Space-time
The concept of space-time was introduced in the early 1900′s and endorsed notably by Minkowski in 1908 in a presentation on the mathematical geometry of space and time as it was defined by the theory of relativity of Albert Einstein . It was published in 1905 an article on the basic laws of electromagnetism on the electrodynamics of moving bodies 1 .
This theory is one of the great upheavals in the early xx th century in the field of physics . (See also the problem of “ether” .)
The dimensions of space-time continuum
The continuum spacetime has four dimensions: three dimensions for space, x, y, and z, and for a time t. In order to handle more easily, it is seen that these four variables are homogeneous at a distance by multiplying by the constant t c (speed of light in vacuum).
An event is positioned in time and space by its coordinates ct, x, y, z which depend all the repository .
It is very difficult to imagine that time is not the same after the repository where it is measured. It is however well confirmed by the observation in particle accelerators of CERN [ref. needed] and the study of cosmic rays where the distance traveled by unstable particles would be impossible if their own time was not significantly slowed their speed. See Little thought experiments .
The time depends on the repository where it is measured and is not absolute. It is the same for space. The length of an object can be different according to the reference measurement.
In the present state of knowledge, the only space-time as a unified concept, which is mathematically a Minkowski space in special relativity and curved space in any general relativity is invariant regardless of the chosen reference, while its components space and time are aspects that depend on the point of view (reference).
The relationship between measures of space and time given by the universal constant c is used to describe a distance d in terms of time: d = ct with t the time required for light to travel to .
The sun is 150 million km that is to say eight light minutes from Earth . By saying “light minutes”, we speak of a measure of time multiplied by c, we obtain a distance measurement, in this case, for miles. In other words c is used to convert units of time in units of distance. Miles and light-minutes are two units of distance measurement.
What unifies space and time in the same equation is that the measuring time can be converted to distance measuring equipment (by multiplying t, expressed in units of time, c), and t can thus be associated with three other contact distance in an equation where all measurements are in units of distance. In this sense one could say that time is of space! (Or rather a movement in space)
Under certain conditions, the edge of a wormhole , the direction in which we are inevitably drawn to this implacable character of the time (the ” arrow “of time), then one can in theory, according to Kip Thorne , up by respect to time 2 .
But John Wheeler cautions that the time and space have large differences in nature, are not fully identifiable and do not turn that part into one another in a change of reference frame.
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Albert Einstein
Albert Einstein in 1947.
Birth 14 March 1879
Ulm ( German Empire )
Death 18 April 1955 (76 years)
Princeton ( USA )
Nationality Germany (1879-1896 and 1919-1933) Switzerland (1901-1955) Austrian (1911-1912) American (1940-1955) Einstein was stateless , and has had several dual nationality
Fields Physical
A graduate of ETH Zurich
Known for His work on relativity, particle nature of light, and its influence beyond the world of physics
Awards Nobel Prize in Physics (1921) Copley Medal (1925) Max Planck Medal (1929)
Signature
change
Albert Einstein (born 14 March 1879 in Ulm , Württemberg , and died 18 April 1955 in Princeton , New Jersey ) is a theoretical physicist who was successively German and stateless person (1896), Switzerland (1901), and finally in the double nationality Helvetian – American (1940) 1 .
He published his theory of relativity in 1905 , and a theory of gravity called general relativity in 1915 . It contributes significantly to the development of quantum mechanics and cosmology , and received the Nobel Prize for Physics in 1921 for his explanation of the photoelectric effect 2 . His work is especially known for the equation E = mc 2 , which establishes an equivalence between matter and energy of a system.
His father, Hermann Einstein, was born on 30 August 1847 at Buchaun, and died on 10 October 1902 in Milan . He married Pauline Koch on 8 August 1876 . Three years later, on 14 March 1879 , Albert Einstein is born in their apartment in Ulm in Germany , it is their first child. His interest in science was awakened in her childhood by a compass at age five, and the book The Little Bible of the geometry , at thirteen.
Einstein died on 18 April 1955 of a ruptured aneurysm , and the autopsy revealed that his brain is marked hypertrophy of the left hemisphere. His ashes were scattered in an undisclosed location, according to his will. But despite his last wishes, his brain and his eyes are preserved by the medical examiner who performed the autopsy .
Training
He completed his primary and secondary education at the Hochschule of Aargau in Switzerland , where he graduated on 30 September 1896 . It has excellent results in mathematics , but refuses to learn in biology and human sciences , because it does not see the interest in learning the disciplines he considers already widely explored. It then considers science as the product of human reason and reflection. He asks his father to give him the Swiss to join his family emigrated to Milan in Italy .
He entered the Federal Institute of Technology Zurich (ETH) in 1896 , however, after having missed his first entrance examination. He made friends with the mathematician Marcel Grossmann , who helps later in non-Euclidean geometry . He also met Mileva Maric , his first wife. He obtained his degree in accurately 1900 admitting himself in his autobiography, “unable to attend classes, take notes and to work in a school 3 . ”
During this period, he deepened his knowledge of self trottinette freestyle by reading reference books, such as Ludwig Boltzmann , the Helmholtz and Hermann Walther Nernst . His friend Michele Besso introduced him to the ideas of the mechanics of Ernst Mach . According to several biographies, this period of 1900 to 1902 was marked by the precariousness of his situation: he applied for many jobs without being accepted. The misery of Albert Einstein concerned his father, who tried in vain to find a job. Albert resigned while away from academia for a job in administration.
Career from 1901 to 1916
In 1901 , he published his first scientific paper in the Annalen der Physik , and this article is dedicated to his research on the capillary .
at the end of 1902 was born the first of the children of Albert Einstein , Lieserl . Its existence was long ignored by historians, and there is no available information on its future. Albert and Mileva were married in 1903 , his father had finally given his permission on his deathbed. In 1904 , the couple gave birth to Hans Albert , and in 1910 was born Eduard Einstein .
In 1902 , he was hired at the patent office 4 of Bern , which enables him to live well while continuing its work. During this period, he founded the Academy Olympia with Conrad Habicht and Maurice Solovine , who translated his works later in French. The Talking Circle meets at 49 Street Kramgasse and organizes mountain walks. Einstein shared the results of its work with Conrad Habicht and sends the articles he published during the year 1905 on the foundations of special relativity , the quantum hypothesis of light and the theory of Brownian motion , and that open new directions in research in nuclear physics , celestial mechanics , etc.. The article on the Brownian motion is based on work that Einstein developed later and which lead to his thesis , titled Eine neue Bestimmung der Moleküldimensionen (“A new determination of molecular dimensions” in German ), and its degree Ph.D. Joann Fabric coupons January 15, 1906 3 .
In 1909 , Albert Einstein is recognized by his peers, especially Planck and Nernst who wish to invite him to the University of Berlin. On 9 July 1909 , it is distinguished honorary doctorate by the University of Geneva 3 . The jobs are increasing. In 1911 , he was invited to the first Solvay Conference in Belgium, which brings together the most famous scientists. There he met among others Marie Curie , Max Planck and Paul Langevin . In 1913 , Albert was appointed to the Prussian Academy of Sciences.
In 1914 , he moved to Germany and lived in Berlin for many years. He became a member of the Royal Academy of Sciences and Arts in Berlin . The job offers he receives allow him to devote himself entirely to his research. Mileva and Albert separated, and the latter begins to attend a cousin in Berlin, Elsa. At the beginning of the conflict of the First World War, he says his pacifist views. The city of Berlin had undertaken to provide a home, but Albert Einstein finally gets a ground on which he built a house at his expense. Located in Caputh, near Lake Havelsee, the place is quiet and allows him to frequently sail.
In 1916 he published a book presenting his theory of gravitation, known today as the general relativity . In 1919 , Arthur Eddington realized the extent of the deviation that the light undergoes a star near the Sun, this is a deviation from predictions of this theory. This event is publicized, and Einstein began in 1920 traveled extensively throughout the world. In 1925 he won the Copley Medal , and in 1928 he was appointed president of the League of Human Rights . He participated in 1928 the first university course in Davos , with many other French and German intellectuals. In 1935 , he became a recipient of the Franklin Medal .
The situation in Germany in the dark year 1920 , and it is under attack for its origins Jewish and opinions pacifist . Its security is threatened by the rise of nationalist movements including that of the Nazi party. Shortly after the arrival of Hitler to power in early 1933, he learned that his house in Caputh was looted by the Nazis, and he decides not to return to Germany. After a short stay on the Belgian coast, he moved to the United States , where he worked at the Institute for Advanced Study in Princeton . His research aims to develop a theory unifying gravitation and electromagnetism, denver injury attorney but without success, which can be diverted from other research in areas most successful.
On 2 August 1939 , under pressure from Eugene Wigner and Szilard Leó , physicists from Germany, he wrote a letter to Roosevelt that helps initiate the Manhattan Project 5 .
His son Eduard, suffering from a possible schizophrenia , spends most of his life in a clinic in Switzerland, and his other son Hans Albert became an engineer in California.
Scientific work
The year 1905
The year 1905 was a successful year for Einstein, four of his articles being published in the journal Annalen der Physik :
The first article, published in March, presents a revolutionary point of view on the corpuscular nature of light , the study of the photoelectric effect . Einstein entitled: On a heuristic point of view concerning the production and processing of light . He describes his research on the origin of particulate emissions, based on the work of Planck who, in 1900 , established a formula for a quantized radiation, that is to say discontinuous. Planck was forced to approach the light radiation emitted by a hot body in a way that disconcerted him: to align its formula and the experimental results, he had to assume that the stream of particles was divided into blocks of energy, which he called quanta . Although he thought that these quanta had no real existence, his theory seemed promising, and many physicists worked there. Einstein reinvests the results of Planck to study the photoelectric effect, and concludes by stating that light behaves as both blu cigs coupon a wave and a stream of particles . The photoelectric effect has provided a simple confirmation of the hypothesis of quanta of Max Planck . In 1920, the quanta were called photons .
Two months later, in May, Einstein published a second paper on Brownian motion . He explained this movement by a complete breach with the principle of entropy , as set out following the work of Newton on the mechanical forces: according to him, the molecules would derive their kinetic energy to heat . This article provides a theoretical evidence (verified experimentally by Jean Perrin in 1912) the existence of atoms and molecules. Brownian motion was explained at the same time as Einstein by Marian Smoluchowski and Louis Bachelier in 1900.
The third article is even more important because it represents the breakdown of Einstein with the intuitive Newtonian physics . In the On the electrodynamics of moving bodies , the physicist tackles the assumption of a space and absolute time, as defined by Newtonian mechanics, and the existence of the ether , the interstellar medium inert support, which was light as the water or the air support in the sound waves travel. This article, published in June, leads to two conclusions: the ether does not exist, and the time and space are relative. The new absolute Einstein builds is detached from the quantitative nature of these two notions of space and time, but are bound by the conservation of their relationship through the various repositories of study. The consequences of this revolutionary vision of physics, which stems from the idea that Einstein had of how physical laws should compel the universe, have pushed both theoretical physics as its practical applications. The exact contribution of Einstein from Henri Poincaré and some other physicists has now played enough (see Controversy over the authorship of relativity ).
The last article, published in September, gives under the inertia of a body depend upon its energy content? answer famous formula of mass-energy equivalence, E = mc 2 . This is a result of the new relativity , which derive a large field of studies and applications: nuclear physics, celestial mechanics, and weapons and nuclear power plants , for example.
Recognition years (1910-1935)
Albert Einstein and Niels Bohr at the Solvay Congress of 1930
Albert Einstein in 1921
His former classmate Marcel Grossmann help in its work by providing knowledge in differential geometry: they publish an article on the Ricci tensor and Riemann-Christoffel in 1913. In October 1914, Einstein published an article on differential geometry, and in June 1915 , he lectured at the University at Göttingen Hilbert and Klein.
In 1916 , Einstein published his theory of the so-called general relativity . The “field equations” are the cornerstone of this theory. They describe the behavior of the gravitational field (the metric of space-time) based on energy content and material. The theory of relativity and his works of 1905 and 1916 form the basis of modern physics.
The theory of general relativity published, Einstein begins work on quantum physics and introduced in 1917 the concept of stimulated emission, which allows it to recover the Planck’s law from purely quantum assumptions about how the quanta light ( photons ) are absorbed and emitted by atoms 6 . Fruitful idea which underlies the development of the maser and laser . The same year, Einstein shows that should be involved in a momentum quantum light hypothesis will be validated by experience in 1923 through the work of Arthur Compton on X-ray scattering 6 .
The relationship of quantum physics with Einstein nascent is remarkable: on the one hand, many of his works are the basis for the development of this new physics, such as his explanation of the photoelectric effect, on the other hand, it criticize a lot of ideas and interpretations of quantum mechanics , the non-determinism in particular. The debate between the group formed by Einstein and Erwin Schrödinger , and that of Niels Bohr and Werner Heisenberg was at the border of physics and philosophy.
In 1927 , invited to the fifth Solvay Congress , he has many conversations with Niels Bohr about it. He said: ” Gott würfelt nicht “(” God does not play dice “
to mark its opposition to the interpretation of probability in quantum physics, what Niels Bohr said, “Who are you to tell Albert Einstein God what to do? “. The EPR paradox specified in 1935 with Boris Podolsky and Nathan Rosen in Princeton today remains an important example of an attempt to question the foundations of quantum mechanics.
Verification by the eclipse
To verify general relativity, a measure of the deviation of light rays around a mass during a solar eclipse is electronic cigarettes considered. The first shipment is expected in 1915 , but is prevented by the First World War . In 1919 , Arthur Eddington realized this and announced that the results are consistent with Einstein’s theory. It appears much later that because of cloudy weather, the margin of error was far superior to the phenomenon being measured. The physicist Stephen Hawking says in 1988 in his book A Brief History of Time that this kind of false positive result is common when you know what to expect. Like other measures had since confirmed the deflection of light, the validity of general relativity was not shaken.
Personality
Einstein and politics
Political positions taken by Einstein’s opinions are marked by peace , sometimes it into perspective, for example by discouraging the conscientious objection to a young European who wrote it during the year 1930 , “to safeguard the country and civilization “. In 1913 , he co-signer of a petition for peace three other German scientists agree to sign. Einstein felt a strong antipathy vis-à-vis the military institutions, publishing in 1934: “The worst is named institutions gregarious army. I hate her. If a man can experience some pleasure to march in rank to the sounds of music, I despise this man … He does not deserve a human brain, spinal cord, since the content. We should get rid of as soon as possible this cancer of civilization 7 . “Einstein is linked to many causes peace, as it appears open to supporting multiple proposals it receives, and often agrees to commit to causes it deems just.
During the Cold War , he spoke against the arms race and calls, for example with Bertrand Russell and Joseph Rotblat , scientists more responsibility, governments in a common renunciation of the proliferation of nuclear weapons and their use, and people to look for other ways to achieve peace (creation of the Emergency Committee of Atomic Scientists in 1946 , Russell-Einstein Manifesto in 1954). He repeatedly expressed his conviction on the need to create a world state. He spoke strongly against the United States, saying: “The United States of America is a country that has gone directly from barbarism to decadence without ever having known civilization. ”
Einstein and Robert Oppenheimer .
On 2 August 1939 , he wrote a letter to Roosevelt that helps initiate the Manhattan Project 8 . In 1945 , when he understands that the U.S. will make the first atomic bomb in history, he took the initiative to write again to Roosevelt asking him to give up this weapon 9 . After the war, Einstein argues for a global nuclear disarmament, to the threshold of his death in 1955 , where he confesses to Linus Pauling : ” I made a big mistake in my life when I signed the letter [of 1939]. ”
Einstein gives strong support to the movement Zionists . In 1920, he accompanied and the Zionist leader Chaim Weizmann in the United States during a campaign fundraising. It also makes mandatory Palestine as part of the inauguration of the Hebrew University of Jerusalem to which he bequeathed his personal archives Denver Divorce Attorney later. His appearances give political prestige to the Zionist cause. Following an invitation to settle in Jerusalem, he wrote in his travel diary that “the heart says yes [...] but the reason for saying no.” According to Tom Segev , Einstein enjoys his trip to Palestine and the honors that are made. He registered his disapproval, however, seeing the Jews pray at the Wailing Wall , Einstein says that these people stuck in the past and but for this 10 .
It has a clear vision of the developments between the wars in Germany : “For now, I am a German scientist, but if I have to become a pet peeve, I will be a Swiss Jew.” He received death threats since 1922 . Violent attacks take place against his theory of relativity in Germany and Russia . Philipp Lenard , “head of the Aryan or German Physics” attributed to Friedrich Hasenöhrl the formula E = mc 2 into a creative Aryan 11 , 12 . Einstein resigned – just free iPhone ringtones in time – of the Academy of Prussia in 1933 and is excluded from that of Bavaria. In March 1933, as honorary president of the League against Anti-Semitism, he appeals to the civilized peoples of the universe, trying to “raise awareness of all countries who remain faithful to humanism and political liberties “in the appeal he protested against” acts of brute force and oppression against all people of free spirit and against the Jews, held in Germany 13 . “In that year, Einstein is traveling abroad, and he chose not to return to Germany, where Hitler took power in January. After a stay in Belgium, he declined a proposal by France to welcome him as a professor at the College de France, and left for the United States, at Princeton .
After the Second World War, his commitment vis-à-vis the Jewish community and Israel, is qualified by his pacifist views. He prefaces the Black Book , a collection of stories about the extermination of Jews in Russia by the Nazis during the war 14 . And December 1948 , he co-signed a letter condemning the Deir Yassin massacre committed by Israeli fighters of the Irgun and Lehi during the Palestine war of 1948 15 .
Ben-Gurion offered him in 1952 as President of the State of Israel , he refused: “First, if I know the laws of the universe, I know almost nothing about human beings. In addition, it appears that a president of Israel should sign some of the things he disapproves, and no one can imagine that I can do that. ”
Einstein stayed for six months to De Haan ( Belgium ) in 1933. Johnny Werbrouck created a bronze statue in 2006.
Einstein spoke about his socialist convictions in 1949 , at the height of McCarthyism , in an essay entitled Why Socialism , published in the Monthly Review 16 . It seems that the principle of government by the people themselves, the fact of working for themselves, is more conducive to personal development than the exploitation of many by the few. But he is disappointed by what he can learn from the Soviet Union , and he believes that people must engage primarily in the Pacific to establish conditions for an evolution towards socialism . His correspondence reveals that he sees a connection between McCarthyism and the events of the year 1930 in Germany. He wrote to the judge in the Rosenberg case to ask for their grace and help of many people who wish to immigrate to the United States. Contacted by William Frauenglass, a high school English teacher suspected of Communist sympathies, he wrote a text denouncing McCarthyism openly and encouraging intellectuals to resist what he calls “evil.” The FBI opened a file on him, now available on their website 17 . Joseph McCarthy Einstein attack in Congress, calling him an “enemy of America.” His secretary, Helen Dukas (in) , is suspected of espionage in the service of the USSR . The American media is virulent in their handling of the case, and only a few personalities, such as Bertrand Russell , take its defense. Case closed in 1954, no conclusive evidence have been provided to substantiate the charges.
Social life
Although Einstein had met many important figures of his time in the scientific, political and artistic, leaving a rich correspondence, he described himself as a real loner “who never belonged to any heart to the State, native to the circle of friends and family even in the narrow sense, but has always had the respect of all these connections never weakened a sense of their being abroad 18 . ”
Among Crossfit Denver his famous relations include a friendship with Queen Elizabeth of Belgium , with whom he plays the violin , Arnold Berliner which he testifies to the affection in his 70 th birthday 19 , George Bernard Shaw about which he wrote “we rarely find men enough to realize independent weaknesses and follies of their contemporaries, without being infected themselves, 20 “or Bertrand Russell 21 .
Modest and thinking about him, “Everyone should be respected in his person and no one should be idolized. “He joked about his celebrity and its effects:” This may well come from the unattainable desire for many to understand some ideas I found in a constant struggle with my feeble forces 22 . ”
His first wife, Mileva Maric is suffering from hip disease , which makes it lame. It is also a bright young woman, a student of Polytechnic. She becomes pregnant while they are still married, and she gives birth to her parents in Serbia of a daughter, Lieserl. Einstein was very hard with his girlfriend next Elsa. They were in separate rooms and he happened to forbid his desk, doing almost used “I treated my wife as an employee, an employee but I could not fire [ref. needed] . ”
He sees not his son Hans Albert, who, as adults, working in California. The mental health of his other son, Eduard, deteriorates sharply when he was twenty years old and must be committed for the first time in Zurich in 1930. His father makes one last visit in 1933. First criticism of psychoanalysis, he refused to follow his son Eduard new psychoanalytic treatment [ref. needed] , but finally accepted the essential ideas of Sigmund Freud. In 1933 , he chose Sigmund Freud to publish an exchange of letters titled Why War? .
Einstein and Religion
Einstein wrote several texts dealing with the relations between science and religion . In his article published in 1930 23 , Einstein distinguished three forms of religion:
the first is due to the fear and misunderstanding of causation of natural phenomena, hence the invention of supernatural beings.
The second is social and moral.
The third, that Einstein called “cosmic religiosity” is a contemplation of the structure of the universe . It is compatible with science and not associated with any dogma or belief. Einstein said to be religious, but only in this third sense that it sees the word religion.
When, in 1929, Rabbi Herbert S. Goldstein asked “Do you believe in God? “Einstein replied:
“I believe in the God of Spinoza , which proves itself in the harmonious order of what exists, not in a God who cares about the fate and actions of human beings. ”
Einstein has often used the word God, however, the meaning he gave to this word is the subject of various interpretations. Part of the clergy found that Einstein’s views were consistent with the faith. In contrast, the Vatican denounced then “genuine atheism even if it is hidden behind a pantheistic cosmic 24 . ” If Einstein rejects traditional beliefs, it stands personally atheists and repeats that he is “a deeply religious nonbeliever. “In a letter to philosopher Eric Gutkind , Einstein wrote:
“The word God is for me nothing more than the expression and product of human weaknesses, the Bible a collection of legends, but certainly honorable primitives which are nevertheless pretty childish. No interpretation, as subtle as it is, in my opinion can not change that ” 25 “.
Einstein also respond to a reporter asking him if he believes in God:
“Set me first what you mean by God and I will tell you if I believe 26 . ”
A militant atheism as Richard Dawkins also believes that Einstein’s position was only atheism embellished poetically 27 . During the poster campaign with slogans in favor of atheism on London buses in 2008 (supported by Dawkins), a quote from Einstein was used. This caused protests because such use has a tendency to equate Einstein an atheist 28 .
Einstein and philosophy
The philosophy is not one of his areas of expertise, but Albert Einstein expressed interest in the vision of humanity’s proposed Friedrich Nietzsche [ref. needed] and some ideas present in the thoughts of Spinoza . However, it brings a new vision of the modern world by Wire Shelving his scientific work as unscientific by his works. Thus, in his book How I see the world published in 1934 , a year after its installation in the United States , Albert Einstein presented his vision of humanity, and raises the question of the place of science vis-à-vis humanity. This work may have some influence on philosophers like Martin Heidegger and Jean-Paul Sartre [ref. needed] .
Einstein and astrology
Unlike the quote attached to it by many publications, particularly that of the astrologer Elizabeth Teissier , Einstein did not believe in the astrology .
The apocryphal quote attributed to him is: “Astrology is a science in itself illuminating. I learned a lot from her and I owe him a lot. Geophysical knowledge highlight the power of the stars and planets on earthly destiny. In turn, in a sense, astrology reinforces it. That’s why it’s a kind of elixir of life for humanity. ”
This originates from the false Huter astrologischer Kalender in 1960 , published in 1959 . The phrase has been coined about five years after Einstein’s death 29 .
His negative opinion about astrology is expressed in an introduction written in 1951 for the work of Carola Baumgardt 30 . Einstein said that Kepler was able to accept that experience alone could decide the validity of a mathematical theory, as beautiful as it is. He then quotes astrology as an illustration, in the thought Keplerian, a balance of thinking theologically oriented animist and omnipresent in the “scientific” research of the time.
Einstein and vegetarianism
Albert Einstein supported the cause vegetarian . He sees vegetarianism as an ideal not yet the practice itself, despite some problems of conscience 31 . His arguments are mainly based on health reasons, but he also believes in the beneficial effect of vegetarian diet on the temperament of men 32 . A year before his death, he decides to put his ideas into practice and started a vegetarian diet 33 .
Einstein’s brain
In 1978 , journalist Steven Levy tells his employer the newspaper New Jersey Monthly as the brain of the scientist would have been preserved and asks him to retrieve it.
Levy is accompanied by a cameraman in his quest and the film is released in the year 1990 on television in France . After a lengthy investigation, he found, in fact, Wichita ( Kansas ), in the pathologist who had conducted its extraction, D r Thomas Harvey. This information raised media interest.
The D r Harvey said he had found nothing special about the physical structure of Einstein’s brain may explain his genius. But more recent studies, including published and Life Science , conclude that Einstein’s brain had a high number of astrocytes . According to the first physician licensed to autopsy the brain of Albert Einstein in the 1980s, Marian Diamond, some areas of the brain reserved for the highest duties, had a proportion of glial cells incredibly high, “there is evidence that glial cells play a key role in the development of intelligence 34 . ”
A thorough study of brain structure also reveals that the Sylvian fissure has a particular inclination, increasing the size of the area of abstract reasoning to the detriment of the area of language, which could explain that Einstein had been able to speak very late.
Inventions and Patents
Einstein also invented devices and many patents in collaboration with friends:
Voltmeter sensitivity: In 1908, with Paul Habicht, he developed a voltmeter capable of measuring voltages of the order of one ten-thousandth of a volt . This “multiplier potential Einstein-Habicht” was marketed from 1912.
Refrigerator: With his former student and friend Leó Szilárd , it creates several types of refrigerators (an absorption system, a system and broadcast an electromagnetic system). The latter system uses an “electromagnetic pump” which is still used to transport sodium in fast reactor sodium-cooled (2005). Refrigerators have been sold.
Hearing aid: A forty patents with Leó Szilárd .
Various
An einstein is a unit of measurement equal to Avogadro’s number times the energy of a photon (light). There is a chemical element : the einsteinium .
2005 was the World Year of Physics, but also the year of Einstein, in commemoration of the centenary of the annus mirabilis .
Awards
1921 : Nobel Prize in Physics
1929 : Max Planck Medal
1931 : Jules Janssen Award
1935 : Franklin Medal
Scientific articles (selection)
Zur Elektrodynamik bewegte Körper . In: Annalen der Physik 17/1905, pages 891-921, translated into French (Gauthier-Villars, 1925, edition Gabay 2005) “On the Electrodynamics of Moving Bodies.”
Über einen und die Erzeugung Verwandlung of Lichter betreffenden heuristischen Gesichtspunkt . In: Annalen der Physik 17/1905, pp. 132-48, trans. “A heuristic point of view regarding the design and transformation of light”
Ist die eines Trägheit Körpers von seinem Energieinhalt abhängig? In: Annalen der Physik 18/1905, pages 639-641, translated into French (Gauthier-Villars 1925) “The inertia of a body depend upon its energy capacity ? ”
Zur Quantentheorie der Strahlung. In: Mitteilungen der Gesellschaft Zürich Physikalischen 18/1916 und Physikalische Zeitschrift 18 / 1917, p. 121 et seq., Trans. “On the quantum theory of radiation”
Über Gravitationswellen , Reports of the Prussian Academy of Sciences (Berlin), 1918, 154, trans. “Gravitational waves”
(With Boris Podolsky and Nathan Rosen ) Can Quantum Mechanical Description of Physical Reality Be Considered Complete? , Physical Review , May 15, 1935, trans. “The description of physical reality by quantum mechanics can be regarded as complete? ”
In addition, a selection of works of Einstein, including his original scientific articles, are available in French translation with commentary under the title Selected Works by Editions du Seuil / CNRS editions in the collection of knowledge sources (6 volumes published since 1989).
Françoise Balibar (ed.), Albert Einstein: physics, philosophy, politics , Editions du Seuil, ( ISBN 978-2-02-039658-5 ) . Paperback that contains “selected passages” from the previous selection.
Other works
Albert Einstein ‘s theory of special and general relativity . (1916, French edition Gauthier-Villars 1956)
Why War ? . (1933) Shores, 2005, ( ISBN 978-2-7436-1364-8 ) , with Sigmund Freud .
How I see the world . (1934, French edition Flammarion 1934), Flammarion edition, 1989, 183 Fields collection, ( ISBN 978-2-08-081183-7 ) . Politico-philosophical essay, which Einstein explains his positions in different areas: social, economic, political, religious, cultural and scientific.
Albert Einstein: Relativity . Gauthier-Villars (1956) . Pocket-sized, a statement of basic principles of the theory of special and general relativity, by its author.
Albert Einstein & Leopold Infeld : The Evolution of Physics . Collection Champs, Flammarion (1993), ( ISBN 978-2-08-081119-6 ) . In paperback, a history of physics, Newtonian mechanics to the modern theories (relativity, quantum), written in 1936 by Einstein and one of his disciples to Princeton, to finance the stay of the latter.
Albert Einstein Why Socialism?
Technical Institute of California ( Caltech ) shall, with the help of the Hebrew University of Jerusalem , the complete writings of Einstein, The Einstein Papers Project . It is rather an issue for libraries
Relativity
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For items uses, see relativity .
The relativity is the formal theory developed by Albert Einstein in 1905 to draw all the physical consequences of the Galilean relativity and the principle that the speed of light in vacuum has the same reputation management value in all inertial frames , which was implicitly stated in the Maxwell equations (but interpreted very differently so far, with “absolute space” of Newton and the ether ).
Galilean relativity states, in modern language, that every experiment in an inertial frame would run exactly the same way in any other inertial frame. Become a ” principle of relativity , “his statement as modified by Einstein to be extended to non-inertial reference systems : the “restricted”, relativity become ” general “.
The theory of relativity introduced new formulas to move from one inertial frame to another. The corresponding equations lead to phenomena that offend common sense (but none were set aside by the experience ), one of the most surprising is the slow moving clocks one who helped design the thought experiment often called twin paradox . The phenomenon is also sometimes used in science fiction 2 .
Relativity also had an impact in philosophy by eliminating any possibility of existence of an absolute time and duration across the universe (Newton) or as a framework a priori from our experience ( Kant ). As a result of Henri Poincare , it forced the philosophers to ask the different question of time and space .
Origins of the theory
Stamp Soviet representative Albert Einstein.
A Brief History
History of Relativity
In Newtonian mechanics , the speed add up to a change of reference is the Galilean relativity : if a rocket moving at the speed of 7 km / s relative to Earth is pulled a cannonball forward at a speed of 1 km / s relative to the rocket projectile velocity relative to Earth will be 8 km / s. If the ball is pulled back, its speed will be 6 km / s.
At the end of xix th century , James Clerk Maxwell establishes the equations governing the electromagnetic waves, including light waves 3 . According to this theory the speed of light should depend only on the electric and magnetic properties of the medium, which was a problem if the medium is the vacuum because it suggests an independence of the speed of light relative to the repository the measuring instrument: if one emits a light beam from the rocket forward or backward, the speed of light measured relative to the Earth will be the same, unlike the ball. The hypothesis of the ether , the propagation medium of light, therefore quite natural assumption was to remove light to this property and its spread compatible with Galilean relativity. In 1887 an experiment was conducted by Michelson and Morley to measure the speed of the Earth relative to this ether: experience similar to that of the rocket described above, and where the earth is itself the role of the rocket . They wanted to measure the speed by highlighting the difference in the speed of light between different possible directions of propagation. Did not detect a significant difference, the result of this experiment proved difficult to interpret, so much so that their authors went so far as to imagine a contraction, unexplained, measuring instruments in certain directions: relativity justify this later.
The transformation formulas to go from one observer to another were established by Hendrik Antoon Lorentz before 1904 [ref. needed] and it was compatibility equations whose meaning was not clear to the author. Other physicists had taken a similar approach even earlier. Henri Poincaré published articles to find free ipad an interpretation, shortly before Einstein 4 . The roles of any scholar in the emergence of the theory of relativity has been the subject of controversy , especially in the 2000s.
In 1905 , in his article On the Electrodynamics of Moving Bodies 5 , Albert Einstein introduced relativity as follows:
Ether is an arbitrary concept that is not useful for the expression of the theory of relativity.
The speed of light relative to observers does not depend on their speed.
The laws of physics respect the principle of relativity .
Lorentz equations that are derived are consistent with physical reality. Have unintended consequences. Thus an observer attributes to a moving body length shorter than the length assigned to the same body at rest and the duration of the phenomena that affect the body in motion is lengthened compared to the “same” time measured by observers immobile report to this body.
Einstein also rewrote the formulas that define the momentum and the kinetic energy in order to make them invariant in a Lorentz transformation.
Time and three space coordinates play inseparable roles in the equations of Lorentz, Hermann Minkowski ‘s interpretation in a space-time four-dimensional. Note however that the time and space are different in nature and we can not equate one to the other. For example you can turn around in space while it is impossible over time.
Attitude of the Nobel Committee
In 1912, Lorentz and Einstein were nominated for a Nobel Prize for their joint work on the theory. The recommendation was to Wien , winner of 1911, which states that “although Lorentz must be considered to be the first to have found the mathematical content of the principle of relativity, Einstein succeeded in reducing it to a simple principle. We should therefore consider the merits of the forex software reviews two researchers as comparable ” . Einstein never received a Nobel Prize for relativity, this price being, in principle, never allowed for a pure theory. The committee then waited an experimental confirmation. By the time it arises, Einstein was spent on other important work 6 .
Einstein will be finally awarded the Nobel Prize for Physics in 1921 7 “for his contributions to theoretical physics , especially for his discovery of the law of the photoelectric effect ” 8 .
Theory
The postulates of Einstein (1905)
Einstein’s theory is centered on the principle of relativity for observation and measurement hcg diet drops of phenomena based on the repository from which the observer (or measuring apparatus) performs the steps of the experiment.
Relativity only consider the case where the observer is in an inertial frame , the other repositories are the subject of study of general relativity . Recall that a repository is called inertial if any single object (which is exerted any force or on which the net force is zero) is either stationary or in uniform rectilinear translation movement. For example: a rocket into space away from any mass is an inertial frame if no motor is turned on.
The two postulates of special relativity are:
The laws of physics have the same form in all inertial frames
The speed of light in vacuum has the same value in all inertial frames
The first assumption is the principle of relativity itself, in its design restricted to the class of inertial frames. It formalizes a finding of Galilee that the uniform motion is “like nothing” for the observer belonging to the moving frame.
The second assumption formalizes the interpretation of Maxwell’s equations according to which there is no ether , and is consistent with experiments. One consequence is that light can be used identically in any inertial frame, as a means of communication in order to synchronize the clocks that are stationary.
We can do without the second postulate to determine the equations of the Lorentz transformations provided to introduce an additional assumption in the first premise: the space-time is homogeneous and isotropic. This fact was discovered in 1910 by Kunz 9 and independently by Comstock 10 . The hypothesis leads to an additional group of transformations depending on a parameter c 2 , physically homogeneous to the square of speed. These transformations are identified with changes in Galilee if c 2 is infinite and the Lorentz transformations if c 2 is positive over 11 . Identification of c the speed of light, as determined by the finite observations, results in the second postulate. Jean-Marc Levy-Leblond noted that this approach requires only the existence of a speed limit c , which is that all massless particles, and thus the light in our current theories. If the photon have a mass should be (see on this subject the physical properties of the photon ), relativity would not be questioned, but the light would have a speed slightly less than c , which depend on the reference 12 .
Synchronization of clocks
Main article: Time synchronization .
Let us in an ideal situation where the technical difficulties are overcome without even thinking.
In the reference of an observer, given a clock still used as a reference, it must be synchronized to another clock in the repository (that is to say a clock stationary in this reference). For this, we must determine the distance between the two: a unit for measuring length is known, and knowing that the speed of light (also known) does not depend on the repository, it is sufficient to determine the time taken by light to make the round trip between the two clocks, but a more manual might as well do the trick. Then, to set the two clocks so that they have the same unit of measurement of time and the same time zero, just that they communicate to the speed of light, and for the initialization of the zero time, we take into account the time taken for information to go from one to another.
Thus, if an event takes place far from the reference clock, it can be precisely located and dated by a clock close and motionless (in the repository).
Measuring time and length in the repositories
Two inertial frames are given, in uniform rectilinear translation with respect to another, how to make sure they have the same system of measuring time and length 13 ?
First, in a single repository, the assumptions of isotropy and the homogeneity of space implies that the measures that can be done on an object do not depend on its position in the repository.
By submitting duplicates of the unit of measurement and the reference clock of an inertial reference frame to another, they are subjected to an acceleration (to go from one to immobility in the immobility in the other), which implies that the double is not in an inertial reference frame during this phase but in an accelerated frame of reference: one can imagine that in this repository transitional properties are the same. But once acquired immobility in the new repository, the principle of relativity implies that they have the same properties as in their previous inertial frame: the units of measurement are the same in the two repositories. This will be the relative speed between the two standards that will give differences in measurements for the same experience.
The phenomenon of ” slow moving clocks “can not synchronize the clocks in motion relative to a reference, with those who are immobile.
Lorentz transformations
Main article: Lorentz Transformations .
System with axes parallel to facilitate the work
We consider two frameworks and the first reference speed being driven from the reference . To simplify the calculation we work primarily in the context of transformations “special”, characterized by the fact that the system of axes x, y, z and x ‘, y’, z ‘ are parallel, the axes O ‘x’ and Ox are common and parallel to the velocity , and assuming that when the origins of the two spatial reference systems were combined, the clocks (fixed in the respective repositories, O and O ‘ showed both t = 0 and t = 0 (initialization of clocks). This restriction does not at night to the generality of the results. We write the following formulas for velocity pointing in any direction.
Einstein’s assumptions lead to transformations so-called ” Lorentz “. The Lorentz formula can express the coordinates ( x , y , z , t ) of a given event in the repository “fixed” (say the Earth) according to the coordinates ( x ‘ , y ‘ , z ‘ , t ‘ ) of the same event in the repository “mobile” (say a rocket). They are written:
where β and γ are dimensionless factors defined by
These expressions are simplified and take a shape close to a rotation if it involves the hyperbolic functions of parameter θ , called speed , which is an angle of “rotation” in the Minkowski space , defined by
With these notations we obtain and
For the formulas corresponding to the inverse transformation simply change β by – β , so θ in – θ .
Recipe: To find the sign to put in front of sinh θ it suffices to consider a point at rest in one of the repositories (say that of the rocket, with x ‘ = 0 for example) and see what should be the sign of the spatial coordinate in the other repository (say the reference set in which x increases if the rocket has a positive velocity).
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Lorentz transformations for an arbitrary direction of the velocity
Relativity of simultaneity, time and length
Lorentz transformations lead to a revolutionary vision of the physical phenomena and show that offend common sense.
In the following examples we will be asked to consider two successive events. We therefore rewrite the above formulas by replacing x and t by Ax and DELTA.t representing the difference between the spatial or temporal event and the first second.
Relativity of simultaneity
Main article: Simultaneity .
Relativity limits the notion of simultaneity to events seen from a single inertial frame, if in two simultaneous events in two different points , in general they are not simultaneous in another reference frame moving with respect to .
Lorentz transformations can to ensure this: In general we know that , so if the repository when the repository was so .
It may be noted that while in the line segment connecting the two points is perpendicular to the relative velocity between the two standards, that is to say , but and / or when the two events are simultaneous in both the one in the other repository. This is an example showing that the relativity of measurements from one repository to another, there are differences in effects between the direction of the relative velocity between the two repositories and perpendicular directions.
Dilation of durations
Main article: Expansion of the time .
The interval time between two events in a reference frame is measured by a different amount in another repository. A clock in motion in a reference appears to be slowing compared with an identical clock and motionless in the repository.
Suppose that in a reference two events occur at the same location but at two different times: then and . This is what happens to a clock stationary in this reference: the same place but at different times, it displays different times. In the repository , in translation at constant speed over the previous repository, these two events are not held to the same place, and even the time between two events is not the same: if . As it was : after the lapse of a minute on the clock stationary with respect to ( ), then this time interval, seen since , has passed in a time greater than 1 minute ( ). The clock is moving relative to and seems slow: we can speak of expansion durations or slowing of the clock in motion.
A paradox seems to appear then: how can it be that the clocks slow down when viewed from , and, by symmetry, clocks slow down when viewed from ? This does not pose a problem: each repository has the other idling, and if a common zero of two reference clocks, each sees what comes from the past of another in relation to elapsed time on its own clock still. If two clocks there is a meeting and then a distance and then another meeting, to compare the time close to the two meetings in one or the other, is the subject of the twin paradox .
We note here if , but and then according to the formula of the Lorentz dilation of time between two events is identical to the case .
Length contraction
Main article: length contraction .
Suppose that a rule of length L is still in the repository , oriented in the direction of the relative velocity between the reference and it is measured and, in passing , using the same rule and still in the repository . This will give a smaller result: the rule appears shorter measured from a reference frame in motion.
The Lorentz transformations are, assuming the velocity parallel to the axis (ox) and asking and :
For the measurement made in the repository , it has been , and are obtained .
Note that and : measurements of lengths perpendicular to the relative velocity between the repositories are unchanged.
It also shows the non-simultaneity of the determination of the end view from the other repository: This allows to say that moving from the repository, the measurement made in one where the rule is still not well done.
As with the slowing of clocks in motion, one can come across many paradoxes 14 . One of the most popular on the relativistic length contraction is supposed to return the car in a garage it shorter, provided to drive fast enough: the paradox of the train .
Simple illustration
In the following experiment, which illustrates the simple time dilation under relativity, we consider a photon shows where a speck of light at a speed c of light back and forth between two mirrors.
The duration of a round trip in a repository is equal to the quotient of the journey in this repository by the speed of light, which does not depend on the repository. If the watch is fixed relative to the observer, the journey is the distance at rest between the two mirrors and a hard time 2 t ‘. If the watch moves relative to the observer, it will follow the photon a broken line longer than the segment covered in the previous repository. 2 The duration t of the course is greater than 2 t ‘: the watch in motion delay (there is time dilation ).
The length of the hypotenuse of the triangle ABH of the figure is ct , the height is ct ‘and that of the base is vt if there v travel speed of the clock in the repository “fixed”. So we ( Pythagorean theorem ):
from which one derives immediately
We thus find a simple formula giving the previous time dilation .
The speed of light is about 300,000 km / s, an aircraft flying at 0.3 km / s (or 1000 km / h) at a speed close to the millionth of the speed of light so that the error using the Galilean approximation is less massage Seattle than a millionth of a millionth (10 -12 ), completely negligible in practice. However, for very precise measurements of travel times used in space experiments and also by the GPS , it is imperative to take into account the relativistic corrections (both those of special relativity and general relativity by the way).
For a body moving at a speed equal to one tenth of that of light, the relativistic effect is about one percent. And relativistic effects become significant for speeds close to the speed of light, impossible to achieve in real life (but not in laboratory: particle accelerators can instead reach speeds of up to several meters per second less than c only 15 ). This is one reason why we have difficulty understanding the practical operation of relativity.
The spacetime interval between two events
Main article: space-time interval .
The relativistic theory can give the impression (even if only by name) to make things completely dependent on the reference (inertial) from which measurements are made. Yet relativity seeks instead to identify what is invariant under change of coordinates. With this in mind the invariance of the interval of space-time between two events is a founder of the relativistic theory 16 .
In a repository, an event is characterized by its space-time coordinates, “such a place as yet.” Two events located respectively in x 1 , y 1 , z 1 , t 1 and x 2 y 2 , z 2 , t 2 are separated by a “space-time interval” whose square is defined by
We will write simply
This , called the “square of the interval of space-time”, is a relativistic invariant : its value does not depend on the inertial frame in which it is assessed, the Lorentz transformations show that .
As a result of the presence of “-” sign in the formula of the “square”, it may be positive or negative: the name “square” is only conventional . This makes all the difference with the square of the Euclidean distance, which itself is always positive quantities and are “real” square, and as positive.
The sign of the invariant space-time Δ s 2 is used to classify two events with respect to the other, imaged by the light cone , this classification in nature absolute and reflects their ability or not be bound by a relationship causal .
Main article: Light cones .
Time and space play symmetric roles in the range of space-time, so it makes sense to measure the same way. This is the view taken by the new definition of the speed of light , which, being fixed arbitrarily, establishes a de facto equivalence between length and time, by redefining the meter from the second . Specifically, because the speed of light is the same in any inertial frame, one can measure a distance or time either in inches or seconds.
The proper time
Main article: Time clean .
Time own a clock is the time that the rhythm in which it displays. The proper time of a particle is the proper time of a clock that is in place, the time elapsed in a repository where it is stationary. Due to the “slowing of clocks in motion,” an observer (at least in an inertial frame) believes that the proper time of the clock is slower than in its own time to it, unless the observer is itself stationary relative to it. The proper time of a reference is usually noted .
In the repository (assumed inertial) where it is stationary, the particle flow of his own time and changes in its spatial coordinates are zero , and given another inertial variations are and . Because of the invariance of the square of the interval of space-time was well : the proper time and the interval of space-time are equal to the coefficient close. At least as a result, the proper time is invariant under change of reference frame.
And since then where is the relative velocity and constant between the two repositories, formula found directly from the Lorentz transformations.
Note well that a particle moving at the speed of light does not own time, or his own time does not flow: . This in fact applies only to particles of mass zero.
Space-time diagram
Trajectories of particles in space only
Trajectories of particles in the same space-time
Main article: Minkowski diagram .
In Newtonian mechanics, the space is separated from time and we study the motion of a particle as a function of absolute time. Graphically we represent the trajectory in space (but not in time!). For example, draw the ellipse described by a planet around the Sun according to Kepler’s laws . The following figure shows the path against space made by a number of particles A, B, C, D, E, etc.. animated by a constant rate during the same period, say one second, way proportional to sports physical therapy the speed of the mobile. In the general case we can trace the trajectory of a point M ( x , y , z ) in a Cartesian coordinate system in three dimensions.
In special relativity we follow the events in a space of four dimensions, three space and one time, and therefore it is impossible in the most general case to visualize the curve representing the sequence of events resulting in the displacement of particle both in time and space . This curve is called the world line of the particle. To address the difficulty of representing four dimensions it is often limited to two dimensions, a space and time. In other words we consider only the motion along the axis of x , the coordinates y and z remaining unchanged. Only remain while the variables x and t , which can draw in a two-dimensional Cartesian trajectory of a particle in space-time: the world line.
The two figures below illustrate the passage against the point of view Newtonian relativistic point of view. At the top we took the distance traveled in one second by a variety of particles constant speed. While still at the same point A, B moves a certain amount, C is faster and goes further, even while D E moves in the opposite direction. In the bottom figure, we brought in a space-time diagram the sequence of events constituting the motion of the particle. Since the particle velocity is constant, their abscissa is obviously x = v t so that their world line is a straight line. The slope of the latter is proportional to the velocity v .
The remarkable thing is that the world line of the particle at rest is a single point but the line segment OA. Indeed, if the particle does not move ( x = constant) time continues to flow during the period!
Space-time diagram
If a line segment in this diagram represents a movement at constant speed, in the general case is a curve that will translate the motion of a particle. For example consider the world line here against representing a mobile x-axis starting from the x = 0 and returning to a time T HDMI switch later, say measured time on Earth. This could be a rocket carrying a round trip interstellar and will continue to reason in this example 17 .
The line segment between “start” and “arrival” along the time axis represents the world line of the Earth, the space coordinate, 0, does not vary. The curved line represents the sequence of events constituting the travel of the rocket. The curvilinear coordinate for identifying a point on this curve is the proper time of the rocket, the one measure the embedded clock.
The relativistic formulas show that the proper time along the curvilinear path is shorter than the proper time along the straight path (in this case one that represents the Earth time). This is the foundation of the twin paradox . One brother is a return to nearly the speed of light (which is also impossible, but it is a thought experiment ) while his brother remains to Earth. In return the traveler finds himself younger than his brother.
Thus, while in Euclidean geometry ( x , y ) the shortest path between two points A and B is the straight line, Lorentzian geometry ( x , t ) the time interval between two events A and B is maximum for the particle moving along the straight path AB. The longest journey is the one that corresponds to the straight path AB in the space-time diagram. In this case this path is that followed by a mobile free of force and therefore advancing at constant speed. This property is so much capital that it allows you to find the equations of general relativity 18 by extending the principle of maximizing the time course of the free motion of a particle in a gravitational field (in the vicinity of a black hole or sun) 19 .
Speed and quad-speed
Composition law of velocities
In a rocket moving at the speed relative to the Earth is pulled a cannon ball at the speed measured in the rocket. What is the speed of the ball measured on Earth?
In Galilean kinematics speeds and it would add
Relativistic kinematics in the composition law of velocities is different:
Assuming that we write and
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Elements of demonstration
This relation shows that the composition law of velocities in special relativity is no longer an additive law and that the speed c is a speed limit regardless of the repository in question (when he adds a speed, it falls to c ).
However, if the two speeds and are parallel , there is a setting to obtain an additive law. Simply move the speed v in angular velocity parameter θ introduced above , and called speed .
Show that in a composition of angular speed settings plus speed.
By asking , , and using the addition formula for hyperbolic functions , we find
The parameter corresponding to the angular velocity c is infinite since artanh ( x ), the hyperbolic tangent of x , tends to infinity as x approaches 1. We thus find that c is a speed limit independent of the chosen reference. This speed limit is unattainable for a massive particle, only massless particles such as photons , can move at the speed of light.
Numerical application
Imagine a shell is fired with velocity w ‘ = 0.75 c in the repository of a rocket moving itself to the speed v = 0.75 c relative to Earth. What is the speed of the ball measured on Earth? Clearly the value 1.5 c we give the formula is false because the Galilean velocity obtained would exceed that of light. Relativistic formulas invite us to do the following. The parametric angle speed of the shell relative to the rocket is the parametric angle of the speed of the rocket from the Earth has the same value of the speed shell relative to the Earth is , it which corresponds to the speed
We can obviously find this result directly to the formula for w according to w ‘ and v .
The four-vector velocity
Main article: four-vector .
In Newtonian mechanics we study the motion of a mobile according to its position versus time t , this time being assumed absolute, independent of the clock that far. In relativity we abandon this view to consider the motion of a particle as a succession of events , the curve described by this event in a space of four dimensions (three space, one for time) while taking the name of “world line”.
As in classical mechanics we define the velocity of a particle by taking the derivative
position with respect to time, as in relativistic mechanics we define the four-dimensional velocity vector (or four-vector velocity)
where is the proper time of the particle.
In explaining the components of this four-vector in a given reference frame we can write
expression in which we introduced the factor c to work with homogeneous coordinates.
Because of the invariance of the square of the space-time interval by changing the inertial frame, the square of the pseudo-standard of quadrivitesse is also an invariant under change of reference frame. And as in the inertial own (tangential and snapshot) of the particle, only the spatial quadrivitesse of the particle is non-zero and equals c (because the time of this reference is its own time and its speed is zero ) are for the four-vector velocity components (c, 0, 0, 0). Therefore in any inertial frame we have the relation
square of the pseudo-norm = (temporal part of ) 2 – (spatial part of ) 2 = c 2 .
It is the invariance of the standard that allows to talk about the four-vector of a particle independently of any coordinate system.
The energy-momentum four-vector
Just as the momentum of a particle, whose variation is often mistakenly called “Pulse” by Anglicism, was the product ” “of the mass and velocity, and the product” m “of the four-vector velocity ‘ ” by the mass ” m “of buy backlinks the particle becomes a four-vector momentum. It is often called vector ” energy-momentum “in expressing the fact that energy and momentum (the least amount of motion ) are combined into a physical concept inseparably, the same way that space and time up space-time. Indeed, if the spatial components of this four-vector to identify obvious to those of a classical momentum, physicists have been led by Einstein to identify the temporal component of this four-vector with the energy of the particle considered.
In an inertial frame (eg the terrestrial reference frame as a first approximation, hereafter called laboratory frame ) details of the events related to the particle are followed ( t , x , y , z ) and the components in the repository energy-momentum four-vector of the mobile are:
; With:
As this four-vector is proportional to the quadrivitesse (which is standard pseudo-c) with coefficients invariant change inertial reference frame, we have, in any inertial frame:
Application of the Lorentz transformations
The definition of the four-vector energy-momentum , using the elements and the proper time is invariant under change of reference frame allows to easily apply the Lorentz transformations for a change of inertial frame in the event that is parallel to the relative velocity between the two reference 20 :
Expression relativistic energy
Due to the definition of the energy-momentum four-vector, in particular its time coordinate, we obtain the expression of the total energy of the particle in the laboratory frame , one against which the particle is moving speed ( because the energy depends on the repository where it is calculated!) in the form of:
In relativity, the total energy of a particle is equal to the sum of the rest energy mc 2 contained in its mass and kinetic energy K . Taking into account the relativistic expression of energy, we see that the kinetic energy of a particle is given by the expression:
To “low” speed (that is to say little to that of light, or all the common cases “classic”, we obtain (first approximation):
This formula shows that the total energy of the particle is the sum of rest energy mc 2 unknown of Newtonian mechanics and classical kinetic energy (1 / 2) mv 2 , the “low” speed.
For speeds very close to that of light is the quantity 1 – β = [1 - (v / c)] that counts.
We have:
So that the total energy can be written (in first approximation):
Expression relativistic pulse
On the other hand, as the components of the velocity of the particle in the laboratory frame are:
Taking into account the factor of time dilation between t and τ , we arrive at another important formula giving the value of the pulse in the laboratory frame :
Equivalence of energy and rest mass
The energy-momentum four-vector has the characteristic of having the standard or its scalar square (within the meaning of the square of space-time interval), invariant when changing repository. In short the quantity:
is independent of the repository where it is calculated. Or in the repository of the particle velocity is zero, as the pulse, so that the standard of this quantity is invariant (mc ) 2 . In any reference frame was then the relationship capital as follows:
or:
(The factors c that enter these formulas ensure homogeneity, pa-wide ( mv ), that of E ( mv 2 ).)
We can make several observations:
(I) The value of the total energy of the particle depends on the reference of the observer. However, the value of the mass energy is the same in all repositories, particularly in the proper frame of the particle. It is therefore an intrinsic characteristic of the particle.
(Ii) If v tends to c , γ tends to infinity, which means it takes an infinite energy to accelerate a particle to reach the speed of light . This is obviously impossible. It happens, however, to accelerate particles to speeds very close to c.
(Iii) The relativity appears in all physical phenomena, even when the speeds involved are not “relativistic” 21 . A glaring example is the mass defect of the simplest atom: the mass of the hydrogen atom is less than the sum of the masses of the electron and the proton by an amount exactly equal to the equivalent mass of the ionization energy of the atom. Mass defect of the order of a tenth of a billionth. The reality of the mass defect appears of course for all other atoms, and in their molecular bonds.
The equivalence of mass and energy is given by the famous E = mc 2 . Ask this equivalence was not a revolutionary, because the concepts of matter and energy were previously separate, although some scientists such as Poincaré and Lorentz , had independently attempted reconciliation in the field of electromagnetism. Today, do not overestimate this equivalence, because while the mass is the standard four-vector energy-momentum, energy is one of the components of this vector. The mass given by:
is invariant by change of reference (it is the same in any reference frame). chiropractic marketing The energy on the other hand depends on the chosen reference, obviously, since changing the speed, the kinetic energy also changes.
Conservation of energy-momentum four-vector of an isolated system
In classical physics, the momentum and the kinetic energy of an isolated system overall can be stored over time, at least when the shocks are elastic . It is a property compatible but independent of the Galilean principle of relativity. A change of inertial frame gives new values to the kinetic energy and the coordinates of the momentum of the system, but these values are also conserved in time in this repository.
In special relativity, the energy-momentum four-vector of a global isolated system is conserved and is also a property compatible and independent of the principle of relativity of Einstein. The coordinates of this vector in four dimensions ( four-vector ) contains the energy and momentum, and keep whatever the interactions between elements of the isolated system . As in non-relativistic physics, a change of reference gives new values to the energy (time coordinate) and the coordinates of the pulse (spatial coordinates), and in this new repository conservation values of these coordinates , over time, is still valid.
The principle of consistency is:
Regardless of the details of the experiment, the four-vector of an isolated system of particles is conserved in any interaction internally.
In other words we can write:
Since the four-vector is conserved, each component in a given reference system (whose values depend on the chosen system) is also conserved in collisions. The time component representing the energy E of the system and the space component representing its momentum , so we end repository for each two conservation laws, one for power and one for the momentum (or impulse) .
Conservation of energy-momentum four-vector in a collision
An example (academic)
A collision of two particles is shown in the figure against. A particle of mass 8 (in arbitrary units) driven with a speed v / c in 15/17 pointing to the right hits a particle of mass oncoming 12 with a speed v / c 5 / 13 (the numbers were selected 22 for the calculations “just fall”. After the collision, bounced the other way having communicated to B part of its momentum. The total energy, sum of the energies of particles A and B is preserved, as well as the total momentum. The quantities E and p are given in reality (I / c 2 ) and (p / c) and are expressed in units of mass, arbitrary. With these quantities we have the relation E 2 = p 2 + m 2 . The factor γ is always defined by γ = [1 - (v / c) 2 ] -1 / 2 .
Elastic collision
In a particle accelerator, sometimes a very high energy particle hits a particle at rest and communicates to the latter part of its kinetic energy. If the only energy exchanges involve exactly this kinetic energy (conservation of momentum of the system), we say that the impact is elastic . The formulas expressing the conservation of four-vector of the system formed by these two particles is used to analyze the collision. Newtonian mechanics in the direction of the two particles after a collision at a right angle. This is not the case in the case of collisions between relativistic particles where their directions form an acute angle. This phenomenon is clearly visible on the recordings of collisions performed in bubble chambers .
Elastic collision between two particles of equal mass
Consider an electron of mass m and very high energy striking another electron initials at rest. Vector pulse of the two particles are plotted against the figure. Before the shock pulse of the electron incident . After the shock, the pulses of the two electrons and . By writing the energy of an electron as the sum of its rest energy mc 2 and its kinetic energy K , we can write the total energy of the system before the collision as:
Similarly,
The law of conservation of energy says that E = E 1 + E 2 and therefore
form indicating that the kinetic energy is also conserved (elastic collision).
The law of conservation of momentum says that
and therefore if we call θ the angle between two vectors and , we have the relation
from which it derives
In expressing the square of the momentum of individual electrons by their energy and their mass using the formulas given above we obtain
for the incident electron and
for electrons after the collision.
Since K = K 1 + K 2 we arrive easily to the simple formula finally
This formula shows that cos θ is positive and therefore the directions of the final state electrons form between them an acute angle.
Are readily available in the literature 23 cases where the treatment of the shock is symmetric, the two electrons each with the same energy K 1 = K 2 = K / 2. In this particular situation the general formula becomes
for a symmetric collision.
In the Newtonian limit of low speeds, the kinetic energies are much smaller than the rest energy mc 2 and therefore
tends to zero, which means that the angle θ tends to π / 2. This is the nonrelativistic result.
Within the contrary, very high energies, it is the kinetic energy terms are much larger than the term mc 2 and therefore
In this case the cosine approaches 1, which means that the angle between the velocities of electrons tends to zero. This implies a behavior completely different from the Newtonian case.
The formulas obviously apply to the case of collision between two protons.
Compton scattering
A physical application of the formulas of conservation of energy and momentum of a particle system is provided by the analysis of the collision between a photon of high energy and an electron at car insurance quote rest, constituting what impact the is called Compton scattering .
Main article: Compton scattering .
Central repository of inertia and mass of a particle system
Suppose known an isolated system and consists of particles without interaction, into a repository R : and are known and remain unchanged over time in this repository.
In classical physics, the definitions of center of mass , and an inertial frame where the center is still, do not pose a problem: we use the vector distances and masses of bodies. In relativistic physics, a similar definition faces a difficult choice (should I choose mass or energy?) Without decisive criterion 13 .
The definition used is that which allows the use of relativistic equations in the simplest: the repository called “the center of inertia” is the repository R * where the total momentum is zero, either .
In this framework, the energy E * of system checks equality because it is only a change of reference, so .
The relative velocity between the reference R and R * , denoted , checks , but this speed is rarely used in the calculations.
The value of the total mass M * of the system thus obtained is independent of the repository where it is assessed: The invariance with respect to changes in repository, and verification of the formulas are four-vector momentum of the system that this definition meets all properties expected for a mass .
By energy conservation, and the lack of interaction (so there is no energy in the system that will be spent), we have:
Or the energy E j * of each particle j (in the coordinate R * ) is the sum of the energy m j c 2 corresponding to its rest mass m j added to its kinetic energy K j * (always in the frame R * ), that is to say . Where:
This shows that: the total mass of a system of independent particles is greater than the sum of the masses of individual particles .
The non-conservation of mass
The conservation of energy-momentum four-vector in a reaction that explains the mass of a system can not be stored to be transformed into energy, in part or in full. This is what happens in the reactions of fission of fusion and of annihilation of particles .
Spontaneous fission of a particle
Suppose a body at rest, mass M , decays spontaneously into two parts of masses ( masses at rest ) respectively , and : it shows that while the mass M is greater and the difference is in the form of an energy Orlando personal injury attorney Kinetic 24 .
The law of conservation of energy gives because and therefore .
In case , this decay can not be spontaneous, it can only be achieved after an energy input of at least equal to its “binding energy” equal to .
The law of conservation of momentum gives , therefore , from which we draw .
Finally, ties and to determine the energies of the two new particles: and . The difference in mass was converted into kinetic energy for the two new particles, energy found in and .
We can also calculate the standard pulses of the two particles, and therefore their speed.
A fission particle also implies the conservation of quantum numbers : the electric charge , the spin , etc..
Case of massless particles
The expressions giving E and p as a function of m and v lead immediately to the formula
If the particle velocity equals the speed of light, so p = E / c by calculating E 2 – p 2 c 2 we see that the mass of the particle is always zero. Conversely, if the mass of the particle is zero, then p = E / c and therefore v = c .
We come to the conclusion that the double major material particles can not reach the speed of light and that only massless particles travel at the speed of light.
The set is perfectly consistent: any mechanism of energy propagation at the speed of light corresponds to a momentum p equal to the energy and thus a “rest mass” zero. Conversely, a massless particle always moves at the speed of light.
Examples of cosmic rays and muons
Is detected in Astronomy particles carry a huge energy: the cosmic rays . Although their production mechanism is still mysterious, we can measure their energy. Considerable numbers obtained show that their analysis requires the use of the formulas of relativity. Cosmic rays thus provide an ideal illustration of Einstein’s theory.
Particles are detected up to energies of the incredible range of 10 20 electron volts , or one hundred million TeV . Suppose a cosmic ray or a proton of 10 20 eV. What is the speed of this particle?
In the term giving the energy E , the term mc 2 represents the energy of the rest mass of the particle. The proton is about 1 GeV, or 10 9 eV. The relationship between E and mc 2 is equal to 10 20 / 10 9 = 10 11 and none other than the famous stretch factor of time . What is the speed of the proton? In writing we find that
In other words the speed of the proton is considered almost equal to the speed of light. It differs by less than 10 -22 (but in no case the match).
Let’s see what these numbers mean for the relativistic factors between the proper frame of the particle and the terrestrial reference frame. Our own galaxy , about one hundred miles in diameter, light years is traversed by light in one hundred thousand years. Therefore for a terrestrial observer the proton through the galaxy at the same time. The extraordinary is that the repository relativistic proton, the corresponding time is 10 11 times smaller, and is therefore 30 seconds (one year is 3 × 10 7 seconds)!
Our ultra-relativistic protons and ultra-energy through our Galaxy within 30 seconds of his own time but in 100 000 years of our time on earth.
Cascade triggered by airborne particles incident proton
When this cosmic ray hits an atom of oxygen or nitrogen from the atmosphere at an altitude of about 20 to 50 km above the ground, a spray of elementary particles containing sounds especially muons . One of them head to the ground with a speed almost equal to that of light, 300,000 kilometers per second in the terrestrial frame. These particles then pass through the approximately 30 km of atmosphere in 10 -4 seconds (or 100 microseconds).
In the repository where it is at rest, a muon has a half life of 2 microseconds (2 microseconds, or 2 × 10 -6 s). This means that among a set of muons produced at the top of the atmosphere, half will be gone after 2 microseconds, transformed into other particles. Half of the remaining muons disappear even after 2 microseconds, and so on. If the half-life was the same (2 microseconds) in the terrestrial reference in 10 -4 seconds to cross the atmosphere muons have counted 10 -4 / 2 × 10 -6 = 50 half-lives. Therefore their number would be reduced to the arrival on the ground by a factor of (1 / 2) 50 or about 10 -15 so that in practice no muon not reach.
However, the measurements indicate that about 1 / 8 or (1 / 2) 3 , the initial muons reach the Earth’s surface, which proves that they suffered only three divisions of their number by 2 and not 50. Ie the crossing time of the atmosphere in their own repository is 3 half-lives and not 50, or 6 microseconds only (not 100 microseconds). This result is strong evidence of the correctness of special relativity, including the phenomenon of time stretching own (here that of the muon) when making measurements in an external repository (here that of the Earth). In the numerical example chosen the time dilation factor γ = [1 - ( v / c ) 2 ] – (1 / 2) is 100 / 6.
This suggests the speed and energy of muons. Indeed, it was like in the previous calculation
which leads to
As the mass of a muon is about 100 MeV , the energy of the particle is 100 / 6 times larger, at about 2000 MeV to 2 GeV .
Electromagnetism and relativity
In Newtonian space of three dimensions, a particle of charge q placed in an electric field and magnetic field is subject to the Lorentz force and the equation governing its motion is
To implement this approach in relativistic mechanics, we must consider the energy-momentum four-vector instead of vector and evaluate the rate of change of the four-vector not in the repository of an observer but in any Galilean proper frame of the particle. The left side will be of the form , where τ is the proper time of the charged particle. On the right we find an object independent of the chosen reference, and also will inevitably be a linear function of the speed of the particle. Indeed the spatial part of the equation is linear in the momentum as it is written
In this expression , and are the Plastic Containers components in a repository of Lorentzian four-vector velocity , which How to Lose Weight Fast can be written:
Explicitly the above equation is divided on the three axes as follows:
For its part the temporal component of the equation of dynamics (which is the law giving the variation of energy) can be written
where W is the work of the force
By bringing together the equations written above in the context of a space-time four-dimensional, the rate of change of the energy-momentum four-vector is given by
The matrix equation we have to write special relativity shows that the magnetic field and the electric field as a single entity. In fact the previous presentation is somewhat incorrect to the extent to harness the power of the relativistic theory it is necessary to appeal to tensors. The matrix equation above is the translation in terms of tensor components of the equation, independent, it, of any coordinate system
is the electromagnetic field tensor (or tensor or Maxwell tensor Faraday). It is this physical object that represents the electromagnetic field. Components in a coordinate system are given by the matrix written above.
Vocabulary
Observer: human or screening device with a timer allowing it to read the time and eventually, if it is part of a group formed, bearing a mark indicating its position.
Inertial frame , also known as “Lorentz reference” or “inertial” all observers moving freely in space far from any mass, whose mutual distances do not change over time (they are at rest together compared to the other) and have their clocks synchronized .
Event: An event is an event (!), Such as the birth of an individual, the departure of a rocket or shooting a firecracker. It is independent of the coordinates of time and space that may allow to locate it. However in practice it is convenient to identify the events by their coordinates relative to a benchmark, ie the point at which the event occurs and when it occurs in this benchmark.
In special relativity length and time should be measured with the same unit (which we have not done this in a systematic way). In astronomy we choose the unit of time and distance is measured by the time it takes light to cover that distance. For example a galaxy is located five million light years from us means that light takes five million years to travel the distance that separates us. Note that in real life we can say easily that Paris, for example, is three hours by train from Montpellier, which is exactly measure distance in time. Moreover, since 1983, the unit of time (seconds) is the only one to be defined directly by the International System of Units (SI), the unit of length (meter) is defined as the distance traveled light in a specific time (which is to be finalized and the exact value of c at 299,792,458 m / s) 25 .
References
A selection of works of Einstein, including its original articles are now available in French translation with commentary under the title Selected Works by Editions du Seuil / CNRS editions in the collection of knowledge sources (6 volumes published since 1989). Volumes 2 and 3 are exclusively devoted to the theories of relativity.
Popular works
Albert Einstein, Relativity , Gauthier-Villars (1956). Reissued by Payot (1990) ( ISBN 978-2-228-88254-5 ) . Pocket-sized, a statement of basic principles of the theory of special and general relativity, by its author.
Banesh Hoffmann story of a great idea: relativity , Pour La Science Publishing (1985), diffusion Belin ( ISBN 978-2-84245-019-9 ) . A statement remarkable for its clarity and simplicity of relativity, by a former collaborator of Einstein at the Institute for Advanced Studies in Princeton.
Thibault Damour, if Einstein Tales , Editions du Cherche-Midi, Paris (2005) ( ISBN 978-2-7491-0390-7 ) . The great French specialist in theories of relativity finally gives us “his” free Einstein equations. Thibault Damour is a tenured Professor at the Institut des Hautes Etudes Scientifiques (IHES) in Bures-sur-Yvette, he has long taught general relativity to the DEA for Theoretical Physics at the Rue d’Ulm.
Albert Einstein & Leopold Infeld, The Evolution of Physics , Collection Champs, Flammarion (1993) ( ISBN 978-2-08-081119-6 ) . In paperback, a history of physics, the mechanics of Newton to the modern theories (relativity, quantum), written in 1936 by Einstein himself and one of his disciples at Princeton, to finance the stay of this last.
Brian Greene, The Elegant Universe , Folio tests (2005) ( ISBN 978-2-07-030280-2 ) . A presentation of the attempt to unify physics by string theory .
Structures initiation formalism
Available at the school (First S).
Ponce and Alexandre Guillaume Lebrat (2010), Relativity . An article that is intended for students and offers an unambiguous notation in the proofs.
Accessible at the undergraduate level.
James H. Smith, Introduction to relativity , InterEditions (196
. 2 e edition with corrected exercises (1979) ISBN 978-2-7296-0088-4 . Reissued by Masson (Wiley – 3 e edition – 1997), ISBN 978-2-225-82985-7 . A French book that exposes the foundations of the theory clearly.
Boratav M. & R. Kerner, Relativity , Ellipses (1991), ISBN 978-2-7298-9145-9 . A very good book in French, written in a lively style by two professors at the University Paris 6. Contains many examples and applications from recent experiences.
EF Taylor and John A. Wheeler, Discovering time-space , Wiley (1970). This original work is a basic introduction, though rigorous, theory of relativity, Wheeler is an undisputed expert in the field. The target audience is the undergraduate student beginning physics, in particular, knowledge of electromagnetism is not necessary. This is the perfect complement to extend the reading of the book Banesh Hoffman quoted above. Many years, much of which resolved. Unfortunately most published in French, this book is available in English: Spacetime Physics , WH Freeman (2 e edition – 1992), ISBN 978-0-7167-2327-1 .
Jean-Marc Levy-Leblond, relativities , Cahiers de Fontenay 8, Ecole Normale Supérieure de Fontenay-aux-Roses (1977). Notes very educational, unfortunately unpublished. Available in good university libraries, and in pdf format, courtesy of Jean-Marc Lévy-Leblond and Ecole Normale Supérieure de Fontenay-aux-Roses http://o.castera.free.fr/pdf / The%% C3% 20relativit A9s.pdf
Max Born, The theory of relativity of Einstein and its physical basis , Gauthier-Villars (1923). Reissued by Jacques Gabay (2003) ISBN 978-2-87647-230-3 . This book, written by a great German theorist, Nobel Prize 1954, is remarkable for its clarity. The place of the mathematics is extremely limited.
Albert Einstein ‘s theory of special and general relativity , Wiley (2005) ISBN 2100487167 . The English version is on the Project Gutenberg
Albert Einstein, Four lectures on relativity theory , Wiley (2005) ISBN 2100492292 . Text of four lectures delivered at Princeton University in 1921.
Thibault Damour & Stanley Deser, Relativity , Encyclopeadia Universalis 19 (1995) 739-748. A presentation of a non-technical clarity, a world-renowned specialist: Thibault Damour is a tenured Professor at the Institut des Hautes Etudes Scientifiques (IHES) in Bures-sur-Yvette, he has long taught general relativity in DEA Theoretical Physics in Paris.
Jean-Pierre Provost & Marie Antoinette Tonnelat, Space-time , Encyclopeadia Universalis 8 (1995) 743-745. An introductory statement simple enough, or the essence of relativity in four pages.
Hubert Lumbroso, Relativity – Resolved , Édisciences (2 th edition 1996) ISBN 978-2-84074-127-5 . Classic work of mole: a summary of progress, with a large number of issues fixed.
Wolfgang Rindler, Introduction to Special Relativity , Oxford University Press (2 e -edition 1991) ISBN 978-0-19-853952-0 . An introduction written by a professor at the University of Dallas (Texas), the world in the field.
ND Mermin, It’s about time: understanding Einstein’s relativity , Princeton University Press (2005), ISBN 978-0-691-12201-4 .
David Bohm, The Special Theory of Relativity , Benjamin (1965), reissued by Routeledge (London-1996) ISBN 978-0-415-14808-5 . This is the course taught at Birkbeck College, University of London by David Bohm, quantum theorist, who died recently. The mathematical formalism is reduced to the minimum necessary to discuss the underlying physical ideas. Undergraduate level.
Wolfgang Rindler, Relativity: special, general and cosmological , Oxford University Press (3 th edition-2001) ISBN 978-0-19-850836-6 . A brilliant introduction to all aspects of relativity, a professor at the University of Dallas (Texas), the global specialist in the field. Available at the undergraduate level.
Wolfgang Rindler, Essential relativity: special, general and cosmological , Texts and Monographs in Physics, Springer-Verlag (2 e -revised edition 1977) ISBN 978-3-540-10090-4 . Previous edition of the previous book, always interesting.
George FR Ellis & Ruth M. Williams, Flat & curved space-times , Oxford University Press (2 e -edition 2000) ISBN 978-0-19-850656-0 . Another excellent introduction to relativity, by an expert, a professor at the University of Cape Town (South Africa) and his assistant. Available at the undergraduate level.
Clifford M. Will, Tests of special relativity , Poincaré Seminar “Einstein, 1905-2005″ (April 9, 2005). This text in English, written by the global specialist in experimental aspects of two relativistic theories of Einstein, describes some experimental tests of special relativity. Download it here in PostScript or PDF.
Julian Schwinger, Einstein’s Legacy – The Extensions of Relativity , The World of Science Collection, Library for Science (198. A relatively simple presentation of Einstein’s theory by an American theorist, Nobel Prize in Physics 1965 (with Feynman and Tomonaga) for the theory of quantum electrodynamics. Extension of the undergraduate level (there are a few simple equations).
Lewis C. Epstein, Relativity Visualized .
Historical aspects
Olivier Darrigol, Should we review the history of relativity? , The Newsletter of the Academy of Sciences 14 (Winter 2004) 6-7. The author is a theoretical physicist training. He works at the research laboratory epistemological and historical sciences and scientific institutions (REHSEIS) of the CNRS and the University of Paris VII.
Albert Einstein, Selected Works – Volume 2: I Relativities , Seuil / CNRS Editions (1999), ISBN 978-2-02-010179-0 .
Albert Einstein, Selected Works – Volume 3: Relativity II , Threshold / CNRS Editions (1999), ISBN 978-2-02-010180-6 .
Marie-Antoinette Tonnelat, History of the principle of relativity , New Science Library, Flammarion (1971) ISBN 2082101630. A monumental history, from antiquity to Einstein’s theories. Includes an extensive bibliography. Although it contains few equations, this book demands the attention of the reader. Some technical sections devoted to the theory of general relativity are graduate-level minimum.
Abraham Pais, Einstein – His life, his work , The Free (1993). Reissued by Wiley (2005) ISBN 978-2-10-049389-0 . The scientific biography which is now authority since its publication in English in 1982 [ref. required] , by a professor at Rockefeller University who knew Einstein in the last years of his life. Extremely rich content. The technical level of some passages is that of a university graduate (at least).
Arthur I. Miller, Albert Einstein’s special theory of relativity – Emergence (1905) & early interpretation (1905-1911) , Addison-Wesley (1981). Reissued by Springer-Verlag (199 ISBN 978-0-387-94870-6 . A very scholarly study of the first steps of the theory. [ref. required]
Wolfgang Pauli, Theory of Relativity , Dover Publications, Inc.. (1981) ISBN 978-0-486-64152-2 . This book is an English edition of a journal article written in German in 1921 for the Encyklopadie der Wissenschaften Mathematischen by Pauli . Here is what Einstein said in a letter to Born, his teacher at Göttingen, dated December 30, 1921: “Paul is a great fellow for his 21 years and can be proud of his article for the Encyclopedia. “.
Françoise Balibar, Galileo, Newton read by Einstein – Relativity & Space Collection Philosophies, Presses Universitaires de France (1984) ISBN 978-2-13-043493-1 . Historical reflections on the principle of relativity, in 128 pages (paperback). This is not a statement of Einstein’s theory.
( in ) Who Invented Relativity?
Biographies of Einstein
Banesh Hoffmann, Albert Einstein, creator and rebel , Science Collection Points, Le Seuil (1975) ISBN 978-2-02-005347-1 . Pocket-sized biography, by a former associate of Einstein at the Institute for Advanced Studies in Princeton.
Philip Frank, Einstein – His Life and Times , Collection & Scientists around the world, Albin Michel (Paris, 1950). Reprint in the collection bag Champs, Flammarion (1993) ISBN 2080812424 . A biography authorized first-hand by one who was Einstein’s successor to the chair of theoretical physics at the University of Prague, appointed on his Chinese translation recommendation. Well-documented, it describes beautifully the historical context (scientific and political) of the genesis of Einstein’s work.
Abraham Pais, Einstein – His life, his work , The Free (1993). Reissued by Wiley (2005) ISBN 978-2-10-049389-0 . The biography is now scientific authority since its release no no hair removal in 1982 by a professor at Rockefeller University who knew Einstein in the last years of his life. Extremely rich content. The technical level of some passages is that of a university graduate (at least).
Jacques Merleau-Ponty , Einstein Collection Champs, Flammarion (1997) ISBN 2080813382 . Another pocket-sized biography, a professor of epistemology at the University of Paris X – Nanterre. The book is divided into three parts: the man, his scientific work and philosophy.
Françoise Balibar, Einstein: The joy of thinking , Discovery Collection, Gallimard (1993), ISBN 978-2-07-053220-9 .
Boris Kuznetsov, Einstein his life / his ideas / theories , Belgium, Marabout University Press, Gerard & co, 1967, p. 336