About gravity and time and space relationships of modern physical theory. 1915-1916 proposed by Einstein. Basic assumption is that (1) General Principle of Relativity; (2) principle of equivalence. The main conclusions are (1) Mercury perihelion precession law; (2) light in the gravitational field should bend; (3) spectral lines in the gravitational field to the red end of movement; (4) the existence of gravitational waves; (5) there is gravitational lens phenomena.
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No. 2
Einstein's second theory of relativity (1916). The theory is that gravity is the space - time geometry (that is, not only consider the space between points, but consider the point in space and time distance between the geometric) distortion caused by the gravitational field and thus affect the time and distance measurements. General relativity: Einstein's science-based laws for all observers (regardless of how they exercise) must be the same concept of the theory. It will follow four-dimensional gravitational space - time curvature to explain. General relativity (general relativity) Einstein in 1915 to establish a geometric language from the gravitational theory, the integration of special relativity and Newton's law of gravity, the gravitational description of the causes of change in time and space matter and energy and curved space-time, to replace the traditional gravity is a force for the view. Therefore, the special theory of relativity and the law of gravity, general relativity is just a special case under special circumstances. Special theory of relativity when gravity is not the case; and the law of gravity is in proximity to, small and slow gravity when the situation. Background In 1907 Einstein published a paper in light of special relativity, gravity and acceleration of its impact papers, begins to form the prototype of general relativity. In 1912, Einstein published another paper on how to use gravity to describe the language of geometry. Thus, the kinematics of general relativity appeared. To 1915, Einstein's field equations were published, the entire dynamics of general relativity was finally completed. After 1915, mostly concentrated in the development of general relativity field equations solved on the physical interpretation and the search for answers to experiment and observation may also account for a large part. But because the field equation is a nonlinear partial differential equations, it is difficult to arrive at the solution, so the computer before starting the application in science, only a small number of solutions are solutions to them. The most famous of which there are three solutions: Schwarzschild solution (the schwarzschild solution (1916)), the reissner-nordström solution and the kerr solution. Observation in general relativity, but also has a lot of progress. Mercury's precession is the first evidence that general relativity is correct, this is the theory of relativity has been measured before the appearance of the phenomenon, until after the discovery of general relativity by Einstein, it has been a theoretical description. The second experiment is the Eddington 1919 eclipse in Africa to take advantage of the time measurement of starlight by the sun produces gravitational deflection, and general relativity predicted exactly the same. At this time, general relativity theory has been widely popular, and most physicists accepted. After many more experiments to test the theory of general relativity, general relativity and confirmed the correct. In addition, the expansion of the universe also created a general theory of relativity of another climax. From 1922, researchers discovered that the resulting field equation is a solution in the expanding universe, Einstein did not believe the universe at that time will come naturally expand and contract, so he added a presence in the equation cosmological constant to make the field equations can be solved given a hidden universe out of solution. But this solution has two problems. In theory, a _set_ of the universe hidden in the mathematical solution is not stable. Also in the observations on the 1929, Hubble discovered the universe is in fact expanding, Einstein abandoned the experiment result that the cosmological constant, and claim that this is the biggest mistake of my life (the biggest blunder in my career). However, according to a recent form of supernova observations, expansion of the universe is accelerating. Therefore, the Ministry of the cosmological constant seems to have lost the possibility of resurrection, the existence of dark energy universe with a cosmological constant may be explained. Basic assumptions Equivalence principle: gravity and inertia are completely equivalent. Now some scholars have found that gravitational and inertial forces are not equivalent. General principle of relativity: the laws of physics in the form in all reference frames are the same. Main content Einstein's "equivalence principle", that gravitational and inertial forces are equivalent. The principle established in the gravitational mass and inertial mass equivalence on. According to the principle of equivalence, Einstein relativity principle narrowly to broadly promote the principle of relativity, that physical laws in all forms of reference are the same. Equations of motion of objects that the reference system geodesic equation. Geodesic equation has nothing to do with the inherent properties of the object itself, depends only on local geometric properties of space-time. The attraction is the local geometric properties of space-time performance. Material quality will result in the presence of curved space-time, in curved space-time, the object is still the shortest distance along the motion (ie along geodesics - in Euclidean space that is linear motion), such as causing the Earth to the sun curved space-time geodesic motion, is actually around the sun, causing gravitational effects. As in the curved surface of the earth, if the straight-line motion, is actually a circle to go around the Earth's surface. Local geometric properties gravity is space-time performance. Although Einstein's general theory of relativity is founded, but it is the source of the mathematical foundations of Euclidean geometry can be traced back to several centuries of axioms to prove Euclid's fifth postulate (the parallel lines always remain equidistant) did efforts, these efforts in Lobachevsky, bolyai, Gauss's work reached its apex: They pointed out that Europe's fifth postulate is a postulate can not be used to prove the first four. The general mathematical theory of non-Euclidean geometry by Gauss's student Riemann developed. It is also known as Riemannian geometry or surface geometry, the development of a general theory of relativity before Einstein, it is assumed that non-Euclidean geometry can not be applied to the real world in the past. In general relativity, gravity is "geometric" - means: Min's special theory of relativity space background with the physical picture of gravity in general relativity into the context of Riemannian space without power (assuming no and electromagnetic interactions) the physical picture of the freedom of movement, the kinetic equation has nothing to do with the quality of their geodesic equation becomes: The law of gravity is replaced by Einstein's field equation: <math> r_ - fracg_ r = - 8 pi {g over c ^ 2} t_ </ math> Where g is Newton's gravitational constant The equation is a space-time as independent variables to the metric as the dependent variable with a second-order elliptic bound hyperbolic partial differential equations. It is known to complex and beautiful, but not perfect, the calculation can only be approximate solution. Eventually it got real spherical symmetry of the exact solution - Schwarzschild solution. After adding the cosmological constant field equation: <math> r_ - fracg_ r + lambda g_ = - 8 pi {g over c ^ 2} t_ </ math>
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Basic assumptions
Equivalence principle: the weak equivalence principle and strong into the principle of equivalence, weak equivalence principle states that the gravitational mass and inertial mass are equivalent. Strong equivalence principle that the two spaces are subject to gravity and inertia forces with other major role in all these experiments in space, will come to the same physical laws. Many scholars now engaged in the argument of the equivalence principle, but at least now be able to do the precision point of view, has not been experimentally proved the equivalence principle is broken. General principle of relativity: the laws of physics in the form in all reference frames are the same. General Physics (University of textbooks) is described in these two principles: Equivalence principle: in a constant gravitational field is uniform under the influence of the inertial system, all physical phenomena that occur, and one can not influence the gravitational field, but the constant movement of non-inertial acceleration within the same physical phenomena. General relativity theory of relativity: All non-inertial and inertial gravitational field exists for the description of physical phenomena are equivalent.
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The basic concepts of general relativity
General relativity is based on the special theory of relativity. If the latter proved to be wrong, the whole theory of the building will collapse. In order to understand general relativity, we must be clear in the quality of the classical mechanics of how to define it. Quality of the two different expressions: First, let us think about the quality of daily life mean anything. "It is the weight?" In fact, we believe that quality is something to weigh things, such as we measure it: we need to measure the quality of the objects on a balance. We do what is the use of a quality nature? Earth and the fact that the detected objects attract each other. This quality is called "gravitational mass." We call it "gravity" because it determines the universe of all the stars and star running: the gravitational force between Earth and the Sun around the Earth driven by the quality of the latter for nearly circular around the movement. Now, try to push you in a car on the plane. You can not deny the strong resistance of your car with you to give it acceleration. This is because your car has a very large mass. Moving light objects easier than moving heavy objects. Quality can also be defined in another way: "It's resistance to acceleration." This quality is called "inertial mass." So we come to this conclusion: we can use two ways to measure quality. Or we call it the weight of the (very simple), or we measure its resistance to acceleration (using Newton's law). People do a lot of experiments to measure the same object of inertial mass and gravitational mass. All results are reached the same conclusion: the inertial mass is equal to gravitational mass. Newton himself realized that this quality is some kind of equivalence can not explain his theory of causes. But he believes the result is a simple coincidence. In contrast, Einstein found that the existence of an equivalence to replace Newton's theory of the channel. Everyday experience verify this equality: two objects (a light one weight) will be the same speed "fall." However, heavy objects by the Earth's gravity larger than the light. So why it will not "fall" faster? Because of its stronger resistance to acceleration. Concluded that the acceleration of objects in a gravitational field has nothing to do with quality. Galileo was the first person to notice this phenomenon. Is important that you should understand that all the objects in a gravitational field, "the whereabouts of the same speed" is (classical mechanics) inertial mass and gravitational mass equivalent results. Now we look at the "whereabouts" of this statement. Objects "fall" is produced as the Earth's gravitational mass of the Earth's gravitational field. All the same two objects in the gravitational field of the same speed. Whether the moon or the sun, they are accelerated to the same ratio. This means that their speed in the same increments per second. (Acceleration is the rate of value added per second) Gravitational mass and inertial mass equivalence of the third argument is the assumption of Einstein Einstein was looking for "gravitational mass and inertial mass are equal" interpretation. To this end, he made called "equivalent principle" of the third hypothesis. It shows: If a relative to a Galilean inertial system is uniformly accelerated, then we can introduce a relative uniformity of its gravitational field and that it (the inertial system) is stationary. Let's examine a inertial system K ', it has a uniform relative to the Galileo system acceleration. In the K and K 'surrounded by many objects. This object is at rest relative to K. Therefore, these objects relative to the K 'has a same acceleration. This acceleration is the same for all objects, and with the K 'relative to K of the acceleration in the opposite direction. We have said, in a gravitational field in the acceleration of all objects are the same size, so its effect is equivalent to K 'is stationary and there is a uniform gravitational field. So if we establish the same principle, the quality of the two objects are equal only one of its simple logic. This is why the (quality) is equivalent to an important principle to support the same argument. By assuming that K 'and the gravitational field still exists, we will be K' understood as a Galileo system, (so that we can) in which the laws of mechanics. Thus Einstein established his fourth principle.
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Main content
Einstein's "equivalence principle", that gravitational and inertial forces are equivalent. The principle established in the gravitational mass and inertial mass equivalence on. According to the principle of equivalence, Einstein relativity principle narrowly to broadly promote the principle of relativity, that physical laws in all forms of reference are the same. Equations of motion of objects that the reference system geodesic equation. Geodesic equation has nothing to do with the inherent properties of the object itself, depends only on local geometric properties of space-time. The attraction is the local geometric properties of space-time performance. Material quality will result in the presence of curved space-time, in curved space-time, the object is still the shortest distance along the motion (ie along geodesics - in Euclidean space that is linear motion), such as causing the Earth to the sun curved space-time geodesic motion, is actually around the sun, causing gravitational effects. As in the curved surface of the earth, if the straight-line motion, is actually a circle to go around the Earth's surface. Local geometric properties gravity is space-time performance. Although Einstein's general theory of relativity is founded, but it is the source of the mathematical foundations of Euclidean geometry can be traced back to several centuries of axioms to prove Euclid's fifth postulate (the parallel lines always remain equidistant) did efforts, these efforts in Lobachevsky, Bolyai, Gauss's work reached its apex: They pointed out that Europe's fifth postulate is a postulate can not be used to prove the first four. The general mathematical theory of non-Euclidean geometry by Gauss's student Riemann developed. It is also known as Riemannian geometry or surface geometry, the development of a general theory of relativity before Einstein, it is assumed that non-Euclidean geometry can not be applied to the real world in the past. In general relativity, gravity is "geometric" - means: Min's special theory of relativity space background with the physical picture of gravity in general relativity into the context of Riemannian space without power (assuming no and electromagnetic interactions) the physical picture of the freedom of movement, the kinetic equation has nothing to do with the quality of their geodesic equation becomes: The law of gravity is replaced by Einstein's field equation: <math> R_ - fracg_ R = - 8 pi {G over c ^ 2} T_ </ math> Where G is Newton's gravitational constant The equation is a space-time as independent variables to the metric as the dependent variable with a second-order elliptic bound hyperbolic partial differential equations. It is known to complex and beautiful, but not perfect, the calculation can only be approximate solution. Eventually it got real spherical symmetry of the exact solution - Schwarzschild solution. After adding the cosmological constant field equation: <math> R_ - fracg_ R + Lambda g_ = - 8 pi {G over c ^ 2} T_ </ math> Cosmic phenomena of general relativity and research applications According to general relativity, in the local inertial period, there is no gravity, one-dimensional time and three-dimensional space composed of four-dimensional flat Euclidean space; in any reference frame, the existence of gravity, bend space-time caused by gravity, which is four-dimensional curved space-time Non-Ou Liman space. Einstein found the spatial and temporal distribution of matter affect the geometry of the gravitational field equation. Time and space bending structure depends on material and energy density, momentum density distribution in time and space, and time and space structure, in turn, determine the bending motion of the object track. In the gravity is not strong, bending time and space is very small cases, prediction of general relativity with Newton's law of universal gravitation and Newton's laws of motion predictions are consistent; and strong gravity, time and space bending larger case, the two are different. General relativity has been proposed, predicted anomalous perihelion precession of Mercury, optical frequency gravitational redshift, gravitational light deflection and radar echo delay, have been confirmed by astronomical observation or experiment. In recent years, observations of binary pulsar also provides information on general relativity predicts the existence of gravitational waves strong evidence. General relativity because it is amazing to confirm their theory, and the beautiful, soon to be recognized and appreciated by people. However, due to Newton's gravitational theory gravitational phenomena is sufficient for most accurate, general relativity provides only a very small correction, it does not need it in practical, so half a century after the establishment of general relativity, has not been fully attention has not been developed rapidly. To the 1960s, the situation changes, found strong gravitational objects (neutron stars) and the 3K cosmic background radiation, so that general relativity research flourished. General relativity for the study of structure and evolution of celestial bodies and the structure and evolution of the universe is important. The formation and structure of neutron stars, black hole physics and black holes detected, gravitational radiation and gravitational wave detection theory, big bang cosmology, quantum gravity and large-scale topology of space-time are in-depth study of issues, general relativity as an important theoretical basis for physics research .
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Experimental tests of general relativity
In general relativity was established, Einstein proposed three experimental tests, one of Mercury's perihelion precession, the second is the light in the gravitational field of the bending and the third is the gravitational redshift of spectral lines. Only Mercury's perihelion is the confirmed fact that the other two only later before being confirmed. 60 years later, and it was suggested that observation radar echo delay, gravitational waves and other programs. 1 Mercury perihelion In 1859, astronomer Levy Liere (Le Verrier) found that the Mercury perihelion observations, according to Newton's law than the theoretical value calculated 38 angle seconds per century faster. He guessed there may be less than the Mercury asteroid, the asteroid result of Mercury's gravity deviation between the two. But after years of searching, never found the asteroid. 1882, Niu Kangmu (S. Newcomb) After re-calculated the Mercury perihelion precession of the excess value of 43 arc seconds per century. He suggested that Mercury may be filled with the material resulting from the issue of the zodiacal light of Mercury's motion to be damped. But this can not explain why other planets have similar a few extra precession. Niukang Mu was suspected whether to obey the inverse square law of gravity. Was also used electromagnetic theory to explain the Mercury perihelion anomaly, all without success. In 1915, according to Einstein's general relativity on the motion of planets around the sun as a gravitational field in its movement, causing the sun's mass bends space around, so that one revolution of the planet every public perihelion precession as: ε = 24π2a2/T2c2 (1-e2) Where a is the planet's long axis, c is the speed of light, to cm / s, said, e is the eccentricity, T is the orbital period. For Mercury, the calculated ε = 43 "/ century, consistent with the results coincided with Niukang Mu, one solution to the Newtonian gravity theory to resolve the outstanding issues for many years and this was the result of general relativity has become one of the most powerful evidence of Mercury is the closest the sun's inner planets. away from the central object closer, the stronger the gravitational field, the greater the curvature of space-time curvature coupled with the eccentricity of Mercury's large orbital motion, so the precession corrections for large than the other planets later measured to Venus, Earth and the asteroid Icarus, the excess precession with theoretical calculations are also basically. 2 light bend in a gravitational field Einstein in 1911, "Gravitational light propagation," a paper discussed the light near the sun through the solar gravity will produce bending. He projected angle of 0.83 ", and pointed out that this phenomenon can be observed in the total solar eclipse in 1914 the German astronomer Froude (EFFreundlich) tour to the Crimea peninsula, to prepare for the year to observe the total solar eclipse in August, are having a World War I broke out, could not be observed. Thanks to this, because there were only taking into account the Einstein equivalence principle, the results have half the 1916 Einstein's general relativity based on the full gravitational field of the light in were calculated in re-bending, he not only take into account the solar gravity, also taking into account the mass of the sun lead to geometric deformation space, light angle is: α = 1 ".75 R0 / r, in which R0 is the radius of the Sun, r is the distance to the center of the sun light. During a total solar eclipse in 1919, the British Royal Society and Royal Astronomical Society dispatched a Eddington (ASFEddington), who led two teams dispatched to the West African Gulf of Guinea observed the Principe Island (Principe) and Brazil Sorbian Lap children Seoul (Sobral) two observations. By comparison, the two observations are 1 ".61 ± 0" .30 and 1 ".98 ± 0" .12. The angle was measured to the data compared with Einstein's theory of expectations, basically. This observation precision is too low, but also the interference by other factors. People have been looking for possible other than a total solar eclipse. Developed in the 1960s, radio astronomy has brought hope. Found using radio telescopes radio sources like stars. 1974 and 1975, the results of quasar observations, theory and observations of the deviation is less than one percent. 3 The gravitational redshift of spectral lines General relativity that the clock in a strong gravitational field in more slowly to some, the great mass of the star from the Earth's surface-emitting light, will move to the red end of the spectrum. Einstein in 1911 in the "gravity of light propagation," a discussion paper on this issue. He said the solar surface and Φ the gravitational potential difference between the Earth, ν0, ν, respectively, in the sun light to reach Earth's surface and the frequency, too: (Ν0-ν) / ν =- Φ/c2 = 2 × 10-6. Einstein pointed out that this result with Fabry (C. Fabry), who observed line, and Fabry was originally thought it was the impact of other reasons. In 1925, the United States Adams, Mount Wilson Observatory (WSAdams) observations of the companion star Sirius Sirius A. The so-called white dwarf companion star Fengyun, a thousand times the density than platinum sophomore. Lines issued by observing it, get the expected frequency shift is basically consistent with the general theory of relativity. In 1958, the Mossbauer effect has been found. This effect can be measured with high resolution of r-ray resonance absorption. In 1959, Pound (RVPound) and Lei Buka (G. Rebka) first proposed the use of Mossbauer effect of the gravitational frequency shift detection scheme. Then, they successfully carried out experiments, the results obtained with the theoretical value difference of about five per cent. Gravitational frequency shift measured with atomic clocks can also get good results. 1971 FLYER (JCHafele) and Kai Ding (REKeating) cesium atomic clock with several time to compare different high rate, including one placed in the ground as a reference clock, while a few carried by the civil aircraft register empty, 10,000 m altitude flying around the Earth along the equator. Experimental results and theoretical expected value within 10% match. 1980 Weisuo Te (RFCVessot) and others to experiment with atomic hydrogen. Hydrogen atomic clocks they use rocket launchers to ten thousand kilometers in space, the results obtained with the only difference between the theoretical value of ± 7 × 10-5. 4 radar echo delay After the light bending around massive objects can be seen as a phenomenon of refraction, is equivalent to the speed of light slows down, so a point from a signal space, if the pass near the Sun, reaching the Earth will be the time delay. In 1964, Shapiro (IIShapiro) first put forward this proposal. His group has on Mercury, Venus and Mars radar experiment to prove that indeed the radar echo delays. In recent years, people began to use man-made objects as reflective target, the experimental accuracy has improved. The results of these experiments compared with the general relativity theory of value, a difference of about 1%. With astronomical observations there are many examples of testing general relativity. For example: binary gravitational wave observations and observations, the Hubble law expansion of the universe, the discovery of black holes, neutron star that, the discovery of the microwave background radiation and so on. Through a variety of experimental tests of general relativity more convincing. However, it should be emphasized: we can use a negative test a theory, not a limited number of experiments can ultimately prove a theory; a not very high precision experiments may be able to overturn a theory, but can not high precision of the final series of experiments is certainly a theory. For general relativity is correct, one must take a very cautious approach, strictly and carefully make a reasonable conclusion.
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The fourth assumption Einstein
The fourth assumption is that Einstein's assumption of its first promotion. It this way: the laws of nature in all lines are the same. Denied, claiming that all the lines are the same laws of nature known only in the Galileo system than in the same laws of nature sounds more "natural." But we do not know (outside) the existence of a Galileo system. This principle is called "general relativity theory." Dead lift Let's supposedly a free-fall within the skyscraper elevator, there are a fool. The man let his watch and handkerchief while falling. What will happen? For a lift to the earth as a frame of reference outside of the people, table, handkerchief, and the elevator is fully consistent with the speed of falling. (Let's review: Based on the equivalence principle, the movement of objects in a gravitational field does not depend on its quality.) So the table and the floor, handkerchiefs and floor, and tables, and a fixed distance from the handkerchief. So for the elevator of people, tables and just throw his handkerchief to stay where they are. If this person to his watch or his handkerchief to a particular speed, they will be a constant speed along a straight line. Elevator behave like a Galileo system. However, this will not last forever. Will sooner or later crashed elevator, the elevator will go to outside observers to attend a funeral of an accident. Now we do a second idealized test: our lift away from any massive object. For example, is deep space. Our big moron escape from the last accident. He spent several years in the hospital, decided to return to the elevator. Suddenly a creature began to drag the elevator. Classical mechanics tells us: constant force will produce a constant acceleration. (For very high-speed situations this rule does not apply because the quality of an object increases with increasing speed in our tests, we assume that it is correct.) Thus, the elevator in the Galileo system will have a accelerated motion. Our talented fool to let him stay in the elevator and watch the whereabouts of the handkerchief. Outside the Galileo system in the elevator who watch and handkerchief that will hit the floor. This is due to acceleration and to the floor because they (the handkerchief and watches) hit over. In fact, people outside the elevator will find tables and floors as well as the distance between the handkerchief and the floor at the same rate of reduction. On the other hand, the elevator will note that his watch and handkerchief have the same acceleration, he would this be attributed to gravitational field. These two interpretations seem the same: one side is an accelerated motion, on the other side is the same movement and gravitational field. Let's do an experiment to prove the existence of gravitational field. A beam of light shot through the window on the opposite wall. Our two observers is explained this way: Outside the elevator told us: the light through the window at a constant speed (of course!) Along a straight line horizontally fired into the elevator, according to the opposite wall. However, due to the upward movement of the elevator is so light radiation incident at this point should be slightly under the point position. Elevator who said: We are in a gravitational field. Since there is no quality of light, it is not affected by the impact of the gravitational field, it will just fall on the incident point is on the point. Oh! Problems arose. The two observers disagreed. However, in the elevator of a person who commits a mistake. He said the light did not quality, but the light has energy, and energy to have a quality (remember the one joule of energy quality is: M = E / C ^ 2) so the light will have a curved trajectory to the floor, just as an external observation person put it. As the quality of the energy minimum (C ^ 2 = 300,000,000 × 300,000,000), this phenomenon is only in very strong gravitational field near the observed. This has been confirmed: the sun's enormous mass, close to the sun light will bend. This test Einstein theory (general relativity) the first empirical. From all these experiments we conclude that: through the introduction of a gravitational field we can speed up the system as a Galileo system. Its extension, we believe that it applies to all movements, whether they are rotating (centripetal force is interpreted as a gravitational field) or non-uniform acceleration (not meet Riemann (Riemann) conditions for the gravitational field to be converted by mathematical methods ). You see, consistent with general relativity and practice everywhere. The above example taken from "L'évolution des idées en Physique" with Einstein and Leopold Infeld.
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General relativity - the application of astrophysics
Gravitational lensing Einstein cross: a celestial object with gravitational lensing of the four imaging Deflection of light in gravitational field effect is a new class of astronomical phenomenon. When the observer and the distant celestial objects still exist between a massive object, when observing the quality and relative distance of objects when the observer will see the appropriate number of distorted images of objects, this effect is called gravitational lensing. By the system structure, size and mass distribution of the effects of multiple imaging can even be called the Einstein ring can form a ring or ring part of the arc. The first gravitational lensing was discovered in 1979, it has been found over a hundred gravitational lens. Even if these images are very close to each other that they can not tell - this situation is called microlensing - this effect can still be observed by measuring the total light intensity changes, a lot of microlensing has been discovered. Gravitational lensing has become an important tool of observational astronomy, it is used to detect the existence of dark matter in the universe, and distribution, and for observing distant galaxies as a natural telescope, the Hubble constant can be made for independent estimates. Gravitational lensing observations of the statistical results also study the evolution of galaxy structure is important. Gravitational wave astronomy Artist's concept map: Laser Interferometer Gravitational-wave detector LISA space of binary pulsar observations are indirectly confirmed the existence of gravitational waves strong evidence (see above section the orbital decay), but the depths of the universe from the direct observation of gravitational waves has not been able to achieve, it has also become the main topics relativity of cutting-edge research. Now a considerable number of ground gravitational wave detectors in operation, most notably GEO600, LIGO (Laser Interferometer including three gravitational wave detectors), TAMA300 and VIRGO; and the United States and European cooperation, space laser interferometer LISA detector is now is in development stage, the first test plan by LISA Pathfinder (LISAPathfinder) will be formally launched before the end of 2009. The detection of gravitational waves will be largely based on electromagnetic observations extend the traditional view of observational astronomy, it is able to detect the gravitational wave signal aware of its wave source of information. These have never been truly understood the information may come from black holes, neutron stars or other dense white dwarf star, probably from some of the supernova, or even the birth of the universe from very early times some of the stigma of the boom, for example, the hypothetical cosmic strings. Black holes and other compact stars General relativity theory, computer simulation based on a star collapses to black holes and gravitational waves in the process release a general theory of relativity predicted the existence of black holes, dense enough that when a star, its gravity makes the space-time distortion in a region so that light is extreme can not escape. In the current widely accepted model of stellar evolution, the evolution of massive stars is generally believed that the final phase of the case, including about 1.4 times the solar mass stars evolve into neutron stars, and several times to several times the mass of the sun as a stellar-mass stellar evolution black hole. With hundreds of billions of times times to the supermassive black hole mass of the sun is the law of nature that exist in the center of each galaxy, their presence is generally believed that galaxies and larger-scale structure of universe, the formation has an important role. In dense stellar astronomy on one of the most important attribute is that they can very efficiently to the gravitational energy is converted to electromagnetic radiation. Stellar mass black holes or supermassive black hole of interstellar gas and dust accretion process is considered to be some very bright objects in the formation mechanism, and a variety of well-known examples include the galaxy-scale active galactic nuclei and star-scale micro-quasars. In certain situations the process of accretion in these objects in the excitation strength of a strong relativistic jet, a jet speed close to light speed and direction of a strong high-energy plasma beam. In the modeling of these phenomena in the process have played a key role in general relativity, and experimental observations also support the existence of black holes and all the predictions made by general relativity provides strong evidence. Black hole gravitational wave detection is an important goal: the merger of binary black holes may radiate to the process of being received by the detector on Earth some of the strongest gravitational wave signals, and in the pre-merger binary chirp signals can be as a "standard candles" to the distance to merger speculation, and further into the large scale expansion of the universe as a means of detection. The stellar mass black holes and other compact stellar-mass black holes falling into supermassive the process of gravitational wave radiation can be directly and completely restore the space-time around a supermassive black hole geometry. Cosmology Wilkinson Microwave Anisotropy Probe (WMAP) shooting day microwave background radiation temperature fluctuations is based on the modern model of the universe with a cosmological constant of Einstein's field equations established, the cosmological constant value for large-scale dynamics have an important impact on the universe. The modified Einstein field equations with an isotropic and homogeneous solution: Friedman - Lemaitre - Robertson - Walker metric, in this based on the solution built from a hundred physicists four billion years ago, the hot big bang model of the universe evolved. This model as long as one of the few parameters (for example, the average density of the material universe) to be determined by astronomical observations, it can be obtained from the experimental data further test this model is correct. The model predictions are successful, many, including too Type of Application synthetic chemical elements were formed during the initial abundance, the universe of large-scale structure and temperature of the early universe left behind in today's "echo": cosmic microwave background radiation. From astronomical observations of the cosmic expansion rate can be further estimate the amount of material present in the universe, but the nature of matter in the universe is still a problem to be solved. Now estimate the universe about 90% of the material are all dark matter, they have quality (ie in the gravitational interaction), but does not participate in electromagnetic interactions, that is, they can not (by electromagnetic waves) directly observed. Currently known theories of particle physics, or any other framework has no way to make a satisfactory description of the substance. In addition, the redshift of distant supernovae observations and the cosmic microwave background radiation measurements show that the evolution of our universe, the universe is heavily influenced by the impact of constant value, and it determines the value of the cosmological constant the universe now accelerating expansion. In other words, the universe's accelerating expansion is a non-usual sense of the energy equation of state of some form of decision, this energy is called dark energy, its nature is still not known. In the so-called surge model, the universe was born very early in the (~ 10-33 seconds) experienced a dramatic acceleration of the expansion process. This is the 1980s is due to the hypothesis put forward by some confusing and classical cosmology can not explain the observations made, for example, the height of the cosmic microwave background radiation, isotropic, and now all of the microwave background radiation anisotropy observations support the evidence of inflation models. However, the boom may be also a variety of ways, today's observations can not make this constraint. A larger issue is about the very early universe physics, which involves in-boom, predicted by the model of classical cosmology the big bang singularity. Which are more authoritative opinion is that this issue need to have a complete quantum gravity theory to answer, but this theory has not yet been established (participants below the quantum gravity).
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General relativity - Advanced Concepts
Causal structure and global geometry An infinite static Minkowski universe in general relativity in the Penrose diagram has no rest mass of an object to catch up or exceed the beam of light pulses, that occur in a particular event A little light from that point spread to space anywhere in the position of X before X can not influence. Thus, a time line of all the light of the world (zero of the geodesic) contains information about the causal structure of space-time critical information. Describe the causal structure of the Penrose - Carter figure, the figure in this region of space and infinite time interval through the conformal transformation is "contraction" (mathematically known as compactification) can be accommodated in limited space areas inside, while the line is still the world of light and the Minkowski diagram as indicated by the diagonal. Penrose and other researchers noted the importance of causal structure, in order to develop the so-called global geometry. Global geometry of the object is no longer one of Einstein field equations specific solution (or a family of solutions), but the use of all geodesics are some of the established relationship, such as the Raychaudhuri equation, as well as non-specific nature of the material assumptions (usually in the form of so-called energy conditions to express) to derive universal conclusions. Vision Can be proved under the global geometric space there is some horizon line is called, they will in time and space as part of the region isolated. The most famous example of such a black hole: when the mass is compressed into the space of a small enough area after (correlation length for the Schwarzschild radius), no photons escape from the house. And because the quality of any particle velocity can not exceed the speed of light, the material inside a black hole can be closed within the event horizon. However, from horizon to horizon outside of the channel is still there, suggesting that the black hole's event horizon as a dividing line is not the physical nature of the barrier. A rotating black hole can layer, in extracting energy from rotating black holes play an important role during the early study of black holes depends on the obtained exact solutions of Einstein's field equations, known solutions include the Schwarzschild spherically symmetric solution ( used to describe a static black hole) and antisymmetric Kerr solution (used to describe the steady-state rotating black hole, and thus the introduction of other interesting properties can layer). Later, research by the global geometry reveals more about the universal nature of black holes: study after a considerable period of time after the black hole are gradually evolved into a class of relatively simple parameters can be used to determine the eleven stars, including energy, momentum, angular momentum, a time location and its charge. This property can be summarized as the black hole uniqueness theorems: "black hole no hair," that is different from the black hole is not like human hair as different tags. For example, the gravitational collapse of stars to form black holes after the process is very complex, but the properties of the final forming of the black hole is quite simple. It is worth mentioning that the black hole research has been a general _set_ of laws restricting the behavior of black holes, which is called the black hole (thermal) mechanics, the laws and the laws of thermodynamics have a strong analogies. For example, according to the second law of black hole mechanics, a black hole horizon area will never spontaneously decrease over time, similar to the entropy of a thermodynamic system; also determined by the laws of classical methods (for example, Penrose process) does not may be from a rotating black hole indefinitely extract energy. These are the laws of mechanics strongly suggests a black hole is actually a sub_set_ of the laws of thermodynamics, and black hole entropy is proportional to surface area and its. From this assumption can further refine the law of black hole mechanics. For example, because the second law of black hole mechanics is part of the second law of thermodynamics, then we can see the black hole's surface area may also be reduced, as long as there is some other process to ensure the system's total entropy is increased. The third law of thermodynamics that the temperature of absolute zero there is no object, we can further infer that there should be a black hole thermal radiation; semi-classical theory calculations show that they do exist there is thermal radiation, in this mechanism as a black hole's surface gravity Planck blackbody radiation law in the role of temperature, this radiation is called Hawking radiation (see below section of quantum theory). General relativity also predicted that other types of horizon model: In an expanding universe, the observer may find that certain areas of the past can not be observed (the so-called "particle horizon"), certain areas of the future can not be affected (the event horizon ). Even in flat Minkowski space-time, when the observer is in an accelerated frame of reference will be present when the event horizon, the horizon will be accompanied by semi-classical theory of Ang Lu radiation. Singular point Another popular theory of general relativity but disturbing feature is the dividing line between space and time - the emergence of singularities. Class through time and space and class of light along the geodesic to explore these paths are photons and other particles in free fall all the possible trajectories, but some solutions of Einstein's field equations with the "rough edges" - this is called space-time singularity, these singular points of light on the class or classes of geodesic will suddenly stop, and there is no singularity for these space-time geometry defined to describe. It should be noted that the "singularity" may often not a "point": those field equations of the "rough edges" in both coordinates, may not only be a "point", but also in other geometric form (such as Kerr black hole "strange loop", etc.). General sense of the curvature singularity is the singularity, it is said that these points describe the curvature of space-time geometry, such as Ridge tensor is infinite (the so-called curvature singularity is a coordinate singularity relative terms, the odd coordinates point essentially does not belong to the scope of singularity: some degree of regulation in a specific coordinates will have infinity, but the essence of these points does not have a singularity, in other suitable coordinates is smooth, it will not produce infinite curvature tensor). Describe the future singularity (the end of the world line) is always a well-known examples include static Schwarzschild black hole singularity inside, and always within rotating Kerr black hole of the ring singularity. Friedman - Lemaitre - Robertson - Walker metric, and the other to describe the universe of space-time geometry has a singularity in the past (the beginning of the world line), which is called the big bang singularity, and some also have future singularity (big crunch). Given these models are highly symmetric and thus has been simplified, it is easy to guess whether the emergence of the singularity is not only an ideal state of the natural product. However, the overall geometry by the famous singularity theorems prove that the singularity is a common feature of the results of general relativity, and the quality of any entity that gravitational collapse occurs and it reaches a certain stage will form a singularity, and in a series of expanding universe The same model exists in singularity. However, the basic content of the singularity theorems do not involve the nature of singularity, which determine the singularities of the general structure (for example, the so-called BKL hypothesis) problem is the main subject of the current research. On the other hand, due to the destruction of the physical laws in terms of being wrapped in a singularity of vision is considered among the better than a "naked" singularity, therefore the universe monitoring hypothesis was proposed, it believed that all future real singularity (ie not a perfect symmetry with the formation of the actual nature of the singularity of objects) will be hidden within the event horizon, which is not visible outside face of the observer, that nature hates naked singularities. Although there is no actual evidence of this, there are numerical simulation results support this hypothesis is correct. Evolution equation Each solution of Einstein's field equation is a universe, where the meaning of both the entire universe of space, including the past and the future - they are not just something to reflect a "snapshot", but the complete description of the space-time photo. Each solution in its own particular universe can be described at any time and anywhere in the space-time geometry and material status. For this characterization, Einstein's theory looks different from most other physical theories: most of the physical theory need to specify a physical system of evolution equations (such as quantum mechanics 埃伦费斯特 theorem), that If a physical system at a given moment the state is known, the evolution equations describing the system can allow past and future state. Einstein's theory of the gravitational field and other fields of the former is more difference lies in the interaction itself (is, it appears in no other field when it is still non-linear), and does not have a fixed background structure (in evolution will occur on the cosmic scale). To better understand the Einstein field equations in this time-related partial differential equations, it can be written to describe a form of cosmic evolution over time. This form is called "3 +1" decomposition, in which space is divided into three-dimensional space and one dimension of time. The most famous form is called the ADM form, break down in this space-time evolution equations of general relativity has a good nature: at the appropriate initial conditions for a given equation solvable and the case is unique. Field equations of the "3 +1" decomposition of the form of numerical relativity research base. The amount of global and local level The concept of evolution equations of general relativity in physics and another in close contact: in Einstein's theory, a system of total mass (or energy) of this seemingly simple concept can not find a universal definition. The reason is that, in principle, the gravitational field is not like other games, as with the energy can be localized. However, trying other ways to define a system's total mass is still possible in classical physics, mass (or energy) can be defined from time translation invariance of conserved quantities, or by the system Hamiltonian form. In general relativity, starting from two ways you can obtain the following definition of quality are: * Kema Quality: From the class of Killing vector starting points obtained by Kema invariant under translation in time conserved quantity, expressed as the total energy of a static space-time; If the total mass of a system in place by gravitational waves carry energy to infinity removed, the result is called the zero of the Bondi mass at infinity. These definitions are from the quality of Schon and Yau's positive mass theorem is positive, while the momentum and angular momentum also has a corresponding global definition. Research in this area there are many attempts to establish the amount of so-called quasi-local attempts, for example, the system only through an isolated area where the limited space to construct physical quantities included in the quality of the isolated system. Such attempts hopes to find a better way to describe the isolated system to quantify, such as ring hypothesis of a more precise form.
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General relativity - and the relationship between quantum theory
If general relativity is one of the two pillars of modern physics, then we have to understand quantum theory of elementary particles as well as the basic theory of condensed matter physics is another pillar of modern physics. However, how to apply the concept of quantum theory to the framework of general relativity is still an unresolved issue. Curved space-time quantum field theory Modern physics as the basis for particle physics, the usual sense of quantum field theory is built on the flat Minkowski spacetime, which is in such weak as the Earth's gravitational field in terms of microscopic particles is described a very good approximation. In some cases, the gravitational field is strong enough to affect the substance of which the quantum gravitational field itself, but also not required to be quantized, for the development of a curved space-time physicist in quantum field theory. These theories by means of classical general relativity to describe the background of curved space-time, and define the generalized curved space-time quantum field theory. By this theory, black holes also can be proved by the blackbody radiation released from the particle, which is that Hawking radiation, and through this mechanism may lead to the final black hole evaporation. As mentioned above, Hawking radiation in the study of black hole thermodynamics has played a key role. Quantum gravity Quantum description of the material and the geometry of space-time description does not have the compatibility between each other, and the space-time curvature of general relativity in the infinite (meaning its structure as the micro-scale) and the appearance of singularity, which require a complete the establishment of the theory of quantum gravity. This theory needs to be able very early universe, black holes inside the case and make a full description of which related to the gravitational and quantum space-time geometry need to use the language to describe. Although physicists have made many efforts to this end, and a number of potential candidates for the theory has been developed so far not been able to get a man regarded as complete and self-consistent theory of quantum gravity. A Calabi - Yau manifold projection, made by the string theory compactification of extra dimensions as a method of quantum field theory the basis of particle physics has been able to describe gravity in addition to the other three fundamental interactions outside, but trying to gravity to the generalization of quantum field theory in the framework of a serious attempt has encountered problems. Low-energy region in this attempt successful, the result is an acceptable and effective gravity (quantum) field theory, but in the high-energy region is the divergence of the resulting model (not renormalized). Loop quantum gravity in a simple spin network Attempt to try to overcome these limitations is string theory is one theory, quantum theory in the study of this basic unit is no longer a point-like particles, but the one-dimensional strings. String theory may be able to describe all particles and fundamental interactions including gravity, including the grand unified theory, the cost is resulted in three-dimensional space based on the six-dimensional generated extra dimensions and other abnormal features. Innovation in the so-called second string theory, people speculated string theory, supersymmetry and general relativity and unity of the so-called super-gravity, to form a guess as part of the eleven-dimensional model, this model is called M-theory, it is thought to define a unique and self-consistent theory of quantum gravity. Another attempt from the quantum theory of canonical quantization method. The initial application of general relativity form (see above evolution equation a), the result is Wheeler - have special health equation (whose role is similar to the Schrodinger equation). Although this equation in the general case the definition is not complete, but the introduction of the so-called Asif Teka variable, from this equation can be a promising model: loop quantum gravity. In this theory space is called spin-network network structure, and evolution in discrete time. Depends on general relativity and quantum theory in which nature can be accepted reservations, and in what order of magnitude of energy on the need to introduce changes in the theory of quantum gravity, there are many attempts, such as dynamic triangulation, cause and effect combinations, the amount of theory and twisted path integral based quantum cosmological model. All of these theories are still tentative candidates on the main form and the concept of the problem to be solved, and they are facing a common problem, that is still no way to experimentally verify the predictions of quantum theory of gravity, and thus can not be through multiple differences between the predictions of some theory to determine its correctness. In this sense, the experimental observation of quantum gravity also need to hope for the future of observational cosmology and particle physics experiments related to become possible.
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Current Progress
Gravitation and cosmology in the study, general relativity has become a highly successful model so far has passed every sense of clear observation and experimental testing. But even so, there is still evidence of this theory is not so perfect: the search for quantum gravity and the reality of space-time singularity problems remain to be resolved; experimental observation of dark matter and dark energy to get the support of the existence of the data results are secretly calling the establishment of a new kind of physics; observed from the Pioneer anomalous effect may be explained by the known theory, perhaps it really is a new physics coming notice. However, among the general theory of relativity is still full of possibilities worthy of exploration: mathematical theory of relativity scientists seeking to understand the nature of singularity, and the basic properties of Einstein's field equation; being constantly updated computer value of black hole mergers, and more simulation; the first direct observation of gravitational waves is also moving ahead in the race, the human hope to be able to reach the far stronger than the gravitational field to create more test the correctness of the theory of chance. Einstein published his theory in ninety years later, general relativity is still a highly active area of research.
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Examples of general relativity-based lesson plans
General principle of relativity and the equivalence principle of special relativity that, in different inertial reference system in all physical laws are the same. Einstein On this basis, a major step forward in that in any reference system (including non-inertial) the laws of physics are the same, this is the general principle of relativity. Here is another basic principle of general relativity. Assuming the spacecraft is fully closed, the astronauts and the outside world without any contact, then he is no way to determine the whereabouts of the object to an acceleration of the force is gravitational or inertial force in the end. In fact, not only the free-fall experiments, any physical process within the spacecraft can not tell us to accelerate the spacecraft in the end is in motion or parked in a planet's surface. Here comes the scene and the section of this chapter Galileo described the scene in the ship is very similar. This fact brings us to: a uniform gravitational field with a constant acceleration to do the equivalent of the reference system. Einstein put it as a second basic principle of general relativity, which is the famous principle of equivalence. Starting from these two basic principles can draw some unexpected conclusions. Assuming the universe in gravity can be ignored in the spaceship with a linear motion with constant acceleration to do, a beam of light launched into the direction perpendicular to the spacecraft motion. Outboard stationary observer will see this bundle alone, of course, along a straight line, but the observer spacecraft to spacecraft as a reference system is another to see some scenarios. To record the beam in the spacecraft's track, he placed the ship some of the middle distance translucent screen (pictured), the light through these screens, while leaving the screen on the spot. As the spacecraft in advance, the location of the light to reach the next screen, always on a show than to reach the location closer to the stern. If the spacecraft made uniform linear motion, light on any flight between two adjacent screen, the distance between the spacecraft forward are equal, observers see the light on the spacecraft's track is still a straight line (as shown in the dotted line), although direction of the line outboard stationary observer sees not the same straight line. If the spacecraft to do linear motion with constant acceleration in the spread of light to the right, while also increasing the speed of the spacecraft, so the observer on board to record the tracks of light is a parabola (shown in solid line). According to the principle of equivalence, an observer in the spacecraft is also entirely possible that the ship is not accelerating, but there is a huge aft direction of the object, its gravitational field affects the physical processes inside the spacecraft. Therefore, we conclude: the object's gravity can bend light. Objects are often too weak gravitational field, the early 20th century, the sun can only be observed bending of light caused by the gravitational field. As the sun's gravitational field, and we could see the sun behind the star (pictured). However, the usual bright sky so that we can not stargazing, so the best time is when the total solar eclipse occurred. May 29, 1919 total solar eclipse happen to have one, two British expedition dispatched to the Gulf of Guinea and Brazil, observations, and the results fully confirmed Einstein's prediction. This is the first verification of general relativity. Figure phenomenon that the planet's strong gravitational field can make it light coming from behind convergence, a phenomenon called gravitational lensing. Is likely to exist in the universe, black holes, black hole does not radiate electromagnetic waves, so can not be directly observed, but its great quality and small size make it near a strong gravitational field, so to explore the black hole gravitational lensing is one of the ways. Time interval with the gravitational field gravitational field makes the existence of space time process in different locations differ. We look at a huge rotating disk (Figure). From the ground point of view, except on the axis of rotation of the disc position, the points are made to accelerate the movement, the more close to the edge, the greater the acceleration, direction, point to disk center. Also see from the ground, the more close to the edge of the point, the greater the speed. According to special relativity, the same process, the more close to the edge in position, the duration of this process longer. Or that the location near the edge of the slow process of time. Now and then the disc itself as a reference system to study this phenomenon. People on the disc that disc there is a gravitational field, the direction from the plate center point edge. Given the location near the edge of the slow process of time, people on the plate can be concluded: the lower position in the gravitational potential, the time the process is slower. There are a class of stars in the universe, the volume is small, the quality is not small, called dwarf. Dwarf surface gravity is very strong, gravitational potential is much lower than the Earth's surface. Dwarf surface is relatively slow time course, where the frequency of light atoms than the same atoms in the low frequency of light on Earth, looks reddish. This phenomenon is called gravitational redshift has been confirmed in astronomical observation. Modern technology is also able to verify the gravitational redshift in the earth. The length of the rod and still study the gravitational field of the disc rotation. The same rod, on different locations on the disk, the speed of their movement with the disc not the same, according to the special theory of relativity, they are not the same length, the more close to the edge of the shorter rod. People on the panel also observed this difference, but he Yuanpan as a reference system that the disk is stationary, while he also believes that there are various points on the plate pointing Yuanpan edge of gravity, so he concluded: gravitation potential lower position, the shorter the length of rod. Rod length and the distribution of the gravitational field, this phenomenon reflects the fact that, due to the presence of substances, the actual space is not uniform, and our concept of the past which is very different. Analogy, a piece of cloth is neat grid above (Figure A), if the hand downward pressure on the curved grid (Figure B). Physics borrowed "bending" the word is usually said that due to the presence of substances, the actual space is curved. Planetary motion along the elliptical orbit around the sun, away from the sun, sometimes nearer, sometimes farther. Great mass of the sun bends space around it, the result is that the planets each orbit of public revolution of its major axis than a deflection angle of the previous cycle, a phenomenon called the precession of planetary orbits. Theoretical analysis shows that only the precession of Mercury's orbit more significant, reaching about every century 0.01 °. This phenomenon occurs early in the general theory of relativity has been found before, but can not explain, so it is actually the earliest evidence of general relativity. General relativity and geometry Finally, we turn once again to return the disc. Special theory of relativity tells us that only the length along the direction of motion changes, the length perpendicular to the direction of motion does not change; If the disc as a reference system, we can say, the spatial scale along the direction of gravity has not changed, only the vertical the direction of the spatial scale of gravity has changed. This is a very profound sense, because then measure the circumference and diameter of the disc, and their ratio is 3.141 59 ... no longer, but other values, the angles of a triangle is 180 ° and will not be a ... ... In short, the actual space is curved, we learn geometry no longer applies. Geometry reflects the people's understanding of spatial relationships. People only ever smaller spatial scales in contact with weak gravitational field. This case, the bending of space can be ignored, on the basis of human development, the Euclidean geometry, which reflects the actual flat space. General relativity tells us that the actual space is curved, so the actual description of the space should be more general sense of non-Euclidean geometry. However, as a special case of non-Euclidean geometry, Euclidean geometry in its scope of application is still correct, and will continue to play a role. "Made in China", about the past 60 years China
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Encyclopedia
guangyi xiangduilun General relativity general theory of relativity A. Einstein's gravitational theory. The theory of the gravitational field and space-time structure linked to the introduction of a four-Verona Lenz real space-time manifold as a model, the geometry of this manifold in a small range close to the four-dimensional Minkowski space □ 3, 1 of geometry, but the larger point of view, it is Minkowski space and a significant difference, is a curved space-time. A four-dimensional Lorentz manifold М4, is a measure of four-dimensional Lorenz manifold. Its meaning is as follows: each point in М4 tangent space □ □ □, are defined in the vector inner product, but Riemannian manifold, and the situation is different, this is not a Euclidean inner product, but Min Coffs base type (see Minkowski space). Each of М4 coordinate neighborhood, in which the tangent space at each point □ □ □ introduced natural frame, which consists of four consisting of tangent vector □ frame. Reference in this frame, □ □ □ any vector can be expressed as all □, two vectors □, □ should be a form of inner product □, where (□ □) to form a symbol (+,+,+,-) the symmetric matrix. М □ coordinate area in the metrics on the use of Lorenz □ to represent. And Riemannian geometry, as measured according to manifold, can make its mark Christopher Stoffel (Levi - Qiwei Ta contact), the curvature tensor and Ricci tensor. As the curvature tensor is generally not zero, so that general relativity space-time is curved space-time. Accordance with the tangent space of the inner product, manifolds tangent vector can be divided into classes, the class space, class and other categories of light, particle trajectory, says the М4 of a curve, called the world line, it can not cut the vector is the class empty. The basic idea of Einstein's general theory of relativity is: four-dimensional space-time geometry and the material of which the distribution and movement are interrelated, this link can be used gravitational field equation □ expressed here are Ridge tensor □ □, □ is the scalar curvature, □ is the gravitational constant, □ □ is that the distribution of matter and motion energy-momentum tensor. Especially in the vacuum region should be established □ □ = 0. Another basic idea of general relativity is: a spatial and temporal distribution of matter, a quality only by the gravitational field of a small role in the movement of the test particle trajectory (world line) is the Lorenz manifold, geodesic, so that the gravitational field theory becomes a geometric theory. To 1930, A. Einstein and L. Ying Fei Boulder also pointed out that this conclusion can in fact inferences as field equations. In general relativity, the general is not a clear separation of the three space coordinates and time coordinates, but a movement of the air at this time the observer can still experience his own course record time, if two have joined in an instantaneous observer, the movement of different trajectories through re-join, they will find that they recorded the final "time position" is a separate one, which is the embodiment of space-time curvature . The use of tangent space Lorentz frame, can be a variety of special relativity in general relativity expressed in physical quantities out of the variation of this physical quantity can generally be described with differential equations, can now be _select_ed as the coordinates of a widely than the special theory of relativity much higher, so the laws of physics Einstein asked in a different coordinate system of representation should be according to certain rules (in line with group requirements) can be converted to each other, this is the general principle of relativity. However, in general relativity, as in all the geometry issues, the special coordinates the _select_ion still has its significance. For example, consider a spherical object in the surrounding vacuum gravitational field generated, you can _select_ specific coordinates, and Hilde Schwartz solution obtained by this solution, the following phenomena can be accurately calculated. ① Mercury perihelion precession; ② light near the sun by the gravitational field through the impact produced by bending; ③ spectrum arising due to gravity to shift the direction of long wavelengths (called gravitational redshift). Experimental verification of these three phenomena, so that the position of general relativity to be consolidate. There are many mathematical problems of general relativity to study, for example: ① Cauchy problem and the singularity is known a moment of space-time structure, the instantaneous distribution of matter and motion, seeking the future (or retroactively in the past) the space-time structure and material distribution and movement. Of small-scale and short time, the problem has been resolved, but for a long time