he:-
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- The gravitational equations of the general relativity theory involving the energy-momentum density tensor of matter are generalized to five dimensions.
- Murnaghan biography
- Perhaps it is easiest to understand how he saw the study of mathematics and its applications by quoting from the Preface to his first book Vector analysis and the theory of relativity (1922).
- Over the period up to 1936, in addition to the major texts we have already mentioned, Murnaghan undertook research and published papers on a wide variety of topics such as electrodynamics, relativity, tensor analysis, elasticity, dynamics, aerodynamics, quantum mechanics, and celestial mechanics.
- Cosserat biography
- The bearing of this original and coherent conception was diminished in importance because at the time it was proposed, fundamental ideas were already being called into question by both the theory of relativity and progress in physical theory.
- Relativity Theory and Quantum Physics overtook this period in science and the work of E and F Cosserat was almost rediscovered after 1950 because of the use of liquid crystals.
- Christoffel biography
- Indeed this influence is clearly seen since this allowed Ricci-Curbastro and Levi-Civita to develop a coordinate free differential calculus which Einstein, with the help of Grossmann, turned into the tensor analysis mathematical foundation of general relativity.
- History Topics: General relativity
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- Schwartz Jacob biography
- To illustrate the different areas he worked in we note that he published Lectures on the mathematical method in analytical economics (1961), and two school level textbooks Matrices and Vectors for High-Schools and Colleges (1961) and Relativity In Illustrations in 1964.
- This clear, non-technical treatment makes relativity more accessible than ever before, requiring only a background in high-school geometry.
- Sommerfeld biography
- [He] was at the forefront of the work in electromagnetic theory, relativity and quantum theory and he was the great systematizer and teacher who inspired many of the most creative physicists in the first thirty years of this century.
- Kasner biography
- A rough subdivision of Kasner's scientific career might be made into four periods according to his dominant interest at the time: Differential-Geometric Aspects of Dynamics (1905-1920), Geometric Aspects of the Einstein Theory of Relativity (1920-1927), Polygenic Functions (1927-1940), Horn Angles (1940-1955).
- Stokes biography
- History Topics: Special relativity
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- Godel biography
- It is unclear how much Einstein influenced Godel to work on relativity, but he did indeed contribute to that subject.
- Faraday biography
- History Topics: Light through the ages: Relativity and quantum era
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- Castelnuovo biography
- Castelnuovo also wrote a book on probability, publishing Calcolo della probabilita in 1919 and a text on the theory of relativity in 1923.
- Broglie biography
- History Topics: Light through the ages: Relativity and quantum era
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- Mellin biography
- During the last decade of his life Mellin was, rather curiously for an analyst, preoccupied by Einstein's theory of relativity and he wrote no less than ten papers on this topic.
- Wilson Edwin biography
- Wilson had been inspired by Gibbs to work on mathematical physics and he began to write papers on mechanics and the theory of relativity.
- Lipschitz biography
- In the paper [The history of modern mathematics III (Boston, MA, 1994), 113-138.',4)">4] the author shows convincingly how Lipschitz mechanical interpretation of Riemann's differential geometry would prove to be a vital step in the road towards Einstein's special theory of relativity.
- Schmidt Harry biography
- Physikalische Fragen der Gegenwart was published as was the English text Relativity and the universe.
- Bohr Niels biography
- History Topics: Light through the ages: Relativity and quantum era
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- Peierls biography
- The topics covered are mostly from quantum theory and its applications; statistical physics and even relativity are touched upon.
- Aleksandrov Aleksandr biography
- He published on optics, quantum mechanics, and relativity.
- Roy biography
- in 1931 having submitted a dissertation on the Theory of Relativity.
- Gauss biography
- History Topics: General relativity
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- Kepler biography
- History Topics: General relativity
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- Kaluza biography
- He continued to produce ideas relating to models of the atomic nucleus, and he wrote on relativity.
- Boltzmann biography
- History Topics: Light through the ages: Relativity and quantum era
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- Delsarte biography
- At Nancy he developed a new course on differential equations in the academic year 1933-34 and in the following year, also at Nancy, he gave a course on Riemann spaces and relativity.
- Kahler biography
- In Raum-Zeit-Individuum (1992) Kahler attempts to reformulate the Lorentz metric of space-time relativity physics in order to rid it of the purely imaginary time variable.
- Boscovich biography
- In statements pertaining to methodology he insists on the limits and the relativity of all human knowledge; he describes three sources of knowledge; he defines criteria of the scientific soundness of statements; finally, he deals with the problem of induction in a critical manner and sets out a particular heuristic procedure (the 'method of decipherment').
- Du Val biography
- As we noted above, Du Val's early work before he became a research student at Cambridge was on relativity.
- Clifford biography
- In this work he presents ideas which were to form a fundamental role in Einstein's general theory of relativity.
- Caratheodory biography
- He also made contributions in thermodynamics, the special theory of relativity, mechanics, and geometrical optics.
- Gelbart biography
- Gelbart showed an interest in mathematics and science from an early age, when his father read him newspaper accounts about Einstein and the theory of relativity.
- Fantappie biography
- For example in Deduzione autonoma dell'equazione generalizzata di Schrodinger, nella teoria di relativita finale (1955) Fantappie deduces the Klein-Gordon equation in quantum mechanics as a limit, as the radius of the universe tends to infinity, of a classical (non-quantized) equation in his extension of relativity based on a simple (pseudo-orthogonal) group having the Lorentz group as a type of limit.
- Menger biography
- At the University of Vienna, Menger attended physics lectures by the theoretical physicist Hans Thirring (1888-1976) who had made significant contributions to the theory of general relativity.
- Friedrichs biography
- He attended the Realgymnasium in Dusseldorf, solving while there a problem in relativity, then entered the University of Dusseldorf.
- Fox biography
- This book, designed as a text for undergraduate students, includes a large number of examples, and devotes chapters 5, 6, and 7 to applications to mechanics, relativity, and elasticity.
- Aristotle biography
- History Topics: General relativity
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- Clairaut biography
- History Topics: General relativity
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- Uhlenbeck Karen biography
- I decided Einstein's general relativity was too hard, but managed to learn a lot about geometry of space time.
- Connes biography
- In naming Connes the 2004 Gold Medallist, the CNRS called him "one of the greatest mathematicians of our time." Throughout his career, Connes has applied himself to solving mathematical problems arising from quantum physics and the theory of relativity.
- Davies biography
- Dienes had become interested in this topic after leaving Paris because of its applications to relativity theory.
- Hamilton biography
- History Topics: General relativity
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- Lagrange biography
- History Topics: General relativity
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- Nevanlinna biography
- One such example is his book Raum, Zeit und Relativitat (Space, time and relativity) (1964).
- Galileo biography
- History Topics: General relativity
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- Frank biography
- In mathematics he worked on the calculus of variations, Fourier series, function spaces, Hamiltonian geometrical optics, Schrodinger wave mechanics, and relativity.
- Laplace biography
- History Topics: General relativity
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- Straus biography
- He could solve crossword puzzles in ink in English (his third language) using only the horizontal clues, and in the next minute discourse profoundly on relativity theory, European history, or theology.
- Lobachevsky biography
- Perhaps these finally mark the acceptance of Lobachevsky's ideas which would eventually be seen as vital steps in freeing the thinking of mathematicians so that relativity theory had a natural mathematical foundation.
- Euler biography
- History Topics: General relativity
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- Wigner biography
- discrete symmetries and superselection rules in quantum mechanics, symmetry implications for atomic and molecular spectra, natural line-width theory, contrast of microscopic and macroscopic physics and of general relativity and quantum mechanics, explanation of why symmetry yields more information for quantum than for classical mechanics, philosophical questions such as what nature laws should be, limits on causality, and whether quantum mechanics could in principle explain life.
- Landau Lev biography
- Later he used to describe how at that time he was entranced by the incredible beauty of the general theory of relativity (sometimes he even would declare that such a rapture on first making one's acquaintance with this theory should in general be a characteristic of any born theoretical physicist).
- Jacobi biography
- History Topics: General relativity
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- Eotvos biography
- This was one of the first steps towards relativity theory.
- Plucker biography
- Strangely enough, in the period when four-dimensional manifolds appeared in relativity theory and became fashionable, nobody compared the Minkowski fourfold and the Plucker fourfold which appeared 50 years earlier.
- Faber biography
- In addition to his research areas, Faber lectured on complex analysis, probability theory, the theory of relativity and analytical mechanics.
- Doppler biography
- History Topics: Special relativity
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- Polya biography
- In Vienna he attended mathematics lectures by Wirtinger and Mertens but continued to have a strong interest in physics attending lectures in relativity, optics and other topics.
- Thomson biography
- History Topics: Special relativity
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- Kagan biography
- Kagan studied tensor differential geometry after going to Moscow because of an interest in relativity.
- Schwinger biography
- Schwinger was joint winner of the Nobel Prize for Physics (1965) for his work in formulating quantum electrodynamics and thus reconciling quantum mechanics with Einstein's special theory of relativity.
- Artin biography
- At Hamburg Artin lectured on a wide variety of topics including mathematics, mechanics and relativity.
- Franklin biography
- He published: Generalized Conjugate Matrices (1921) and (with Oswald Veblen) On Matrices Whose Elements Are Integers (1921) both in the Annals of Mathematics; An Arithmetical Perpetual Calendar (1921) and On Curves Whose Evolutes are Similar Curves (1921) in the American Mathematical Monthly; The Meaning of Rotation in the Special Theory of Relativity (1922) in the Proceedings of the National Academy of Sciences of the United States of America; and The Four Color Problem (1922) in the American Journal of Mathematics.
- Abbott biography
- It is worth noting that this remarkable piece of writing by Abbott predated by many years Einstein's four dimensional world of relativity.
- Hoyle biography
- For example Born taught him quantum mechanics, Eddington taught him general relativity, and he was also taught by Dirac.
- Tao biography
- Another area in which Tao has worked is solving special cases of the equations of general relativity describing gravity.
- Dyson biography
- In the following year he read Eddington's The mathematical theory of relativity.
- Weil biography
- At this time relativity was an exciting new topic and he read Arthur Eddington's description of "Einstein's theory".
- See biography
- He spent much effort in his later years arguing against Einstein's theory of relativity.
- Klein biography
- History Topics: General relativity
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- Brill biography
- The treatment is mathematical and didactic, without pretense of originality, and directed toward giving a brief account of the kinematics and dynamics of a particle from the point of view of relativity; electromagnetic phenomena and the theory of radiant energy are omitted.
- Pierpont biography
- In addition to the American Mathematical Society Colloquium Lectures that he gave in Buffalo in 1896, Pierpont address the International Congress of Arts and Science in St Louis in September 1904 on the History of Mathematics in the Nineteenth Century, he addressed the American Mathematical Society summer meeting at Wellesley in 1921 on Some mathematical aspects of the theory of relativity, he gave the Gibbs Lecture in Kansas City in 1925 on Some modern views of space, he addressed the annual meeting at Nashville in 1927 on Mathematical rigor, past and present, he addressed the annual meeting at New York in 1928 On the motion of a rigid body in a space of constant curvature, and the annual meeting at Berkeley in 1929 on Non-Euclidean geometry, a retrospect.
- Helmholtz biography
- History Topics: Light through the ages: Relativity and quantum era
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- Novikov Sergi biography
- In the early 1970s Novikov turned his attention to mathematical physics, initially contributing to general relativity and conductivity of metals.
- Forder biography
- Forder is extremely widely read in mathematical logic and philosophy, pure mathematics, relativity, quantum mechanics and astrophysics, and on these subjects I have heard him speak with knowledge, and authority, and with marked originality.
- Wilson Alexander biography
- Einstein attempted to answer the same question by introducing the 'cosmological constant' into the theory of general relativity.
- Rayleigh biography
- History Topics: Light through the ages: Relativity and quantum era
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- Copernicus biography
- History Topics: General relativity
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- Boggio biography
- Outside of this main line of attack on the relativity theory the authors bring forth against this theory all possible arguments without finding anything to say in its favour.
- Kotelnikov biography
- In 1927 he published one of his most important works, The Principle of Relativity and Lobachevsky's Geometry.
- McLeod biography
- He solved problems with consummate skill across an extraordinary range of areas as diverse as fluid mechanics, general relativity, plasma physics, mathematical biology, superconductivity, Painleve equations, coagulation processes, nonlinear diffusion and pantograph equations, among many others.
- Jeans biography
- We should also note that Jeans' paper was written after the Michelson-Morley experiment disproved the existence of the ether, and in the same year that Einstein published the special theory of relativity.
- Pearson biography
- His book The Grammar of Science (1892) was remarkable in that it anticipated some of the ideas of relativity theory.
- Poisson biography
- History Topics: General relativity
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- Cauchy biography
- History Topics: Special relativity
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- Gardner biography
- We certainly do not want to even list the titles of over sixty works so we will give a selection: Logic Machines and Diagrams (1958); The Annotated Alice (1960); Relativity for the Million (1962); The Ambidextrous Universe: Mirror Asymmetry and Time-Reversed Worlds (1964); Mathematical Carnival: A New Round-up of Tantalizers and Puzzles from "Scientific American" (1975); The Incredible Dr Matrix (1976); Aha! Insight (1978); Science: Good, Bad, and Bogus (1981); Aha! Gotcha: Paradoxes to Puzzle and Delight (1982); The Whys of a Philosophical Scrivener (1983); Codes, Ciphers and Secret Writing (1984); Entertaining Mathematical Puzzles (1986); Time Travel and Other Mathematical Bewilderments (1987); Perplexing Puzzles and Tantalizing Teasers (1988); Fractal Music, Hypercards and More (1991); My Best Mathematical and Logic Puzzles (1994); Classic Brainteasers (1995); Calculus Made Easy (1998); A Gardner's Workout: Training the Mind and Entertaining the Spirit (2001); Mathematical Puzzle Tales (2001); and Bamboozlers (2008).
- Wirtinger biography
- He published results on Einstein's theory of relativity and other areas of mathematical physics.
- Ulam biography
- An uncle gave Ulam a telescope when he was about 12 years old and later Ulam tried to understand Einstein's special theory of relativity.
- Esclangon biography
- pure mathematics, applied celestial mechanics, relativity, observational astronomy, instrumental astronomy, astronomical chronometry, aerodynamics, interior and exterior ballistics, and aerial and underwater acoustic detection.
- Blanch biography
- Since I didn't want to lose my knowledge of mathematics I decided to take [Arnold N] Lowan's course in relativity [at Brooklyn College].
- Borel biography
- a number of valuable contributions to the knowledge of Einstein's theory of relativity.
- Bartlett biography
- I attended further lecture courses for "fun," including Eddington's "Relativity" and Dirac's "Quantum Mechanics," as well as Colin Clark's "Statistical Sources" (which I found rather dull) and Udny Yule's "Vital Statistics" (still given in spite of his retirement).
- Kramer biography
- Her examination of Omar Khayyam and algebra, Newton and calculus, Fermat and probability, Lewis Carroll and logic and Einstein and relativity provides an intriguing book for non-mathematicians and a valuable reference source for teachers and students.
- Walker Arthur biography
- Walker worked on geometry, in particular differential geometry, relativity, and cosmology.
- Frenkel biography
- He had already published a number of major books: The structure of matter I (1922), The theory of relativity (1923), The structure of matter II (1924), Vector and tensor analysis (1925), Electricity and matter (1925), and Electrodynamics (1926).
- Radon biography
- His wide interests led him to study Riemannian geometry and geometrical problems which arose in the study of relativity.
- Cauer biography
- He worked on general relativity and published his first paper on that topic in 1923.
- Adleman biography
- This is so neat.' There were several things I found neat - black holes, general relativity.
- Cartan biography
- He developed this theory between 1894 and 1904 and applied his theory of exterior differential forms to a wide variety of problems in differential geometry, dynamics and relativity.
- Fermi biography
- This paper gave an important result about the Euclidean nature of space near a world line in the geometry of general relativity.
- Zeeman biography
- I suppose I am particularly fond of having unknotted spheres in 5-dimensions, of spinning lovely examples of knots in 4-dimensions, of proving Poincare's Conjecture in 5-dimensions, of showing that special relativity can be based solely on the notion of causality, and of classifying dynamical systems by using the Focke-Plank equation.
- Hubble biography
- Within General Relativity, the theory of gravity proposed by Albert Einstein in 1915, the inescapable conclusion was that all the galaxies, and the whole Universe, had originated in a Big Bang, thousands of millions of years in the past.
- Kruskal Martin biography
- An important paper on astronomy was Maximal extension of Schwarzschild's metric (1960) which showed that, using what are now called Kruskal coordinates, certain solutions of the equations of general relativity which are singular at the origin are not singular away from the origin, so allowing the study of black holes.
History Topics
- General relativity references
- References for: General relativity
.
- A Ashtekar, Chandrasekhar's contributions to general relativity, Current Sci.
- C Cattani, Early debates on general relativity in Italy, in General relativity and gravitational physics (River Edge, NJ, 1994), 93-110.
- S Chandrasekhar, Einstein and general relativity : historical perspectives, Amer.
- J Earman, M Janssen and J D Norton (eds.), The Attraction of gravitation : new studies in the history of general relativity (Boston, 1993).
- J Eisenstaedt, The low water mark of general relativity, 1925-1955, in Einstein and the history of general relativity (Boston, MA, 1989), 277-292.
- J Eisenstaedt and A J Kox (eds.), Studies in the history of general relativity (Boston, 1992).
- J Earman and C Glymour, The gravitational red shift as a test of general relativity : history and analysis, Stud.
- J Earman and C Glymour, Einstein and Hilbert : two months in the history of general relativity, Archive for History of Exact Sciences 19 (3) (1978/79), 291-308.
- R Farwell and C Knee, The end of the absolute : a nineteenth-century contribution to general relativity, Stud.
- F R Hickman, Electrodynamical origins of Einstein's theory of general relativity, Internat.
- D Howard, Einstein and Eindeutigkeit : a neglected theme in the philosophical background to general relativity, in Studies in the history of general relativity (Boston, MA, 1992), 154-243.
- D Howard and J Stachel (eds.), Einstein and the history of general relativity (Boston, 1989).
- J Illy, Einstein teaches Lorentz, Lorentz teaches Einstein : Their collaboration in general relativity, 1913-1920, Archive for History of Exact Sciences 39 (3) (1989), 247-289.
- P Kerszberg, The relativity of rotation in the early foundations of general relativity, Stud.
- C W Kilmister, Relativity, in I Grattan-Guinness (ed.), Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences (London, 1994), 1235-1241.
- A J Kox, Einstein, Lorentz, Leiden and general relativity, Les Journees Relativistes, Classical Quantum Gravity 10 (1993), S187-S191.
- A J Kox, General relativity in the Netherlands, 1915-1920 in Studies in the history of general relativity (Boston, MA, 1992), 39-56.
- A Lichnerowicz, Mathematics and general relativity : a recollection, in Studies in the history of general relativity (Boston, MA, 1992), 103-108.
- M De Maria, The first reactions to general relativity in Italy : the polemics between Max Abraham and Albert Einstein (Italian), Italian mathematics between the two world wars (Bologna, 1987), 143-159.
- J Mehra, Origins of the modern theory of gravitation : the historical origins of the theory of general relativity from 1907 to 1919, Bull.
- A Mercier, General relativity at the turning point of its renewal, in Studies in the history of general relativity (Boston, MA, 1992), 109-121.
- F Morgan, Calculus, planets, and general relativity, SIAM Rev.
- J Norton, Einstein's discovery of the field equations of general relativity : some milestones, Proceedings of the fourth Marcel Grossmann meeting on general relativity (Amsterdam-New York, 1986), 1837-1848.
- J M Sanchez-Ron, The reception of general relativity among British physicists and mathematicians (1915-1930), in Studies in the history of general relativity (Boston, MA, 1992), 57-88.
- J J Stachel, How Einstein discovered general relativity : a historical tale with some contemporary morals, General relativity and gravitation (Cambridge-New York, 1987), 200-208.
- C Vilain, Spherical coordinates in general relativity from 1915 to 1960 : a physical interpretation, in Studies in the history of general relativity (Boston, MA, 1992), 419-434.
- C M Will, General relativity at 75 : how right was Einstein?, in The Sixth Marcel Grossmann Meeting (River Edge, NJ, 1992), 769-786.
- http://www-history.mcs.st-andrews.ac.uk/HistTopics/References/General_relativity.html
.
- General relativity references
- References for: General relativity
.
- A Ashtekar, Chandrasekhar's contributions to general relativity, Current Sci.
- C Cattani, Early debates on general relativity in Italy, in General relativity and gravitational physics (River Edge, NJ, 1994), 93-110.
- S Chandrasekhar, Einstein and general relativity : historical perspectives, Amer.
- J Earman, M Janssen and J D Norton (eds.), The Attraction of gravitation : new studies in the history of general relativity (Boston, 1993).
- J Eisenstaedt, The low water mark of general relativity, 1925-1955, in Einstein and the history of general relativity (Boston, MA, 1989), 277-292.
- J Eisenstaedt and A J Kox (eds.), Studies in the history of general relativity (Boston, 1992).
- J Earman and C Glymour, The gravitational red shift as a test of general relativity : history and analysis, Stud.
- J Earman and C Glymour, Einstein and Hilbert : two months in the history of general relativity, Archive for History of Exact Sciences 19 (3) (1978/79), 291-308.
- R Farwell and C Knee, The end of the absolute : a nineteenth-century contribution to general relativity, Stud.
- F R Hickman, Electrodynamical origins of Einstein's theory of general relativity, Internat.
- D Howard, Einstein and Eindeutigkeit : a neglected theme in the philosophical background to general relativity, in Studies in the history of general relativity (Boston, MA, 1992), 154-243.
- D Howard and J Stachel (eds.), Einstein and the history of general relativity (Boston, 1989).
- J Illy, Einstein teaches Lorentz, Lorentz teaches Einstein : Their collaboration in general relativity, 1913-1920, Archive for History of Exact Sciences 39 (3) (1989), 247-289.
- P Kerszberg, The relativity of rotation in the early foundations of general relativity, Stud.
- C W Kilmister, Relativity, in I Grattan-Guinness (ed.), Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences (London, 1994), 1235-1241.
- A J Kox, Einstein, Lorentz, Leiden and general relativity, Les Journees Relativistes, Classical Quantum Gravity 10 (1993), S187-S191.
- A J Kox, General relativity in the Netherlands, 1915-1920 in Studies in the history of general relativity (Boston, MA, 1992), 39-56.
- A Lichnerowicz, Mathematics and general relativity : a recollection, in Studies in the history of general relativity (Boston, MA, 1992), 103-108.
- M De Maria, The first reactions to general relativity in Italy : the polemics between Max Abraham and Albert Einstein (Italian), Italian mathematics between the two world wars (Bologna, 1987), 143-159.
- J Mehra, Origins of the modern theory of gravitation : the historical origins of the theory of general relativity from 1907 to 1919, Bull.
- A Mercier, General relativity at the turning point of its renewal, in Studies in the history of general relativity (Boston, MA, 1992), 109-121.
- F Morgan, Calculus, planets, and general relativity, SIAM Rev.
- J Norton, Einstein's discovery of the field equations of general relativity : some milestones, Proceedings of the fourth Marcel Grossmann meeting on general relativity (Amsterdam-New York, 1986), 1837-1848.
- J M Sanchez-Ron, The reception of general relativity among British physicists and mathematicians (1915-1930), in Studies in the history of general relativity (Boston, MA, 1992), 57-88.
- J J Stachel, How Einstein discovered general relativity : a historical tale with some contemporary morals, General relativity and gravitation (Cambridge-New York, 1987), 200-208.
- C Vilain, Spherical coordinates in general relativity from 1915 to 1960 : a physical interpretation, in Studies in the history of general relativity (Boston, MA, 1992), 419-434.
- C M Will, General relativity at 75 : how right was Einstein?, in The Sixth Marcel Grossmann Meeting (River Edge, NJ, 1992), 769-786.
- [http://www-history.mcs.st-andrews.ac.uk/HistTopics/References/General_relativity.html]
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- Special relativity
- Special relativity
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- These transformations, with a different scale factor, are now known as the Lorentz equations and the group of Lorentz transformations gives the geometry of special relativity.
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- The most amazing article relating to special relativity to be published before 1900 was a paper of Poincare La mesure du temps which appeared in 1898.
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- Poincare, in his opening address to the Paris Congress in 1900, asked Does the ether really exist? In 1904 Poincare came very close to the theory of special relativity in an address to the International Congress of Arts and Science in St Louis.
- as demanded by the relativity principle the observer cannot know whether he is at rest or in absolute motion.
- The year that special relativity finally came into existence was 1905.
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- June of 1905 was a good month for papers on relativity, on the 5th June Poincare communicated an important work Sur la dynamique de l'electron while Einstein's first paper on relativity was received on 30th June.
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- The first paper on special relativity, other than by Einstein, was written in 1908 by Planck.
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- It was largely due to the fact that relativity was taken up by someone as important as Planck that it became so rapidly accepted.
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- Also in 1908 Minkowski published an important paper on relativity, presenting the Maxwell-Lorentz equations in tensor form.
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- He also showed that the Newtonian theory of gravitation was not consistent with relativity.
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- The main contributors to special relativity were undoubtedly Lorentz, Poincare and, of course, the founder of the theory Einstein.
- When Poincare lectured in Gottingen in 1909 on relativity he did not mention Einstein at all.
- He presented relativity with three postulates, the third being the FitzGerald-Lorentz contraction.
- In fact Poincare never wrote a paper on relativity in which he mentioned Einstein.
- He gave a lecture in 1913 when he remarked how rapidly relativity had been accepted.
- Despite Lorentz's caution the special theory of relativity was quickly accepted.
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- In 1912 Lorentz and Einstein were jointly proposed for a Nobel prize for their work on special relativity.
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- While Lorentz must be considered as the first to have found the mathematical content of the relativity principle, Einstein succeeded in reducing it to a simple principle.
- Einstein never received a Nobel prize for relativity.
- http://www-history.mcs.st-andrews.ac.uk/HistTopics/Special_relativity.html
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- General relativity
- General relativity
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- General relativity is a theory of gravitation and to understand the background to the theory we have to look at how theories of gravitation developed.
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- Poincare, in a paper in July 1905 (submitted days before Einstein's special relativity paper), suggested that all forces should transform according the Lorentz transformations.
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- In 1907, two years after proposing the special theory of relativity, Einstein was preparing a review of special relativity when he suddenly wondered how Newtonian gravitation would have to be modified to fit in with special relativity.
- This assumption extends the principle of relativity to the case of uniformly accelerated motion of the reference frame.
- Einstein was delighted to be able to exchange ideas with Levi-Civita whom he found much more sympathetic to his ideas on relativity than his other colleagues.
- At the end of June 1915 Einstein spent a week at Gottingen where he lectured for six 2 hour sessions on his (incorrect) October 1914 version of general relativity.
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- The final steps to the theory of general relativity were taken by Einstein and Hilbert at almost the same time.
- From 1911 Einstein had realised the importance of astronomical observations to his theories and he had worked with Freundlich to make measurements of Mercury's orbit required to confirm the general theory of relativity.
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- Freundlich attempted other tests of general relativity based on gravitational redshift, but they were inconclusive.
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- On 25 November Einstein submitted his paper The field equations of gravitation which give the correct field equations for general relativity.
- Hilbert's paper contains some important contributions to relativity not found in Einstein's work.
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- Einstein had reached the final version of general relativity after a slow road with progress but many errors along the way.
- Ehrenfest and Lorentz corresponded about the general theory of relativity for two months as they tried to understand it.
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- In March 1916 Einstein completed an article explaining general relativity in terms more easily understood.
- The article was well received and he then wrote another article on relativity which was widely read and went through over 20 printings.
- Today relativity plays a role in many areas, cosmology, the big bang theory etc.
- http://www-history.mcs.st-andrews.ac.uk/HistTopics/General_relativity.html
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- Special relativity references
- References for: Special relativity
.
- M Garca Doncel, The genesis of special relativity and Einstein's epistemology (Spanish), Three lectures about Albert Einstein, Mem.
- E Giannetto, Henri Poincare and the rise of special relativity, Hadronic J.
- J J Gray, Poincare, Einstein, and the theory of special relativity, Math.
- C W Kilmister, Relativity, in I Grattan-Guinness (ed.), Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences (London, 1994), 1235-1241.
- A I Miller, Why did Poincare not formulate special relativity in 1905?, in Henri Poincare : science et philosophie (Berlin, 1996), 69-100.
- A I Miller, The special relativity theory : Einstein's response to the physics of 1905, in Albert Einstein (Princeton, NJ, 1982), 3-26.
- R M Nugayev, Special relativity as a step in the development of the quantum programme : revolution in a revolution, Centaurus 29 (2) (1986), 100-109.
- M Paty, Physical geometry and special relativity, in Einstein et Poincare, 1830-1930 : a century of geometry (Berlin, 1992), 127-149.
- A A Tyapkin, On the history of the special relativity concept, Hadronic J.
- http://www-history.mcs.st-andrews.ac.uk/HistTopics/References/Special_relativity.html
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- Special relativity references
- References for: Special relativity
.
- M Garca Doncel, The genesis of special relativity and Einstein's epistemology (Spanish), Three lectures about Albert Einstein, Mem.
- E Giannetto, Henri Poincare and the rise of special relativity, Hadronic J.
- J J Gray, Poincare, Einstein, and the theory of special relativity, Math.
- C W Kilmister, Relativity, in I Grattan-Guinness (ed.), Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences (London, 1994), 1235-1241.
- A I Miller, Why did Poincare not formulate special relativity in 1905?, in Henri Poincare : science et philosophie (Berlin, 1996), 69-100.
- A I Miller, The special relativity theory : Einstein's response to the physics of 1905, in Albert Einstein (Princeton, NJ, 1982), 3-26.
- R M Nugayev, Special relativity as a step in the development of the quantum programme : revolution in a revolution, Centaurus 29 (2) (1986), 100-109.
- M Paty, Physical geometry and special relativity, in Einstein et Poincare, 1830-1930 : a century of geometry (Berlin, 1992), 127-149.
- A A Tyapkin, On the history of the special relativity concept, Hadronic J.
- [http://www-history.mcs.st-andrews.ac.uk/HistTopics/References/Special_relativity.html]
.
- 20th century time
- Although Poincare was thinking deeply about relativity before Einstein, it was the latter who made the final breakthrough.
- The impact of the special theory of relativity on the understanding of time was enormous.
- There were other remarkable effects on time with special relativity.
- Before we move on from special relativity, we must consider one aspect which seems particularly difficult in Minkowski's 4-dimensional space-time, and indeed in any version of relativity.
- In fact all relativity seems to have done is to make us realise that time is a much more difficult concept than Newton's absolute time.
- General relativity incorporated gravitation into the space-time theory.
- Not only was time affected by velocity, as special relativity showed, but time was also affected by a massive body.
- If we cannot measure the height of the box to arbitrary precision, we cannot measure the height of the clock inside the box with arbitrary precision, so we do not know the rate of the clock with arbitrary precision (by Einstein's own general relativity results).
- In the "clock in the box" thought experiment we have seen how relativity and quantum theory begin to interact.
- Milne developed a complex theory of cosmology, attempting to unify relativity and quantum theory, that included a non-constant value for G, which we know as the gravitational constant.
- There are ways that quantum theory time appears to contradict relativity time, and this is worrying.
- This violates the basic principle of relativity that no information can be transmitted faster than the speed of light.
- Newton's bucket
- After Einstein introduced the special theory of relativity in June 1905 the concept of absolute space was no longer tenable.
- But how can rotation mean anything once the notion of absolute space has been cast aside? Well the special theory of relativity still has absolutes.
- Absolute space-time is a feature of special relativity which, contrary to popular belief, does not claim that everything is relative.
- In special relativity observers moving at constant velocities relative to each other would not agree on the velocity of a bucket moving through space, nor would they agree about the time that has elapsed in the bucket experiment, but they would all agree on whether the bucket was accelerating or not.
- After this Einstein began working on the theory of general relativity which incorporated acceleration and gravity.
- He did so in a letter which he wrote to Mach in 1913 in which he told Mach that his view of Newton's bucket was correct and agreed with general relativity.
- Einstein even included "Mach's principle" into general relativity.
- General relativity does not say that Newton's two rock thought experiment in an empty universe agrees with Mach.
- Hence general relativity reduces to special relativity and now all observers agree when the rock system is spinning (i.e.
- In 1918 Joseph Lense and Hans Thirring obtained approximate solutions of the equations of general relativity for rotating bodies.
- Modern light
- Light through the ages: Relativity and quantum era
.
- Einstein published the special theory of relativity in the following year which is based on the remarkable suggestion that the speed of light remains constant for all observers independent of their relative velocities.
- In 1915 Einstein published the general theory of relativity which predicted the bending of rays of light passing through a gravitational field.
- Although his observations were hampered by the weather he was able to get one good value which confirmed the bending predicted by general relativity.
- There was a time when the newspapers said that only twelve people understood the theory of relativity.
- But after people read the paper a lot of people understand the theory of relativity in some way or other, certainly more than twelve.
- Modern light references
- References for: Light through the ages: Relativity and quantum era
.
- J Illy, Lenin, the electromagnetic form of light and the theory of relativity (Czech), in Revolutionary developments in the field of science and engineering, Conf., Liblice, 1979 (Prague, 1980), 35-38.
- Modern light references
- References for: Light through the ages: Relativity and quantum era
.
- J Illy, Lenin, the electromagnetic form of light and the theory of relativity (Czech), in Revolutionary developments in the field of science and engineering, Conf., Liblice, 1979 (Prague, 1980), 35-38.
- Classical light
- By 'classical' here we meant pre-relativity and pre-quantum theory.
- We will study the developments in relativity-quantum theory era in a separate article; see Light through the ages: Relativity and quantum era.
- Planck, who made one of the next major breakthoughts described in Light through the ages: Relativity and quantum era, said on the occasion of the centenary of Maxwell's birth in 1931, that this theory:-
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- Gravitation
- General relativity
.
- For later developments in the theory of gravitation, the reader should now go to our article General relativity.
- General relativity
.
- Cosmology
- It was soon realised that this had a very natural explanation in terms of Einstein's recently discovered General Theory of Relativity: our Universe is expanding!
.
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- What is most of the matter in the Universe made of? How do we know that there are not black holes or some kind of dark matter out there which does not shine like stars? General relativity tells us that matter curves space-time, so what shape is the Universe? Is there a cosmological constant after all?
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- New technology and satellite experiments, such as the Hubble Space Telescope, have brought us an ever improving picture of our Universe, inspiring theorists to produce ever more daring models, drawing upon the latest ideas in relativity and particle physics.
- Orbits
- In fact this discrepancy in the motion of the perihelion of Mercury was to provide the proof that Newtonian theory had to give way to Einstein's theory of relativity.
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- More details relating to the advance of Mercury's perihelion are contained in the article on general relativity.
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- Cosmology references
- G F R Ellis, The expanding universe : a history of cosmology from 1917 to 1960, in Einstein and the history of general relativity (Boston, MA, 1989), 367-431.
- H Urbantke, Schrodinger and cosmology, in Studies in the history of general relativity (Boston, MA, 1992) 453-459.
- Cosmology references
- G F R Ellis, The expanding universe : a history of cosmology from 1917 to 1960, in Einstein and the history of general relativity (Boston, MA, 1989), 367-431.
- H Urbantke, Schrodinger and cosmology, in Studies in the history of general relativity (Boston, MA, 1992) 453-459.
- Quantum mechanics history
- Dirac, in 1928, gave the first solution of the problem of expressing quantum theory in a form which was invariant under the Lorentz group of transformations of special relativity.
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- Time, according to relativity, is not absolute and the error in the position of the box translates into an error in measuring the time.
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- Greek astronomy
- Perhaps the most telling argument against the above claim by Neugebauer is that our present idea of space-time, as developed from Einstein's theory of relativity, was suggested more by the basic philosophy of simplicity than by experimental evidence.
- History overview
- Think about it and realise how difficult it was to invent non-euclidean geometries, groups, general relativity, set theory, ..
- Neptune and Pluto references
- F Morgan, Calculus, planets, and general relativity, SIAM Rev.
- Classical time
- Quantum mechanics and relativity theory in the 20th century have shown the complexities, and sometime apparent paradoxes, in the notion of time.
- EMS History
- A Course of Five Lectures by A W Conway, Esq., M.A., D.Sc., Professor of Mathematical Physics, University College, Dublin, on The Theory of Relativity and the New Physical Ideas of Space and Time.
- Neptune and Pluto references
- F Morgan, Calculus, planets, and general relativity, SIAM Rev.
Famous Curves
No matches from this section
Societies etc
- AMS/SIAM Birkhoff Prize
- for his leadership, originality, depth, and breadth of work in dynamical systems, differential equations, mathematical biology, shock wave theory, and general relativity.
- LMS Presidential Addresses
- Gibbs Lectures.html
- December 1932; Atlantic City, New Jersey; Richard C Tolman; Thermodynamics and relativity.
- AMS Bôcher Prize
- for his contributions to the mathematical theory of general relativity.
- International Congress Speaker
- Kurt Godel, Rotating Universes in General Relativity Theory.
References
- References for Einstein
- J Earman, M Janssen and J D Norton (eds.), The attraction of gravitation : new studies in the history of general relativity (Boston, 1993).
- D P Gribanov, Albert Einstein's philosophical views and the theory of relativity 'Progress' (Moscow, 1987).
- D P Gribanov, The philosophical views of A Einstein and the development of the theory of relativity (Russian) 'Nauka' (Moscow, 1987).
- D Howard and J Stachel (eds.), Einstein and the history of general relativity (Boston, MA, 1989).
- A I Miller, Albert Einstein's special theory of relativity : Emergence (1905) and early interpretation (1905-1911) (Reading, Mass., 1981).
- M Pantaleo and F de Finis (ed.), Relativity, quanta, and cosmology in the development of the scientific thought of Albert Einstein.
- N L Balazs, The acceptability of physical theories : Poincare versus Einstein, in General relativity : papers in honour of J.
- J B Barbour, Einstein and Mach's principle, in Studies in the history of general relativity (Boston, MA, 1992), 125-153, 460.
- G Berg, On the origin of the concept of an Einstein space, in Studies in the history of general relativity (Boston, MA, 1992), 336-343; 460.
- J Bicak, Einstein's Prague articles on gravitation, in Proceedings of the Fifth Marcel Grossmann Meeting on General Relativity (Teaneck, NJ, 1989), 1325-1333.
- M Biezunski, Inside the coconut : the Einstein-Cartan discussion on distant parallelism, in Einstein and the history of general relativity (Boston, MA, 1989), 315-324.
- C Cattani and M De Maria, Einstein's path toward the generally covariant formulation of gravitational field equations : the contribution of Tullio Levi-Civita, in Proceedings of the fourth Marcel Grossmann meeting on general relativity (Amsterdam-New York, 1986), 1805-1826.
- C Cattani and M De Maria, Gravitational waves and conservation laws in general relativity : A Einstein and T Levi-Civita, 1917 correspondence, in Proceedings of the Fifth Marcel Grossmann Meeting on General Relativity (Teaneck, NJ, 1989), 1335-1342.
- C Cattani and M De Maria, Max Abraham and the reception of relativity in Italy : his 1912 and 1914 controversies with Einstein, in Einstein and the history of general relativity (Boston, MA, 1989), 160-174.
- C Cattani and M De Maria, The 1915 epistolary controversy between Einstein and Tullio Levi-Civita, in Einstein and the history of general relativity (Boston, MA, 1989), 175-200.
- S Chandrasekhar, Einstein and general relativity : historical perspectives, Amer.
- C Curry, The naturalness of the cosmological constant in the general theory of relativity, Stud.
- S D'Agostino, The problem of the empirical bases of Einstein's general theory of relativity : some recent historico-critical research (Italian), Riv.
- B K Datta, Development of Einstein's general theory of relativity (1907-1916), Bull.
- M De Maria, The first reactions to general relativity in Italy : the polemics between Max Abraham and Albert Einstein (Italian), in Italian mathematics between the two world wars (Bologna, 1987), 143-159.
- J Earman and C Glymour, Einstein and Hilbert : two months in the history of general relativity, Arch.
- M Ferraris, M Francaviglia and C Reina, Variational formulation of general relativity from 1915 to 1925 : 'Palatini's method' discovered by Einstein in 1925, Gen.
- Relativity Gravitation 14 (3) (1982), 243-254.
- M Garcia Doncel, The genesis of special relativity and Einstein's epistemology (Spanish), Three lectures about Albert Einstein, Mem.
- H Goenner, The reaction to relativity theory.
- J J Gray, Poincare, Einstein, and the theory of special relativity, Math.
- K Hentschel, Einstein's attitude towards experiments : testing relativity theory 1907-1927, Stud.
- K Hentschel, Erwin Finlay Freundlich and testing Einstein's theory of relativity, Arch.
- F R Hickman, Electrodynamical origins of Einstein's theory of general relativity, Internat.
- B Hoffmann, Einstein and Zionism, in General relativity and gravitation , in Proc.
- H Hora, Einstein's photon distribution for blackbodies and the discovery of the laser, in General relativity and gravitation 1 (New York-London, 1980), 17-21.
- D Howard, Einstein and Eindeutigkeit : a neglected theme in the philosophical background to general relativity, in Studies in the history of general relativity (Boston, MA, 1992), 154-243; 462.
- J Illy, Einstein teaches Lorentz, Lorentz teaches Einstein : Their collaboration in general relativity, 1913-1920, Arch.
- J Illy, The correspondence of Albert Einstein and Gustav Mie, 1917-1918, in Studies in the history of general relativity (Boston, MA, 1992), 244-259; 462.
- M Katsumori, Einstein's philosophical turn and the theory of relativity, in Grenzfragen zwischen Philosophie und Naturwissenschaft (Vienna, 1989), 98-101.
- M Katsumori, The theories of relativity and Einstein's philosophical turn, Stud.
- P Kerszberg, The Einstein-de Sitter controversy of 1916-1917 and the rise of relativistic cosmology, in Einstein and the history of general relativity (Boston, MA, 1989), 325-366.
- L Kostro, An outline of the history of Einstein's relativistic ether concept, in Studies in the history of general relativity (Boston, MA, 1992), 260-280; 463.
- A J Kox, Einstein, Lorentz, Leiden and general relativity, Classical Quantum Gravity 10 (Suppl.) (1993) S187-S191.
- C Lanczos, Albert Einstein and the theory of relativity, Nuovo Cimento (10) 2 (Suppl.) (1955) 1193-1220.
- C Lanczos, Einstein's path from special to general relativity, in General relativity : papers in honour of J L Synge (Oxford, 1972), 5-19.
- Sources of the general theory of relativity (Russian), Latvijas PSR Zinatn.
- Einstein, aim-oriented empiricism and the discovery of special and general relativity, British J.
- H Melcher, Some supplements to Einstein-documents, in Proceedings of the ninth international conference on general relativity and gravitation (Cambridge, 1983), 271-284.
- A I Miller, Albert Einstein's 1907 Jahrbuch paper : the first step from SRT to GRT, in Studies in the history of general relativity (Boston, MA, 1992), 319-335; 464.
- A I Miller, The special relativity theory : Einstein's response to the physics of 1905, in Albert Einstein, Jerusalem, 1979 (Princeton, NJ, 1982), 3-26.
- J Norton, John Einstein's discovery of the field equations of general relativity : some milestones, in Proceedings of the fourth Marcel Grossmann meeting on general relativity (Amsterdam-New York, 1986), 1837-1848.
- J Norton, How Einstein found his field equations, 1912-1915, in Einstein and the history of general relativity (Boston, MA, 1989), 101-159.
- J Norton, What was Einstein's principle of equivalence?, in Einstein and the history of general relativity (Boston, MA, 1989), 5-47.
- M Paty, Physical geometry and special relativity.
- J Stachel, How Einstein discovered general relativity : a historical tale with some contemporary morals, in General relativity and gravitation (Cambridge-New York, 1987), 200-208.
- J Stachel, Einstein's search for general covariance, 1912-1915, in Einstein and the history of general relativity (Boston, MA, 1989), 63-100.
- J Stachel, Lanczos's early contributions to relativity and his relationship with Einstein, in Proceedings of the Cornelius Lanczos International Centenary Conference, Raleigh 1993 (Philadelphia, PA, 1994), 201-221.
- S G Suvorov, Einstein : the creation of the theory of relativity and some gnosiological lessons, Soviet Phys.
- S G Suvorov, Einstein : the creation of the theory of relativity and some gnosiological lessons (Russian), Uspekhi Fiz.
- Y Tanaka, Einstein and Whitehead : The principle of relativity reconsidered, Historia Sci.
- V P Vizgin, Einstein, Hilbert, and Weyl : the genesis of the geometrical unified field theory program, in Einstein and the history of general relativity (Boston, MA, 1989), 300-314.
- C M Will, General relativity at 75 : how right was Einstein?, in The Sixth Marcel Grossmann Meeting, Kyoto 1991 (River Edge, NJ, 1992), 769-786.
- References for Hilbert
- T Sauer, U Majer, A Schirrmacher and H-J Schmidt (eds.), David Hilbert's lectures on the foundations of physics 1915-1927 (German), Relativity, quantum theory and epistemology (Springer-Verlag, Berlin, 2009).
- L Corry, Axiomatics, empiricism, and Anschauung in Hilbert's conception of geometry: between arithmetic and general relativity, in The architecture of modern mathematics (Oxford Univ.
- J Earman and C Glymour, Einstein and Hilbert: two months in the history of general relativity, Arch.
- T Sauer, The relativity of discovery: Hilbert's first note on the foundations of physics, Arch.
- V P Vizgin, Einstein, Hilbert, and Weyl: the genesis of the geometrical unified field theory program, in Einstein and the history of general relativity, North Andover, MA, 1986 (Einstein Stud., 1, Birkhauser Boston, Boston, MA, 1989), 300-314.
- References for Levi-Civita
- U Bottazzini, Ricci and Levi-Civita : from differential invariants to general relativity, in The symbolic universe, Milton Keynes, 1996 (Oxford Univ.
- C Cattani, Levi-Civita's influence on Palatini's contribution to general relativity, in The attraction of gravitation: new studies in the history of general relativity, Johnstown, PA, 1991 (Birkhauser Boston, Boston, MA, 1993), 206-222.
- C Cattani and M De Maria, Einstein's path toward the generally covariant formulation of gravitational field equations: the contribution of Tullio Levi-Civita, in Proceedings of the fourth Marcel Grossmann meeting on general relativity, Part A, B, Rome, 1985 (North-Holland, Amsterdam, 1986), 1805-1826.
- References for Poincare
- N L Balazs, The acceptability of physical theories : Poincare versus Einstein, in General relativity, papers in honour of J L Synge (Oxford, 1972), 21-34.
- A Borel, Henri Poincare and special relativity, Enseign.
- E Giannetto, Henri Poincare and the rise of special relativity, Hadronic J.
- J J Gray, Poincare, Einstein, and the theory of special relativity, Math.
- References for Chandrasekhar
- A Ashtekar, Chandrasekhar's contributions to general relativity, Current Sci.
- N Panchapakesan, Seeing beauty in the simple and the complex : Chandrasekhar and general relativity, in Classical and quantum aspects of gravitation and cosmology, Madras, 1996 (Madras, 1998), 1-10.
- K C Wali, S Chandrasekhar's contributions to general relativity, in The attraction of gravitation : new studies in the history of general relativity, Johnstown, PA, 1991 (Boston, MA, 1993), 332-349.
- References for Weyl
- M Friedman, Carnap and Weyl on the foundations of geometry and relativity theory, Erkenntnis 42 (2) (1995), 247-260.
- T Hawkins, From general relativity to group representations : the background to Weyl's papers of 1925-26, in Materiaux pour l'histoire des mathematiques au XXe siecle, Nice, 1996 (Soc.
- V P Vizgin, Einstein, Hilbert, and Weyl : the genesis of the geometrical unified field theory program, in Einstein and the history of general relativity, North Andover, MA, 1986 (Birkhauser Boston, Boston, MA, 1989), 300-314.
- References for Mathisson
- B Sredniawa, Myron Mathisson's and Jan Weyssenhoff's work on the problem of motion in general relativity, in Studies in the history of general relativity, Luminy, 1988 (Birkhauser Boston, Boston, MA, 1992), 400-406; 465.
- B Sredniawa, Theory of relativity in Jagellonian University in Krakow in the half-century 1909-1959 (Polish), Kwart.
- References for Minkowski
- F W Lanchester, Relativity : an elementary explanation of the space-time relations as established by Minkowski, and a discusson of gravitational theory based thereon (London, 1935).
- L Corry, Hermann Minkowski and the postulate of relativity, Arch.
- L Pyenson, Hermann Minkowski and Einstein's Special Theory of Relativity : With an appendix of Minkowski's 'Funktiontheorie' manuscript, Arch.
- References for Abraham Max
- C Cattani and M De Maria, Max Abraham and the reception of relativity in Italy: his 1912 and 1914 controversies with Einstein, Einstein and the history of general relativity (Boston, MA, 1989), 160-174.
- M De Maria, The first reactions to general relativity in Italy: the polemics between Max Abraham and Albert Einstein (Italian), Italian mathematics between the two world wars (Bologna, 1987), 143-159.
- References for Lemaitre
- O Godart, Contributions of Lemaitre to general relativity (1922-1934), in Studies in the history of general relativity, Luminy, 1988, Einstein Stud.
- References for Larmor
- J M Sanchez-Ron, Larmor versus general relativity, in The expanding worlds of general relativity, Berlin, 1995 (Boston, MA, 1999), 405-430.
- References for McVittie
- W Davidson, George McVittie's work in relativity, Vistas Astronom.
- J M Sanchez-Ron, George McVittie, the uncompromising empiricist, in The universe of general relativity (Einstein Stud., 11, Birkhauser Boston, Boston, MA, 2005), 189-221.
- References for Synge
- Bibliography of J L Synge, in General relativity : papers in honour of J L Synge (Oxford, 1972), 257-265.
- Curriculum vitae of J L Synge, in General relativity : papers in honour of J L Synge (Oxford, 1972), 255.
- References for Fock
- G E Gorelik, Vladimir Fock: philosophy of gravity and gravity of philosophy, in The attraction of gravitation: new studies in the history of general relativity, Johnstown, PA, 1991 (Birkhauser Boston, Boston, MA, 1993), 308-331.
- A Mercier, Obituary: Vladimir Fock, General Relativity and Gravitation 6 (4) (1975), 429-430.
- References for Grassmann
- M E Horn, Grassmann, Pauli, Dirac: special relativity in the schoolroom, in From Past to Future: Grassmann's Work in Context (Basel, 2010), 435-450
.
- References for Huygens
- C Vilain, Huygens and relative motion, in Relativity in general (Gif-sur-Yvette, 1994), 161-169.
- References for Whitehead
- Y Tanaka, Einstein and Whitehead : The principle of relativity reconsidered, Historia Sci.
- References for Helmholtz
- N Ionescu-Pallas, Hermann von Helmholtz - a forerunner of relativity theory? (Romanian), Stud.
- References for Klein Oskar
- Klein, Some General Aspects of Einstein's Theory of Relativity, Astophysica Norvegica 9 (1964) 161-169.
- References for Durell
- F J Dyson, Foreword, in Clement V Durell, Readable relativity (Harper & Brothers, New York, 1960).
- References for Carmichael
- W Weaver, Review: A Debate on the Theory of Relativity by R D Carmichael, W D MacMillan, M E Hufford and H T Davis, Amer.
- References for Lichnerowicz
- M Cahen, A Lichnerowicz and M Flato (eds.), Differential Geometry and Relativity: A Volume in Honour of Andre Lichnerowicz on his 60th Birthday (Reidel, 1976).
- References for Bondi
- G Gale and J Urani, Milne, Bondi and the 'second way' to cosmology, in The expanding worlds of general relativity, Berlin, 1995 (Birkhauser Boston, Boston, MA, 1999), 343-375.
- References for Kaluza
- P G Bergmann, An introduction to the Theory of Relativity (New York, 1942).
- References for Freundlich
- K Hentschel, Erwin Finlay Freundlich and Testing Einstein's Theory of Relativity, Archive for History of Exact Science 47 (1994), 143-201.
- References for Skolem
- I Jane, Reflections on Skolem's relativity of set-theoretical concepts, Philos.
- References for Drach
- J-F Pommaret, Gauge theory and general relativity.
- References for Sitter
- P Kerszberg, Einstein, De Sitter and Cosmology, in Don Howard & John Stachel (eds.), Einstein and the History of General Relativity, Proceedings of the 1986 Osgood Hill Conference, North Andover, MA, Einstein Studies (Birkhauser, Boston, 1989), 325-366.
- References for Lorentz
- J A Kox, Hendrik Antoon Lorentz, the Ether and the General Theory of Relativity, Archive for History of Exact Science 38 (1988), 67-78.
- References for Milne
- G Gale and J Urani, Milne, Bondi and the 'second way' to cosmology, in The expanding worlds of general relativity, Berlin, 1995 (Boston, MA, 1999), 343-375.
- References for Newton
- B G Kuznecov, The teaching of Newton on relativity and absolute motion (Russian), Izvestiya Akad.
- References for Infeld
- General Relativity and Gravitation 1 (1970), 191-208.
- References for Schouten
- H F M Goenner, On the History of Unified Field Theories (Living Reviews Relativity, 2004).
- References for Noether Emmy
- D Rowe, The Gottingen response to general relativity and Emmy Noether's theorems, in J J Gray (ed.), The symbolic universe: Geometry and Physics 1890-1930 (Oxford Univ.
- References for Euclid
- W Theisen, Euclid, relativity, and sailing, Historia Math.
- References for Lanczos
- J Stachel, Lanczos's early contributions to relativity and his relationship with Einstein, in Proceedings of the Cornelius Lanczos International Centenary Conference (Philadelphia, PA, 1994), 201-221.
- References for Cartan
- M Biezunski, Inside the coconut: the Einstein-Cartan discussion on distant parallelism, in Einstein and the history of general relativity, North Andover, MA, 1986 (Birkhauser Boston, Boston, MA, 1989), 315-324.
- References for Hertz Heinrich
- D Howard and J D Norton, Out of the labyrinth? Einstein, Hertz, and the Gottingen answer to the hole argument, in The attraction of gravitation: new studies in the history of general relativity, Johnstown, PA, 1991 (Birkhauser Boston, Boston, MA, 1993), 30-62.
Additional material
- Einstein: 'Ether and Relativity
- Einstein: Ether and Relativity
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- He chose as his topic Ether and the Theory of Relativity.
- Ether and the Theory of Relativity
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- This theory - also called the theory of the stationary luminiferous ether - moreover found a strong support in an experiment which is also of fundamental importance in the special theory of relativity, the experiment of Fizeau, from which one was obliged to infer that the luminiferous ether does not take part in the movements of bodies.
- It may be added that the whole change in the conception of the ether which the special theory of relativity brought about, consisted in taking away from the ether its last mechanical quality, namely, its immobility.
- The space-time theory and the kinematics of the special theory of relativity were modelled on the Maxwell-Lorentz theory of the electromagnetic field.
- This theory therefore satisfies the conditions of the special theory of relativity, but when viewed from the latter it acquires a novel aspect.
- But by the special theory of relativity the same equations without any change of meaning also hold in relation to any new system of co-ordinates K' which is moving in uniform translation relatively to K.
- This conception suggests itself the more readily as, according to Lorentz's theory, electromagnetic radiation, like ponderable matter, brings impulse and energy with it, and as, according to the special theory of relativity, both matter and radiation are but special forms of distributed energy, ponderable mass losing its isolation and appearing as a special form of energy.
- More careful reflection teaches us however, that the special theory of relativity does not compel us to deny ether.
- We shall see later that this point of view, the conceivability of which I shall at once endeavour to make more intelligible by a somewhat halting comparison, is justified by the results of the general theory of relativity.
- The special theory of relativity forbids us to assume the ether to consist of particles observable through time, but the hypothesis of ether in itself is not in conflict with the special theory of relativity.
- Certainly, from the standpoint of the special theory of relativity, the ether hypothesis appears at first to be an empty hypothesis.
- Mach's idea finds its full development in the ether of the general theory of relativity.
- The ether of the general theory of relativity is a medium which is itself devoid of all mechanical and kinematical qualities, but helps to determine mechanical (and electromagnetic) events.
- What is fundamentally new in the ether of the general theory of relativity as opposed to the ether of Lorentz consists in this, that the state of the former is at every place determined by connections with the matter and the state of the ether in neighbouring places, which are amenable to law in the form of differential equations; whereas the state of the Lorentzian ether in the absence of electromagnetic fields is conditioned by nothing outside itself, and is everywhere the same.
- The ether of the general theory of relativity is transmuted conceptually into the ether of Lorentz if we substitute constants for the functions of space which describe the former, disregarding the causes which condition its state.
- Thus we may also say, I think, that the ether of the general theory of relativity is the outcome of the Lorentzian ether, through relativation.
- The contrast between ether and matter would fade away, and, through the general theory of relativity, the whole of physics would become a complete system of thought, like geometry, kinematics, and the theory of gravitation.
- Recapitulating, we may say that according to the general theory of relativity space is endowed with physical qualities; in this sense, therefore, there exists an ether.
- According to the general theory of relativity space without ether is unthinkable; for in such space there not only would be no propagation of light, but also no possibility of existence for standards of space and time (measuring-rods and clocks), nor therefore any space-time intervals in the physical sense.
- Eddington: 'Mathematical Theory of Relativity' Introduction
- Eddington: Mathematical Theory of Relativity Introduction
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- Arthur Stanley Eddington, M.A., M.Sc., F.R.S., Plumian Professor of Astronomy and Experimental Philosophy, University of Cambridge, wrote The Mathematical Theory of Relativity which was published by Cambridge University Press in 1923.
- The Mathematical Theory of Relativity
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- The tendency to this kind of definition had progressed far even in pre-relativity physics.
- Mass is defined by experiments on inertial properties, no longer as "quantity of matter." But for some terms the older kind of definition (or lack of definition) has been obstinately adhered to; and for these the relativity theory must find new definitions.
- We decide that time is relative to an observer; that is to say, we admit that an observer on another star, who carries out all the rest of the operations and calculations as specified in our definition, is also measuring time - not our time, but a time relative to himself The same relativity affects the great majority of elementary physical quantities (the most important exceptions are number (of discrete entities), action, and entropy); the description of the operations is insufficient to lead to a unique answer unless we arbitrarily prescribe a particular motion of the observer and his apparatus.
- In this example we have had a typical illustration of "relativity," the recognition of which has had far-reaching results revolutionising the outlook of physics.
- The principle of relativity goes still further.
- http://www-history.mcs.st-andrews.ac.uk/Extras/Eddington_relativity.html
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- Eddington: 'Mathematical Theory of Relativity' Preface
- Eddington: Mathematical Theory of Relativity Preface
.
- Arthur Stanley Eddington, M.A., M.Sc., F.R.S., Plumian Professor of Astronomy and Experimental Philosophy, University of Cambridge, wrote The Mathematical Theory of Relativity which was published by Cambridge University Press in 1923.
- The Mathematical Theory of Relativity
.
- During the ensuing eighteen months I have pursued my intention of developing it into a more systematic and comprehensive treatise on the mathematical theory of Relativity.
- But it is eminently desirable to- have a general grasp of the revolution of thought associated with the theory of Relativity before approaching it along the narrow lines of strict mathematical deduction.
- G C McVittie papers
- Axiomatic treatment of kinematical relativity (1942).
- A H Taub writes: The fundamental results of E A Milne's kinematical relativity are derived from nine axioms.
- It is argued that kinematical relativity cannot be applied to a physical theory without the addition of a further axiom which would enable one to identify a theoretical observer with a terrestrial one.
- The regraduation of clocks in spherically symmetric space-times of general relativity (1945).
- Arthur Walker writes: This paper gives a preliminary examination of the question as to whether general relativity admits clock regraduations other than trivial coordinate transformations, a question which has been suggested by recent kinematical theories of relativity.
- H P Robertson writes: The first three of the five chapters present a rapid survey of our knowledge of extra-galactic nebulae, of the tensor calculus and of the principles of the general theory of relativity.
- McVittie writes: The possibility of the existence of negative stress in the general relativity treatment of a perfect fluid is used to construct a model universe which is in a 'gravitationally steady state'.
- H P Robertson writes: The author's purpose is to show how, and to what extent, Newtonian cosmological models are derivable from those of the general theory of relativity.
- General relativity and cosmology (1956).
- G Y Rainich writes: In the introduction the author stresses the inevitability of taking, implicitly or explicitly, a definite philosophical position in discussing questions of general relativity and does it rather explicitly.
- Spherical symmetry and mass-energy in general relativity I (1970).
- Cahill and McVittie (the authors) write: The mass-energy of spherically symmetric distributions of material is studied according to general relativity.
- Spherical symmetry and mass-energy in general relativity II (1970).
- Finlay Freundlich's Inaugural Address, Part 2
- This is the crucial assumption on which Einstein's general theory of relativity is based.
- The theory of relativity teaches us that the Earth, placed at a certain distance from the Sun and given an initial speed, will be guided, due to the Sun's gravitation - as if an invisible surface connected the two subsequent orbital positions - along the shortest path which connects these two positions.
- In the theory of relativity no such force is envisaged.
- And, what is of even greater importance, the coincidence between the Kepler orbit and the orbit of a planet moving according to the theory of relativity in a quasi non-Euclidean space, is not complete.
- This difference corresponds accurately, in value and character, to the deviation in the motion of Mercury, which had been discovered long before the theory of relativity was conceived and which I have already mentioned.
- For a full agreement between the predictions of the theory of relativity and astronomical observations has not yet been achieved in all observable effects.
- While the motion of a body, like Mercury, seems to follow the laws set up by the theory of relativity, light, i.e.
- The theory of relativity teaches that between matter and energy no fundamental difference exists in so far as the one may be converted into the other.
- The theory of relativity claims therefore that the same laws of motion hold good for moving energy as for moving matter.
- But the observations yield a considerably larger value for the deflection than is predicted by the theory of relativity.
- Although followers of Einstein's theory of relativity are reluctant, to say the least, even to consider such a possibility, it may not be overlooked that also in other respects a deep gap is dividing the two branches of physics the one approaching the phenomena from a macroscopic point of view; this is the theory of relativity; the other, the quantum theory, based on fundamentally different conceptions, which takes account of the atomic structure of matter and the quantum structure of energy.
- Born Inaugural
- Einstein's theory of relativity of 1905 can be considered as being at once the culmination of classical ideas and the starting-point of the new ones.
- The most important consequences of this conception were deduced by Einstein, who laid the foundations of the quantum theory of light in 1905, the year in which he published his relativity theory, and by Niels Bohr in 1913, when he applied the idea of the quantum to the structure of atoms.
- Relativity gave the first example in which the intrusion of the observer into the description of facts is not so simple, and leads to a new conception to conserve the idea of an objective world Einstein has acknowledged that his studies on this problem were deeply influenced by the ideas of Ernst Mach, a Viennese physicist who developed more and more into a philosopher.
- When I wrote a popular book on relativity in 1920 I was so impressed by this wonderful construction that I represented this method of objectivation as the central achievement of science.
- In the case of relativity this evidence was strong indeed, but consisted to a large extent of negative statements, such as that mentioned above regarding the absence of an ether-wind.
- We thus meet a situation similar to that in relativity, but much more complicated.
- After relativity has changed the ideas of space and time, another of Kant's categories, causality, has to be modified.
- The difficulty is not the two aspects, but the fact that no description of any natural phenomenon in the atomistic domain is possible without referring to the observer, not only to his velocity as in relativity, but to all his activities in performing the observation, setting up the instruments, and so on.
- As I said before, this standpoint has proved itself productive by inducing physicists to adopt a critical attitude towards traditional assumptions, and has helped in the building of relativity and quantum theory.
- The expression "invariant" which I have already used in speaking of relativity, and which appears here in a more general sense, is the link connecting these psychological considerations with exact science.
- Einstein: 'Geometry and Experience
- I attach special importance to the view of geometry which I have just set forth, because without it I should have been unable to formulate the theory of relativity.
- The idea of the measuring-rod and the idea of the clock co-ordinated with it in the theory of relativity do not find their exact correspondence in the real world.
- Not only the practical geometry of Euclid, but also its nearest generalisation, the practical geometry of Riemann, and therewith the general theory of relativity, rest upon this assumption.
- Thence it follows that the above assumption for tracts must also hold good for intervals of clock-time in the theory of relativity.
- Let us call to mind what the general theory of relativity teaches in this respect.
- The general theory of relativity teaches that the inertia of a given body is greater as there are more ponderable masses in proximity to it; thus it seems very natural to reduce the total effect of inertia of a body to action and reaction between it and the other bodies in the universe, as indeed, ever since Newton's time, gravity has been completely reduced to action and reaction between bodies.
- From the equations of the general theory of relativity it can be deduced that this total reduction of inertia to reciprocal action between masses - as required by E Mach, for example - is possible only if the universe is spatially finite.
- For if we inquire into the deviations shown by the consequences of the general theory of relativity which are accessible to experience, when these are compared with the consequences of the Newtonian theory, we first of all find a deviation which shows itself in close proximity to gravitating mass, and has been confirmed in the case of the planet Mercury.
- From the latest results of the theory of relativity it is probable that our three-dimensional space is also approximately spherical, that is, that the laws of disposition of rigid bodies in it are not given by Euclidean geometry, but approximately by spherical geometry, if only we consider parts of space which are sufficiently great.
- Tullio Levi-Civita
- EMS obituary
- There are few modern branches of mathematical physics to which he did not at one time or another contribute - classical mechanics, hydromechanics, thermodynamics, elasticity, the strength of materials, astronomy, electromagnetism, optics, relativity and quantum mechanics - yet some of his greatest work was in pure mathematics.
- Their work gained relatively little attention until, fifteen years later, it was used by Einstein in the formulation of the general theory of relativity.
- Originally it was a technique rather than a separate branch of mathematics, providing as it did a way of writing theorems of differential geometry and the calculus in a form at once concise and general, and it was not until after the development of relativity, followed shortly afterwards by Levi-Civita's definition of parallelism in Riemannian geometry, that it assumed the full place it now holds as one of the main branches of modern mathematics.
- He made numerous other contributions to relativity, and in 1933 interested himself in the problem of reconciling Dirac's equations in quantum mechanics with the relativistic principle of covariance.
- Regarding the last, it is interesting to note that, in his own words, "Dirac's equations must, in my opinion, be abandoned, without, it is understood, giving up the main progress realised by them in the domain of restricted relativity" - this because their transformation-laws seemed to him to require the introduction into space-time of a lattice (a system of four mutually perpendicular congruences of lines) which, having no intrinsic physical significance, should, but in fact did not, disappear from the equations in their final relativistic form.
- This discovery by Levi-Civita, together with the contemporary development of general relativity and the search for a unified theory of gravitation and electromagnetism by Weyl, Eddington, Einstein and others, quickly led to generalisations of Riemannian geometry.
- By his early work with Ricci on tensor analysis and by his later discovery of infinitesimal parallelism, Levi-Civita laid the foundations both for relativity and for the establishment of differential geometry as one of the great branches of modern mathematics.
- Levi-Civita.html
- There are few modern branches of mathematical physics to which he did not at one time or another contribute - classical mechanics, hydromechanics, thermodynamics, elasticity, the strength of materials, astronomy, electromagnetism, optics, relativity and quantum mechanics - yet some of his greatest work was in pure mathematics.
- Their work gained relatively little attention until, fifteen years later, it was used by Einstein in the formulation of the general theory of relativity.
- Originally it was a technique rather than a separate branch of mathematics, providing as it did a way of writing theorems of differential geometry and the calculus in a form at once concise and general, and it was not until after the development of relativity, followed shortly afterwards by Levi-Civita's definition of parallelism in Riemannian geometry, that it assumed the full place it now holds as one of the main branches of modern mathematics.
- He made numerous other contributions to relativity, and in 1933 interested himself in the problem of reconciling Dirac's equations in quantum mechanics with the relativistic principle of covariance.
- Regarding the last, it is interesting to note that, in his own words, "Dirac's equations must, in my opinion, be abandoned, without, it is understood, giving up the main progress realised by them in the domain of restricted relativity" - this because their transformation-laws seemed to him to require the introduction into space-time of a lattice (a system of four mutually perpendicular congruences of lines) which, having no intrinsic physical significance, should, but in fact did not, disappear from the equations in their final relativistic form.
- This discovery by Levi-Civita, together with the contemporary development of general relativity and the search for a unified theory of gravitation and electromagnetism by Weyl, Eddington, Einstein and others, quickly led to generalisations of Riemannian geometry.
- By his early work with Ricci on tensor analysis and by his later discovery of infinitesimal parallelism, Levi-Civita laid the foundations both for relativity and for the establishment of differential geometry as one of the great branches of modern mathematics.
- Eddington on the Expanding Universe
- He found that, on one of two alternative hypotheses arising out of Einstein's relativity theory, the light of very remote objects should be displaced to the red as though they were moving away from us; and he suggested the observed motions of the spiral nebulae (by far the most remote objects known) as a discriminating test.
- We see, then, that according to observation the system of the spiral nebulae is expanding, and that relativity theory had foreseen just such an expansion (except that as an alternative it would have been content with an equally regular contraction).
- That is one of the results of Einstein's theory which has become almost a commonplace of physics; but it was a rather complicated kind of relativity that Einstein considered - relativity to the motion of our frame of reference.
- I am going to refer to another much more elementary relativity of length, viz.
- We can feel little doubt therefore that the observed motions of the nebulae are genuine and represent the expansion effect predicted by relativity.
- EMS 1913 Colloquium
- Professor A W Conway, of the National University of Ireland, is taking for his subject "The Theory of Relativity and the New Physical Ideas of Space and Time;" Dr Sommerville, of St Andrews University, lectures on "Non-Euclidean Geometry and the Foundations of Geometry;" and Professor Whittaker, Edinburgh University, gives a course of five lectures and demonstrations on "Practical Harmonic Analysis and Periodogram Analysis." By the courtesy of the University Court, several rooms have been set aside as reception and writing rooms, and these have been furnished for the comfort and convenience of members of the colloquium.
- The theory of relativity after Einstein started by asserting the impossibility of observing the absolute velocity of the observer.
- Professor A W Conway delivered his second lecture on "Relativity." In the course of the lecture the relations between the coordinates and time in the two systems of reference were deduced.
- Professor A W Conway delivered the third lecture on Relativity.
- The fourth lecture on "Relativity" was delivered by Professor Conway.
- Professor Conway delivered his concluding lecture on "Relativity." The ideas of Minkowsky were explained.
- Whittaker EMS Obituary.html
- Consequently, lectures were given by D M Y Somerville on Non-euclidean geometry and the foundations of geometry and by A W Conway [Arthur Conway] on The theory of relativity and the new physical ideas of space and time.
- Later on, he became intensely interested in the Theory of Relativity and wrote a number of papers on some of its mathematical aspects; these are discussed by J L Synge in a paper on pages 39-55 of this Whittaker Memorial Number.
- His interest in Relativity manifested itself also at the undergraduate level, for the Honours course entitled Higher Algebra and Geometry contained neither Algebra nor Geometry in the ordinary sense of these terms but comprised Tensor Calculus with Riemannian Geometry and its generalisations.
- The second volume, which appeared in 1953, contains an account of the developments which took place between 1900 and 1926 and is mainly concerned with Relativity and the Quantum Theory.
- One of the few subjects on which I have never heard him discourse is Geometry in the Bakerian sense; Geometry for him meant Riemannian geometry which is used in Relativity and contributes to our understanding of the material universe.
- He was also President of Section A of the British Association in 1927 and his presidential address on The Outstanding problems of relativity dealt with a number of matters which are still not settled.
- Eddington on the Expanding Universe
- Levi-Civita: 'Absolute Differential Calculus
- Two new chapters have been added, which are intended to exhibit the fundamental principles of Einstein's General Theory of Relativity (including, of course, as a limiting case, the so-called Special or Restricted Theory) as an application of the Absolute Calculus.
- I have already had occasion to remark in the Preface to the Italian edition that we possess various systematic and well-written expositions of Relativity by celebrated authors.
- The sacrifice is certainly regrettable, since Electromagnetism was historically related in the most intimate way to Einstein's conception, having served indeed as the support and model for Restricted Relativity.
- Furthermore, Electromagnetism, in common with every other physical phenomenon, now comes within the ambit of General Relativity.
- For this reason I have followed the method - which I have adopted sometimes in lectures or articles on special subjects of taking the classical laws as the starting point and then of trying to find inductively what modifications - negligible in ordinary circumstances - should be introduced in order to take account of Einstein's ideas; and in the first place, naturally, to take account of his Principle of Relativity, that is to say, the invariant behaviour of these laws under all transformations of space and time, an auxiliary four-dimensional ds2being duly employed.
- EMS 1934 Colloquium
- Courses of lectures are being delivered on "World-Structure by the Kinetic Methods of the Special Theory of Relativity," by Professor E A Milne, Oxford; on "Ramanujan's Note-Books and their Place in Modern Mathematics," by Professor B M Wilson, Dundee; on "Pictorial Geometry," by Professor H W Turnbull, St Andrews; and on "Some Expansions Relating to the Problem of Lattice Points," by Mr W L Ferrar, Fellow of Hertford College, Oxford.
- The principal course of lectures, delivered by Professor E A Milne (Oxford), dealt with the problem of world-structure by the kinematical methods of special relativity.
- This theory, developed by Prof Milne himself, seeks to account for the structure of the system of the spiral nebulae and the recession phenomenon without using general relativity.
- de Sitter and others took part, it was pointed out that Prof Milne's theory had brought into prominence the fact that in general relativity also the scattering of the nebulae went on independently of gravitation.
- One, delivered by Prof W de Sitter, was a masterly exposition of the subject of the Expanding Universe from the observational point of view and from that of an expert in general relativity.
- EMS 1934 Colloquium 2.html
- The principal course of lectures, delivered by Professor E A Milne (Oxford), dealt with the problem of world-structure by the kinematical methods of special relativity.
- This theory, developed by Prof Milne himself, seeks to account for the structure of the system of the spiral nebulae and the recession phenomenon without using general relativity.
- de Sitter and others took part, it was pointed out that Prof Milne's theory had brought into prominence the fact that in general relativity also the scattering of the nebulae went on independently of gravitation.
- One, delivered by Prof W de Sitter, was a masterly exposition of the subject of the Expanding Universe from the observational point of view and from that of an expert in general relativity.
- Reviews Landau Lifshitz.html
- The presentation is based throughout on two general principles, namely on Galileo's relativity principle and on Hamilton's principle of least action.
- The present edition has been expanded by about 50 pages, mostly by extension of the discussion of the general theory of relativity.
- The authors summarize in neat and compact form those features of the classical theory of the electromagnetic field and the general theory of relativity which theoretical physicists are expected to know.
- The level of sophistication is determined by the fact that the book starts with a discussion of the special theory of relativity, while the derivations of the equations of motion and the field equations are based on variational principles, most of the derivations being purely formal.
- Wien biography
- They had to adopt a policy towards the new discoveries of relativity which were changing the face of physics so they sought to publish papers that illuminated the physical meaning or concepts of relativity; they left manuscripts that stressed mathematical interpretations to their mathematician colleagues in Gottingen.
- History Topics: Light through the ages: Relativity and quantum era
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- History Topics: Special relativity
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- Von Neumann: 'The Mathematician' Part 2
- As I have pointed out before, Euclid's system of geometry was the prototype of the axiomatic presentation of classical mechanics, and similar treatments dominate phenomenological thermodynamics as well as certain phases of Maxwell's system of electrodynamics and also of special relativity.
- Michelson's experiment leading to special relativity, the difficulties of certain ionization potentials and of certain spectroscopic structures leading to quantum mechanics exemplify the first case; the conflict between special relativity and Newtonian gravitational theory leading to general relativity exemplifies the second, rarer, case.
- Élie Cartan reviews
- In the text he develops the theory from the beginning, the first volume being devoted to spinors in three-dimensional space and the second to spinors in n-dimensional space, with special reference to the four-dimensional space-time of Special Relativity.
- The second part is devoted to the theory of spinors in spaces of any number of dimensions, and particularly in the space of special relativity (Minkowski space).
- In this connection, Cartan shows how to derive the "Dirac" equation for any group, and extends the equation to general relativity.
- Max Planck: 'Quantum Theory
- The undetermined additive constant in the expression for energy was fixed later by the relativity theorem of the relation between energy and inertia.
- In the face of these numerous verifications (which could be considered as very strong proofs in view of the great accuracy of spectroscopic measurements), those who had looked on the problem as a game of chance were finally compelled to throw away all doubt when A Sommerfeld showed that - by extending the laws of distribution of quanta to systems with several degrees of freedom (and bearing in mind the variability of mass according to the theory of relativity) - an elegant formula follows which must, so far as can be determined by the most delicate measurements now possible (those of F Paschen), solve the riddle of the structure of hydrogen and helium spectra.
- It must seem a curious coincidence that at the time when the idea of general relativity is making headway and leading to unexpected results, Nature has revealed, at a point where it could be least foreseen, an absolute invariable unit, by means of which the magnitude of the action in a time space element can be represented by a definite number, devoid of ambiguity, thus eliminating the hitherto relative character.
- James Jeans: 'Physics and Philosophy' II
- (3) Einstein's relativity theory of gravitation, which is purely geometrical in form.
- The first is provided by the theory of relativity.
- But the, theory of relativity shows that if motions are attributed to forces, these forces will be differently estimated, as regards both quantity and quality, by observers who happen to be moving at different speeds, and furthermore that all their estimates have an equal claim to be considered right.
- EMS obituary
- Birkhoff made many contributions to the discussion of the theory of relativity, publishing two characteristically original books (Relativity and Modern Physics, 1923; The Origin, Nature and Influence of Relativity, 1925).
- Oswald Veblen Publications
- (b) (With B Hoffmann) "Projective Relativity", Phys.
- (c) "Spinors in Projective Relativity", Proc.
- (b) (With A H Taub and J von Neumann) "The Dirac Equation in Projective Relativity", Proc.
- Arthur Eddington's 1927 Gifford Lectures
- The theory of relativity and the quantum theory have led to strange new conceptions of the physical world; the progress of the principles of thermodynamics has wrought more gradual but no less profound change.
- It would not serve my purpose to give an easy introduction to the rudiments of the relativity and quantum theories; it was essential to reach the later and more recondite developments in which the conceptions of greatest philosophical significance are to be found.
- For that reason I would like to recall that the idealistic tinge in my conception of the physical world arose out of mathematical researches on the relativity theory.
- Tietze: 'Famous Problems of Mathematics
- If a work by Albert Einstein can now be quoted without further ado, at that time the book's chances of appearing were endangered by mere mention in it of the theory of relativity, which had the effect of a red flag on many in those days when, blinded by the universal propaganda, some scientists really believed that this theory was pure humbug and when, worse still, one of our greatest theoretical physicists was replaced by a man, foisted upon us from on high, who tossed Planck's quantum theory into the same kettle of damnation with the theory of relativity, so that our theoretical physicists had great difficulty in interceding on behalf of continued use of the theory of relativity in research and in teaching.
- George Temple's Inaugural Lecture II
- The romantic themes of relativity, plasticity, and gas dynamics have captured the imagination of the young mathematical physicist.
- In physics, the special theory of relativity is justly famous for its power of co-ordinating a vast array of puzzling phenomena, but many a physicist would confess to a feeling of personal loss now that relativity seems to have eliminated the aether and to have offered in its place only the principle of the inaccessibility of the velocity of light.
- EMS 1913 Colloquium
- A Course of Five Lectures by A W Conway, Esq., M.A., D.Sc., Professor of Mathematical Physics, University College, Dublin, on The Theory of Relativity and the New Physical Ideas of Space and Time.
- Each day at ten o'clock Professor Conway of University College, Dublin, discoursed on the Theory of Relativity and the new Physical Ideas of Space and Time.
- We were told that even if the theory of relativity were not true it had taught us truths.
- Max Planck: 'The Nature of Light
- That which has harmed it most is the result, deduced from Einstein's theory of relativity, that there can be no objective substantial ether, i.e.
- For, if that were not so, then when we consider two observers moving relative to one another in space, one at most could correctly assert that he was at rest relative to the ether, whereas, by the theory of relativity, each of the two could do so equally correctly.
- The energy contained in every gram of a substance, according to the theory of relativity, amounts to over 20 billion calories, quite independently of its temperature - more than sufficient to liberate countless electrons.
- Prefaces Landau Lifshitz.html
- From the very beginning it is based on the most general principles: Galileo's principle of relativity, and Hamilton's principle of least action.
- A complete, logically connected theory of the electromagnetic field includes the special theory of relativity, so the latter has been taken as the basis of the presentation.
- the general theory of relativity.
- Schwartz Jacob (print-only)
- To illustrate the different areas he worked in we note that he published Lectures on the mathematical method in analytical economics (1961), and two school level textbooks Matrices and Vectors for High-Schools and Colleges (1961) and Relativity In Illustrations in 1964.
- This clear, non-technical treatment makes relativity more accessible than ever before, requiring only a background in high-school geometry.
- Von Neumann: 'The Mathematician
- The discovery of general relativity forced a revision of our views on the relationship of geometry in an entirely new setting and with a quite new distribution of the purely mathematical emphases, too.
- And these two seemingly conflicting attitudes are perfectly compatible in one mathematical mind; thus Hilbert made important contributions to both axiomatic geometry and to general relativity.
- EMS 1938 Colloquium
- Professor E T Whittaker Is giving a course on "The Interactions between the Elementary Particles of the Universe." The first lecture dealt with the modifications which the Newtonian theory has undergone in consequence of the discovery of Relativity.
- Professor Whittaker covered this immensity, and described the stages in which the transformation took place, through relativity, the early quantum theory and its developments up to the latest speculations on heavy electrons and cosmic rays.
- Schwartz Jacob biography
- To illustrate the different areas he worked in we note that he published Lectures on the mathematical method in analytical economics (1961), and two school level textbooks Matrices and Vectors for High-Schools and Colleges (1961) and Relativity In Illustrations in 1964.
- This clear, non-technical treatment makes relativity more accessible than ever before, requiring only a background in high-school geometry.
- Wien (print-only)
- They had to adopt a policy towards the new discoveries of relativity which were changing the face of physics so they sought to publish papers that illuminated the physical meaning or concepts of relativity; they left manuscripts that stressed mathematical interpretations to their mathematician colleagues in Gottingen.
- Heinrich Weber's books
- He speaks of integral equations and the notion of relativity as two of the more important contributions made to the science since his last edition in 1900, and promises an application of the first in the present volume.
- Undoubtedly the systematic development of integral equations and their applications, of the principle of relativity, and in all likelihood, of Lebesgue's theory of integration, will make necessary at some future time a book treating the same subjects in radically new ways.
- E P Adams
- The most striking theoretical development of the period, the theory of relativity, also attracted Adams, and he was the translator for the lectures that Einstein gave in Princeton in 1921, which appeared as The Meaning of Relativity.
- Edmund Whittaker: 'Physics and Philosophy
- This is, of course, claimed only for the departments of the physical world where General Relativity does not enter.
- The question as to which class does a theory belong has, with the advent of relativity and quantum theory, ceased to have a meaning.
- EMS 1913 Colloquium 6.html.html
- Each day at ten o'clock Professor Conway of University College, Dublin, discoursed on the Theory of Relativity and the new Physical Ideas of Space and Time.
- We were told that even if the theory of relativity were not true it had taught us truths.
- H Weyl: 'Theory of groups and quantum mechanics'Preface to Second Edition
- This extension already leads so far away from the fundamental purpose of the book that I felt forced to omit the formulation of the quantum laws in accordance with the general theory of relativity, as developed by V Fock and myself, in spite of its desirability for the deduction of the energy-momentum tensor.
- The insight into the significance of these constants, obtained by the theory of relativity on the one hand and quantum theory on the other, is most forcibly expressed by the fact that they do not occur in the laws of Nature in a thoroughly systematic development of these theories.
- Science at St Andrews
- Each is distinguished as a geometer; and Sommerville was led in a deep and scholarly way, particularly to the bypaths of Non-Euclidean Geometry years before the advent of relativity brought it into prominence.
- In 1938, and, as a fitting sequel to the celebrations, an astronomer was appointed - Dr Findlay Freundlich, at the recommendation of Sir Arthur Eddington who had been the first to introduce into Britain the general theory of relativity.
- Atiyah reviews
- This book is interdisciplinary and addresses concerns of theoretical physicists interested in elementary particles or general relativity and mathematicians working in analysis or geometry.
- In earlier periods geometry and physics interacted at the classical level, as in Einstein's theory of general relativity, with gravitational force being interpreted in terms of curvature.
- EMS 1913 Colloquium 1.html.html
- Professor A W Conway, of the National University of Ireland, is taking for his subject "The Theory of Relativity and the New Physical Ideas of Space and Time;" Dr Sommerville, of St Andrews University, lectures on "Non-Euclidean Geometry and the Foundations of Geometry;" and Professor Whittaker, Edinburgh University, gives a course of five lectures and demonstrations on "Practical Harmonic Analysis and Periodogram Analysis." By the courtesy of the University Court, several rooms have been set aside as reception and writing rooms, and these have been furnished for the comfort and convenience of members of the colloquium.
- The theory of relativity after Einstein started by asserting the impossibility of observing the absolute velocity of the observer.
- E C Titchmarsh: 'Aftermath
- I once heard a lecture by a physicist in which he derided what he thought were the futilities of pure mathematics; but then he referred to some theorem of pure mathematics which, fifty years after its discovery, had found an application in relativity, and this seemed to him little short of miraculous.
- Jacques Hadamard's failures
- Absolute differential calculus is closely connected with the theory of relativity; and in this connection, I must confess that, having observed that the equation of propagation of light is invariant under a set of transformations (what is now known as Lorentz's group) by which space and time are combined together, I added that "such transformations are obviously devoid of physical meaning." Now, these transformations, supposedly without any physical meaning, are the base of Einstein's theory.
- Menger on the Calculus of Variations
- In this century Einstein's general theory of relativity has as one of its basic hypotheses such a minimal principle: that in our space-time world, however complicated its geometry be, light rays and bodies upon which no force acts move along shortest lines.
- Malcev: 'Foundations of Linear Algebra' Introduction
- At about the same time the development of differential geometry for many -dimensional spaces and of the theory of transformations of algebraic forms of higher powers led to the creation of the tensor calculus, upon which was built the theory of relativity.
- EMS 1934 Colloquium 1.html
- Courses of lectures are being delivered on "World-Structure by the Kinetic Methods of the Special Theory of Relativity," by Professor E A Milne, Oxford; on "Ramanujan's Note-Books and their Place in Modern Mathematics," by Professor B M Wilson, Dundee; on "Pictorial Geometry," by Professor H W Turnbull, St Andrews; and on "Some Expansions Relating to the Problem of Lattice Points," by Mr W L Ferrar, Fellow of Hertford College, Oxford.
- EMS 1913 Colloquium 5.html.html
- Professor Conway delivered his concluding lecture on "Relativity." The ideas of Minkowsky were explained.
- EMS 1938 Colloquium 2.html
- Professor E T Whittaker Is giving a course on "The Interactions between the Elementary Particles of the Universe." The first lecture dealt with the modifications which the Newtonian theory has undergone in consequence of the discovery of Relativity.
- J L Synge: 'Geometrical Optics
- Or we may think of the Newtonian theory of gravitation, long regarded as "perfect", but now "ideal", physically replaced by the "perfect (but not so "useful") general theory of relativity.
- EMS 1913 Colloquium 2.html.html
- Professor A W Conway delivered his second lecture on "Relativity." In the course of the lecture the relations between the coordinates and time in the two systems of reference were deduced.
- A D Aleksandrov's view of Mathematics
- Nevertheless, his ideas laid the foundation for a new development of geometry, namely the creation of theories of various non-Euclidean spaces; and these ideas subsequently became the basis of the general theory of relativity, in which the mathematical apparatus consists of a form of non-Euclidean geometry of four-dimensional space.
- Cartan's books
- On manifolds with an affine connection and the theory of general relativity (Bibliopolis, Naples, 1986).
- EMS 1913 Colloquium 4.html.html
- The fourth lecture on "Relativity" was delivered by Professor Conway.
- Finlay Freundlich's Inaugural Address
- This has been done by Einstein's general theory of relativity.
- W H Young addresses ICM 1928 Part 2
- The fact that Physics, today, is using at one and the same time the Theory of Relativity and the Newtonian Theory, is no indication of a Collapse of Science, preparatory to a Period of Scepticism.
- Keynes: 'Probability' Introduction Ch II
- In conclusion, the relativity of knowledge to the individual may be briefly touched on.
- EMS 1913 Colloquium
- A Course of Five Lectures by A W Conway, Esq., M.A., D.Sc., Professor of Mathematical Physics, University College, Dublin, on "The Theory of Relativity and the New Physical Ideas of Space and Time."
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- Hilbert reviews
- In the succeeding two de-cades, frequently with the help of his assistants, Hilbert applied his recently developed theory of integral equations to physical problems (e.g., the kinetic theory of gases) and discovered, simultaneously with Albert Einstein, the field equations of the general theory of relativity.
- Kline's books
- This account of the contributions made by mathematics to the sciences and arts, philosophy and religion, unfolds like a splendid epic from Euclid's 'Elements' to Einstein's theory of relativity.
- Publications of Gino Fano
- All geometry is theory of Relativity (University College of Wales, Aberystwvth, 1923).
- Aitken: 'Statistical Mathematics
- There thus arose a theory, or rather a succession of supplementary theories, of relativity, formulated on a new axiomatic basis by which the discrepancies of the earlier one might be reconciled, or removed.
- Sommerville: 'Geometry of n dimensions
- A third aspect, which has attracted much attention recently, from its application to relativity, is the differential aspect.
- EMS 1913 Colloquium 3.html.html
- Professor A W Conway delivered the third lecture on Relativity.
- EMS 1914 Colloquium
- A suggestion was then made as to the possibility of a moving aether, in which the laws of conservation of energy and momentum are retained, and which is consistent with the principle of relativity.
- Wolfgang Pauli and the Exclusion Principle
- While, in school in Vienna, I had already obtained some knowledge of classical physics and the then new Einstein relativity theory, it was at the University of Munich that I was introduced by Sommerfeld to the structure of the atom - somewhat strange from the point of view of classical physics.
- Halmos: creative art
- Withal, relativity theory and differential geometry are not the same thing.
- Levi-Civita: 'Lezioni di calcolo differenziale assoluto
- A similar standpoint was subsequently adopted by the most distinguished workers in the field of general relativity, in particular by Weyl, Laue, Eddington, and Birkhoff, all of whom made conspicuous original contributions, both of idea and of method, to the physical theories, in addition to useful and elegant developments of the tensor calculus.
- George Temple's Inaugural Lecture I
- There were the strange and puzzling experimental results of Arago, Fresnel, and Michelson; difficulty after difficulty in the theories of a universal aetherial medium for the transmission of light and electromagnetic action; and finally the sudden discovery by Einstein of the Special Theory of Relativity in the light of which all the optical phenomena form a harmonious whole.
- Hadamard on Hermite
- Hadamard wrote a fascinating article translated into English as How I did not discover relativity which appeared in volume 10, part 2, of the Mathematical Intelligencer in 1988.
- W H and G C Young
- My sister Cecily had impressed our friend Professor Hobson, by questions about Relativity when on her way to the Hospital for an appendictomy! Eventually we both obtained Research Fellowships at our respective Colleges.
- Whittaker RSE Prize
- His recent contributions to much-needed developments in the application of the relativity calculus were the latest instance in point.
- The Edinburgh Mathematical Society: the first hundred years (1883-1983) Part 2
- A W Conway, who was Professor of Mathematical Physics at University College, Dublin, spoke on 'The Theory of Relativity and the new Physical Ideas of Space and Time', Dr D M Y Sommerville, who was then Lecturer in Mathematics at St Andrews, spoke on 'Non-Euclidean Geometry and the Foundations of Geometry', while Whittaker himself lectured on 'Practical harmonic analysis; an illustration of Mathematical Laboratory practice.' The colloquium was a striking success, being attended by 77 participants from all over Great Britain.
- Studies presented to Richard von Mises' Introduction
- In drawing such a picture, the central task is to understand the relation between the direct sense observation of the experimental physicist and the conceptual system of science, which consists of expressions such as "increase of entropy" or "principle of relativity." Most physicists are inclined to say that the picture drawn and the principles devised by our inductive ability are eventually checked by actual measurement of physical quantities like length, weight, electric charge, etc., but they use the expression "measurement of a length" in a perfunctory way, forgetting that no numerical value can ever be assigned to a length by a single measurement.
- Three Sadleirian Professors
- He has applied the methods of differential equations to find systems of invariants and covariants that are algebraically complete, and given a complete discussion of certain differential equations that had been rather cursorily dealt with by writers on relativity.
- EMS 1914 Colloquium 3.html
- A suggestion was then made as to the possibility of a moving aether, in which the laws of conservation of energy and momentum are retained, and which is consistent with the principle of relativity.
- James Jeans addresses the British Association in 1934
- Thus we find that space and time cannot be classified as realities of nature, and the generalised theory of relativity shows that the same is true of their product, the space-time continuum.
- EMS 1938 Colloquium 4.html
- Professor Whittaker covered this immensity, and described the stages in which the transformation took place, through relativity, the early quantum theory and its developments up to the latest speculations on heavy electrons and cosmic rays.
Quotations
- Quotations by Einstein
- Since the mathematicians have invaded the theory of relativity, I do not understand it myself anymore.
- If my theory of relativity is proven successful, Germany will claim me as a German and France will declare that I am a citizen of the world.
- The relativity principle in connection with the basic Maxwellian equations demands that the mass should be a direct measure of the energy contained in a body; light transfers mass.
- Sidelights on Relativity
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- Sidelights on Relativity
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- Sidelights on Relativity
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- Quotations by Bondi
- It does not matter whether this room is created by allowing for arbitrary forces as Newtonian dynamics does, or by allowing for arbitrary equations of state for matter, as General Relativity does, or for arbitrary motions of charges and dipoles, as Maxwell's electrodynamics does.
- Quotations by Russell
- [Upon hearing via Littlewood an exposition on the theory of relativity:]
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- Quotations by Born
- Einstein's Theory of Relativity
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- Quotations by Wiener Norbert
- The modern physicist is a quantum theorist on Monday, Wednesday, and Friday and a student of gravitational relativity theory on Tuesday, Thursday, and Saturday.
Chronology
- Mathematical Chronology
- Levi-Civita and Ricci-Curbastro publish Methodes de calcul differential absolu et leures applications in which they set up the theory of tensors in the form that will be used in the general theory of relativity 15 years later.
- Poincare gives a lecture in which he proposes a theory of relativity to explain the "Michelson and Morley experiment".
- Einstein publishes the special theory of relativity.
- It is a key ingredient of general relativity.
- Einstein submits a paper giving a definitive version of the general theory of relativity.
- Shing-Tung Yau is awarded a Fields Medal for his contributions to partial differential equations, to the "Calabi conjecture" in algebraic geometry, to the positive mass conjecture of general relativity theory, and to real and complex Monge-Ampere equations.
- Chronology for 1900 to 1910
- Levi-Civita and Ricci-Curbastro publish Methodes de calcul differential absolu et leures applications in which they set up the theory of tensors in the form that will be used in the general theory of relativity 15 years later.
- Poincare gives a lecture in which he proposes a theory of relativity to explain the "Michelson and Morley experiment".
- Einstein publishes the special theory of relativity.
- It is a key ingredient of general relativity.
- Chronology for 1980 to 1990
- Shing-Tung Yau is awarded a Fields Medal for his contributions to partial differential equations, to the "Calabi conjecture" in algebraic geometry, to the positive mass conjecture of general relativity theory, and to real and complex Monge-Ampere equations.
- Chronology for 1890 to 1900
- Levi-Civita and Ricci-Curbastro publish Methodes de calcul differential absolu et leures applications in which they set up the theory of tensors in the form that will be used in the general theory of relativity 15 years later.
- Chronology for 1910 to 1920
- Einstein submits a paper giving a definitive version of the general theory of relativity.
This search was performed by Kevin Hughes' SWISH and Ben Soares' HistorySearch Perl script
JOC/BS August 2001