
#REDIRECT General relativity
General relativity (GR) or general relativity theory (GRT) is a fundamental physical theory of gravitation which corrects and extends gravity, especially at the macroscopic level of stars or planets. General relativity may be regarded as an extension of special relativity, this latter theory correcting Newtonian mechanics at high velocities. General relativity has a unique role amongst physical theories in the sense that it interprets the gravitational field as a geometric phenomenon. More specifically, it assumes that any object possessing mass curves the 'space' in which it exists, this curvature being equated to gravity. To conceptualize this equivalence, it is helpful to think, as several author-physicists have suggested, in terms of gravity not causing or being caused by spacetime curvature, but rather that gravity is spacetime curvature. It deals with the motion of bodies in such 'curved spaces' and has survived every experimental test performed on it since its formulation by Albert Einstein in 1915. General relativity forms the basis for modern studies in fields such as astronomy, cosmology and astrophysics. It describes with great accuracy and precision many phenomena where classical physics fails, such as the perihelion motion of planets (classical physics cannot fully account for the perihelion shift of Mercury, for example) and the bending of starlight by the Sun (again, classical physics can only account for half the experimentally observed bending). It also predicts phenomena such as the existence of gravitational waves, black holes and the expansion of the universe. In fact, even Einstein himself initially believed that the universe cannot be expanding, but experimental observations of distant galaxies by Edwin Hubble finally forced Einstein to concede. It is believed that Einstein developed the general relativity from the simple but elegant consideration that no "action at a distance", like the effect of Newtonian gravitation, can propagate through space-time instantaneously. The speed of propagation is limited by the velocity of light, as required by his Special relativity. Unlike the other revolutionary physical theory, quantum mechanics, general relativity was essentially formulated by one man—Albert Einstein. However, Einstein required the help of one of his friends, Marcel Grossmann, to help him with the mathematics of curved manifolds. == Physical Description of the Theory == In relativity theory, physical phenomena are described by observers making measurements in reference frames. In general relativity, these reference frames are arbitrarily moving relative to each other (unlike in special relativity, where the reference frames are assumed to be inertial). Consider two such reference frames, for example, one situated on Earth (the 'Earth-frame'), and another in orbit around the Earth (the 'orbit-frame'). An observer (O) in the orbit-frame will feel weightless as they 'fall' towards the Earth. In Newtonian gravitation, O's motion is explained by the action at a distance (physics) formulation of gravity, where it is assumed that a force between the Earth and O causes O to move around the Earth. General relativity views the situation in a different manner, namely, by demonstrating that the Earth modifies ('warps') the geometry in its vicinity and O will naturally follow the curves (geodesics) in this geometry unless O applies accelerative force (e.g. rockets). More precisely, the presence of matter determines the geometry of spacetime, the physical arena in which all events take place. This is a profound innovation in physics, all other physical theories assuming the structure of the spacetime in advance. It is important to note that a given matter distribution will fix the spacetime once and for all. There are a few caveats here: (1) the spacetime within which the matter is distributed cannot be properly defined without the matter, so most solutions require special assumptions, such as symmetries, to allow the relativist to concoct a candidate spacetime, then see where the matter must lie, then require its properties be "reasonable" and so on. (2) Initial and boundary conditions can also be a problem, so that gravitational waves may violate the idea of the spacetime being fixed once and for all. More specifically, let us ask how the nearly circular path on which the Earth travels can be a geodesic, which we always thought looked more like a straight line. But in the four dimensions of relativity, the principal motion of the Earth is into the future. Consider the situation in four dimensions, but for simplicity assume the Earth's velocity is perpendicular to the Z axis. Considering the time axis vertical, the Earth's path is a spiral (helix) about the t-axis, and not a tightly wound one at that. In one complete turn of the spiral, one year has elapsed, so the coordinate ct has increased one light year, but the Earth is moving in the x-y plane much more slowly, having gone only 2 astronomical units in a year; i.e. the slope of the helix is c divided by the orbital velocity, or about ten thousand. The motion of the observer O in orbit is rather like a ping-pong ball being forced to follow the 'dent' or depression created in a trampoline by a relatively massive object like a medicine ball. The geometry is determined by the medicine ball, the relatively light ping-pong ball causing no significant change in the local geometry. Thus, general relativity provides a simpler and more natural description of gravity than Newton's action at a distance formulation. An oft-quoted analogy used in visualising spacetime curvature is to imagine a universe of one-dimensional beings living in one dimension of space and one dimension of time. Each piece of matter is not a point on any imaginable curved surface, but a world line showing where that point moves as it goes from the past to the future. The precise means of calculating the geometry of spacetime given the matter distribution is encapsulated in Einstein's field equation. === The Equivalence Principle === :''(For more detailed information about the equivalence principle, see equivalence principle)'' Inertial reference frames, in which bodies maintain a uniform state of motion unless acted upon by another body, are distinguished from non-inertial frames, in which freely moving bodies have an acceleration deriving from the reference frame itself. In non-inertial frames there is a perceived force which is accounted for by the acceleration of the frame, not by the direct influence of other matter. Thus we feel acceleration when cornering on the roads when we use a car as the physical base of our reference frame. Similarly there are coriolis effect and centrifugal forces when we define reference frames based on rotating matter (such as the Earth or a child's roundabout). In Newtonian mechanics, the coriolis and centrifugal forces are regarded as non-physical ones, arising from the use of a rotating reference frame. In General Relativity there is no way, locally, to define these "forces" as distinct from those arising through the use of any non-inertial reference frame. The principle of equivalence in general relativity states that there is no local experiment to distinguish non-rotating free fall in a gravitational field from uniform motion in the absence of a gravitational field. In short there is no gravity force in a reference frame in free fall other than tidal gravity forces, which can deform objects but not accelerate them. Indeed, attempts to detect gravitational waves depend on just those tidal forces. From this perspective the observed gravity at the surface of the Earth is the force observed in a reference frame defined from matter at the surface which is not free, but is prevented from falling by the matter below (on and within the Earth, including the continents, furniture, etc.,) and is analogous to the acceleration felt in a car. In the process of discovering GR, Einstein used a fact that was known since the time of Galileo, namely, that the inertial and gravitational masses of an object happen to be the same. He used this as the basis for the principle of equivalence, which describes the effects of gravitation and acceleration as different perspectives of the same thing (at least locally), and which he stated in 1907 as: :''We shall therefore assume the complete physical equivalence of a gravitational field and the corresponding acceleration of the reference frame. This assumption extends the principle of special relativity to the case of uniformly accelerated motion of the reference frame.'' In other words, he postulated that no experiment can locally distinguish between a uniform gravitational field and a uniform acceleration. The meaning of the ''Principle of Equivalence'' has gradually broadened, in consonance with Einstein's further writings, to include the concept that no physical measurement within a given unaccelerated reference system can determine its state of motion. This implies that it is impossible to measure, and therefore virtually meaningless to discuss, changes in fundamental physical constants, such as the rest masses or electrical charges of elementary particles in different states of relative motion. Any measured change in such a constant would represent either experimental error or a demonstration that the theory of relativity was wrong or incomplete. The equivalence principle explains the experimental observation that inertial and gravitational mass are equivalent. Moreover, the principle implies that some frames of reference must obey a non-Euclidean geometry: that spacetime is curvature (by matter and energy), and gravity can be seen purely as a result of this geometry. This yields many predictions such as gravitational redshifts and light bending around stars, black holes, time slowed by gravitational fields, and slightly modified laws of gravitation even in weak gravitational fields. However, it should be noted that the equivalence principle does not uniquely determine the field equations of curved spacetime, and there is a parameter known as the cosmological constant which can be adjusted. === The Covariance Principle === :''(For more detailed information about the covariance principle, see the article principle of general covariance)'' Following on from the spirit of special relativity, the principle of general covariance states that all coordinate systems are equivalent for the formulation of the general laws of nature. Mathematically, this suggests that the laws of physics should be tensor equations. == Geometric Foundations == For a long time, it was believed that the universe obeyed the axioms of Euclidean geometry, including Euclid's parallel postulate. In crude terms, 'space is Euclidean' seemed to be the general rule. Although the development of non-euclidean geometry by Nikolai_Ivanovich_Lobachevsky, Janos Bolyai, Carl Friedrich Gauss and others, opened up a new field of research, the general consensus was still that space is Euclidean. Early on, Gauss decided to test this assumption and found (with experiments using the crude equipment of that age) that the sum of the angles of a triangle was 180 degrees, affirming that to available precision, physical space obeyed the parallel postulate and was Euclidean. Modern experiments are capable of detecting the non-Euclidean geometry of space-time directly. For example, the Pound-Rebka experiment (1959) detected the change in wavelength of light from a cobalt source rising 22.5 meters against gravity in a shaft in the Jefferson Physical Laboratory at Harvard University, and the rate of atomic clocks in Global Positioning System satellites orbiting the Earth has to be "corrected" for the effect of gravity, in order to synchronize these clocks with earth-bound ones. In so "correcting" a clock, of course, one tweaks it so as to be an imperfect or nonstandard clock from the standpoint of the equivalence principle. In other words, in order to establish a more or less global time standard, one has to adjust or modify clocks originally of standard construction and operation so as to, in a sense, violate the equivalence principle. In 1854, Gauss' student Bernhard Riemann gave a famous lecture in which he developed the general mathematics of non-euclidean geometry. In the lecture, he defined what is nowadays called an n-dimensional Riemannian manifold and defined the curvature tensor, a fundamental mathematical object in GR. He also inquired as to the dimension of the space of reality (the dimension of our world's space), as well as wondering about the actual geometry of the world. In retrospect, Riemann's lecture was ahead of its time, it finding fruition when Einstein developed GR. In fact, Einstein began with physical concepts to develop GR and knew that he needed the mathematics of curved spaces to formulate his theory. The required mathematics was precisely that developed by Riemann, the modern designation called manifold theory. == Predictions of GR == :''(For more detailed information about tests and predictions of general relativity, see Tests of general relativity)'' Like any good scientific theory, general relativity makes predictions which can be tested. Some of the predictions of general relativity include the perihelion shifts of planetary orbits (particularly that of Mercury (planet)), bending of light by massive objects, and the existence of gravitational waves. The first two of these tests have been verified to a high degree of accuracy and precision. Most researchers believe in the existence of gravitational waves, but more accurate experiments are needed to raise this prediction to the status of the other two, if one demands direct detection of the waves. Nevertheless, indirect effects of gravitational wave emission have been observed for a binary system of orbiting neutron stars, as described in Tests of general relativity. Other predictions include the expansion of the universe, the existence of black holes and possibly the existence of wormholes. The existence of black holes is generally accepted, but the existence of wormholes is still very controversial, many researchers believing that wormholes may exist only in the presence of exotic matter. The existence of white holes is very speculative, as they appear to contradict the second law of thermodynamics. Many other quantitative predictions of general relativity have since been confirmed by astronomical observations. One of the most recent, the discovery in 2003 of PSR J0737-3039, a binary neutron star in which one component is a pulsar and where the Apsis Precession 16.88° per year (or about 140,000 times faster than the precession of Mercury's perihelion), enabled the most precise experimental verification yet of the effects predicted by general relativity. [http://skyandtelescope.com/news/article_1124_1.asp] [http://skyandtelescope.com/news/article_1473_1.asp]. == Mathematics of GR == :''(For more detailed information about the mathematics of general relativity, see mathematics of general relativity)'' The mathematics of general relativity involves heavy use of tensor calculus. The use of tensors in relativity greatly simplifies many calculations and serves to reflect the fact that all observers are equivalent for the description of physical laws. An important tensor in relativity is the Riemann tensor, which is a matrix of numbers that essentially measures the deviation of a vector that is moved along a curve parallel to itself when a round trip is made. In flat space, the vector returns to the same orientation (the Riemann tensor is zero), but in a curved space it generally does not (in general, a non-zero Riemann tensor). In spaces of two dimensions, the Riemann tensor is a matrix (i.e. just a real number) called the Gaussian or scalar curvature. Curvature can be measured entirely within a surface, and similarly within higher-dimensional manifolds such as space or spacetime. The dynamics of general relativity are incorporated in the Einstein field equation, a tensor equation that describes how matter affects the geometry of spacetime, and the geodesic equation, which describes how objects move in the resulting geometry. Often, approximations are made in working with both these equations. An important feature of the Einstein field equations is that they are a set of nonlinear partial differential equations for the metric. As such, this distinguishes the field equations of general relativity from some of the other important field equations in physics, such as Maxwell's equations (which are linear in the electric and magnetic fields) and Schrodinger's equation (which is linear in the wavefunction). This constitutes another major difference between general relativity and other physical theories. == Relationship to other physical theories == === Special and general relativity === In relativity theory, all events are referred to one or more reference frames. A reference frame is defined by choosing particular matter as the basis for its definition. Thus, all motion is defined and quantified relative to other matter. In the special theory of relativity it is assumed that reference frames can be extended indefinitely in all directions in space and time. The theory of special relativity concerns itself with reference frames that move at a constant velocity with respect to each other (i.e. inertial reference frames), whereas general relativity deals with all frames of reference. In the general theory it is recognised that we can only define local frames to given accuracy for finite time periods and finite regions of space (similarly we can draw flat maps of regions of the surface of the earth but we cannot extend them to cover the whole surface without distortion). The Special relativity (1905) modified the equations used in comparing the measurements made by differently moving bodies, in view of the constant value of the speed of light, i.e. its observed invariance in reference frames moving uniformly relative to each other. This had the consequence that physics could no longer treat space and time separately, but only as a single four-dimensional system, "space-time," which was divided into "time-like" and "space-like" directions differently depending on the observer's motion. The general theory added to this that the presence of matter "warped" the local space-time environment, so that apparently "straight" lines through space and time have the properties we think of "curved" lines as having. Thus Newton's first law is replaced by the law of geodesic motion. There are no known experimental results that suggest that a non-quantum theory of gravity radically different from general relativity is necessary. For example, the Allais effect was initially speculated to demonstrate "gravitational shielding," but was subsequently explained by conventional phenomena. === Quantum mechanics and general relativity === There are good theoretical reasons for considering general relativity to be incomplete. General relativity does not include quantum mechanics, and this causes the theory to break down at sufficiently high energies. A continuing unsolved challenge of modern physics is the question of how to correctly combine general relativity with quantum mechanics, thus applying it also to the smallest scales of time and space. Most scientists consider this unifying theory's leading candidates to be M-theory and loop quantum gravity. This unification would achieve Einstein's dream of a grand unification theory, combining the strong, electroweak, and gravitational forces into one force, as well as successfully creating one set of equations that do not break down under any conditions. === Other theories === The Brans-Dicke theory and the Rosen bi-metric theory are modifications of general relativity and cannot be ruled out by current experiments. See Einstein-Cartan theory for an extension of general relativity to include torsion. There have been attempts to formulate consistent theories which combine gravity and electromagnetism, some of the first being the Kaluza-Klein theory and Weyl's gauge theory. == History == ''Full article: History of general relativity''
''See also: Tests of general relativity'' General relativity was developed by Einstein in a process that began in 1907 with the publication of an article by Einstein on the influence of gravity and acceleration on the behaviour of light in special relativity. Most of this work was done in the years 1911–1915, beginning with the publication a second article of the effect of gravitation on light. By 1912, Einstein was actively seeking a theory in which gravitation was explained as a geometric phenomenon. In 1915, these efforts culminated in the publication of the Einstein field equations, which are a set of differential equations. Since 1915, the development of general relativity has focused on solving the field equations for various cases. This generally means finding metrics which correspond to realistic physical scenarios. The interpretation of the solutions and their possible experimental and observational testing also constitutes a large part of research in GR. The expansion of the universe created an interesting episode for general relativity. In 1922, Alexander Friedmann found a solution in which the universe may expand or contract, and later Georges Lemaître derived a solution for an expanding universe. Einstein did not believe in an expanding universe, and so he added a cosmological constant to the field equations to permit the creation of static universe solutions. In 1929, Edwin Hubble found evidence that the universe is expanding. This resulted in Einstein dropping the cosmological constant, referring to it as "the biggest blunder in my career". Progress in solving the field equations and understanding the solutions has been ongoing. Notable solutions have included the Schwarzschild solution (1916), the Reissner-Nordström solution and the Kerr solution. Observationally, general relativity has a history too. The perihelion precession of Mercury was the first evidence that general relativity is correct. Eddington's 1919 expedition in which he confirmed Einstein's prediction for the deflection of light by the Sun helped to cement the status of general relativity as a likely true theory. Since then, many observations have confirmed the predictions of general relativity. These include studies of binary pulsars, observations of radio signals passing the limb of the Sun, and even the GPS system. For more information, see the Tests of general relativity article. ==Quotes== :''Spacetime grips mass, telling it how to move, and mass grips spacetime, telling it how to curve'' - John Archibald Wheeler. :''The theory appeared to me then, and still does, the greatest feat of human thinking about nature, the most amazing combination of philosophical penetration, physical intuition, and mathematical skill. But its connections with experience were slender. It appealed to me like a great work of art, to be enjoyed and admired from a distance.'' —Max Born ==References== This reading list is loosely based on ===Popular Books=== * Leisurely pace, provides superb intuition for Schwarzschild geometry. * Covers much more ground, while remaining concise and readable. * A delightful romp through the physics of black holes. Features many personal anecdotes from the author's distinguished career. ===Textbooks=== ====Introductory==== * Clearly written, short and sweet; covers less ground than the others but much cheaper. * Readable, well illustrated, fairly comprehensive without becoming encyclopedic--- what's not to love? * Features an outstanding treatment of tensor calculus and the matter tensor, a key topic which beginners often have trouble grasping. The treatment of linearized gravitational waves and stellar models is also outstanding. * Clear and very well organized. Features excellent treatment of far-field and weak-field expansions and linearized gravitational waves, including multipole moments. Offers more on solution techniques than other introductory textbooks. * In contrast to other introductions, these authors use an exceptionally clear comparison of linearized general relativity with electromagnetism to motivate Einstein's field equations. Superb treatment of observational tests and of gravitational lensing. Should be useful for students wishing to master the textbook by Weinberg. ====Advanced==== * Readable, up-to-date. Features an outstanding treatment of the mass, charge, and spin of isolated objects, plus an elementary introduction to quantum field theory on curved spacetimes and Hawking radiation. Further essential material is concisely explained in valuable appendices. [http://pancake.uchicago.edu/~carroll/grbook/ Book website]. * A unique textbook straddling the modern and pre-modern eras in general relativity, this offers a dual introduction to Maxwell's theory of electromagnetism and Einstein's theory of gravitation. Noteworthy topics include a good treatment of multipole moments and background material needed for the BKL conjecture. * A classic general relativity textbook. Features a unique two-track organization, with numerous boxes, tables, figures, and citations. In general, this book focuses more on developing physical and geometrical intuition than the textbook by Wald. * Demanding but full of valuable physical insight and techniques. No pictures, in marked contrast to the textbook by Misner, Thorne & Wheeler. Excellent treatment of topics related to PPN formalism, weak field approximations, gravitons, as well as applications of particle physics to cosmology. No exercises. * Often cited as the definitive graduate level textbook. Features an outstanding introduction to tensors (with a clear distinction between ''abstract indices'' and particular indices, overlooked by most other authors), as well as the basic singularity, stability, and uniqueness theorems, quantum field theory on curved spacetimes, and black hole thermodynamics. Much valuable material is clearly explained in a series of superb appendices. In general, this book focuses more on developing insight into mathematical formalism and techniques than on developing physical insight. ====Special Topics==== * A collection of excellent problems, with sketch solutions in the back. Text your skills! * Don't be fooled by the subtitle; this book explains many key concepts and techniques which are needed by ''all'' contemporary graduate students, but are not adequately explained elsewhere. Essential topics covered here include congruences (expansion, vorticity, and shear), optical scalars, junction conditions for matching interior solutions to exterior solutions, thin shells (including null shells), spatial hyperslices, and energy conditions. * Not easy to read, but one of the few textbooks to offer an introduction to the important Newman/Penrose formalism. Also features much material on gravitational waves. * This book is billed as an introductory textbook, but has no exercises and may be hard to read. Unique features include a chapter on measurement theory for general relativity, plus an introduction to tetrad formalism. ==External Links== ===Online Tutorials=== * Baez, John & Bunn, Ted; This superb expository paper explains the meaning of the field equation in terms of the motion of a cloud of free falling test particles. *Carroll, Sean M.; A concise but very readable overview. ===Webcourses=== * Rappoport, Saul; An elementary introduction to relativistic physics, including a smattering of gtr. * Bertschinger, Edmund; An introduction to general relativity at the level of Misner, Thorne & Wheeler. * Brown,Kevin; An idiosyncratic work, providing in-depth discussions of various aspects of special and general relativity. The subjects are treated exceptionally thoroughly. The book is written for people who already have a firm grasp of relativity. * van Putten, Maurice; An topics course on gravitational wave detectors, featuring the draft of the instructor's forthcoming textbook. General relativity Theories vi:Lý thuyết tương đối rộng
For the purposes of readability perhaps the sentence "Early on, Gauss decided to test this assumption and found (with experiments using the crude equipment of that age)." should be modified to include what he found :) I don't have the knowledge to update and thought I would mention it here so that someone more informed in the area could execute the update. Steve. ---- I put in some links and rescued the field equation from the previous version. I think we also need to explain the differences between Newton's and Einstein's theory a bit, for instance as they relate to :black holes. --AxelBoldt ---- The current text mentions 2 things as fundamental in general Relativity: # You need a reference frame to describe motion # Reference frames can only be defined with respect to material objects; the text seems to imply that these are gravitating and therefore G.R. is a theory of gravitation too. I do not believe the 2nd assumption is true, and esp. not its implication. I have a different perspective: suppose that the principle of General Relativity can be formulated as follows: "Laws of physics must be formulated in such a way that they are independent of the frame of reference of the observer." So G.R. is a theory about theories of physics, as much as a theory of the physical universe itself. It is a recipe for making good theories, which may or may not be consistent with the universe as we actually observe it. The popularity of thought experiments in G.R. demonstrates that its focus is on how we should describe the world, rather than how we actually observe it. The theories work only as far as the universe itself is consistent, understandable, and can be described by logic and mathematics - and there is no a priori reason that it is this way. But to the extent that the universe can be described by theories, the principle formulated above gives an important property of a "good" theory. Implications for the theory of G.R. based on this principle: # Light has a constant velocity. It is well known that Einstein was troubled by the description of induction in a coil in a variable magnetic field: depending if you are in the coil or in the magnetic field, the one generates the other depending from you perspective. Indeed, the Maxwell-Heavyside equations do not require different formulae: exactly the same equations can be used and applied in your local frame of reference, and the results are identical if you go to the other frame. So this is a "good" theory. Now from these equations the velocity of light can be computed, and it is a constant, independent of your frame of reference. Of course an absolute velocity that is not relative to observers is in conflict with Galilean dynamics. Einstein drew the ultimate consequence, and chose to adjust the geometry of space rather than the theory. The Lorentz transformations immediately follow from this choice, and are the only solution consistent with this choice. # Gravity == acceleration. In a thought experiment, you can play billiard in a train that moves with constant velocity, and not notice that it moves. If it accelerates however, you will notice because the inertial mass of the balls will drive them to one end of the table (your local frame of reference). Now exactly the same will happen if the train moves up a slope with constant velocity: they will roll downhill because gravity pulls on their gravitational mass. However, you are unable to distinguish this event from the previous one -- iff inertial mass is identical to gravitational mass. So a "good" theory would describe both events with the same equations. : Now in another thought experiment you are in an elevator that is accelerated, and a beam of light is sent through one of the sides. Because light has a finite velocity, its path in the elevator case (your local frame of reference) is curved. Now from the previous thought experiment, we require that our theory does not distinguish this situation from the situation that the elevator moves with constant velocity in a gravitational field. Therefore a "good" theory of G.R. predicts (requires!) that light is deflected by a gravitational field - and this has been actually observed. -- User:Tompeters ---- I am not a physicist, so I consider myself a good example of the intended audience for this article. Is it fair to say that the theory of General Relativity asserts that one can and should represent gravity and acceleration in the same terms? Parts of the artical seem to suggest this, but in very indirect and wordy ways. I realize that not being a phycisist I may be misunderstanding the article. Whether my supposition is right or wrong, either way it seems to me that this article could be clearer (and I do not mean to diminish the work of specialists who have already done much to put this in accessible prose) User:Slrubenstein : Yes. This is called the principle of equivalence (of Inertial mass and gravitational mass). The problem is "how to design an experiment to distinguish the effects of these posited features". Thus, the use of an eclipse to detect the bending of starlight. Or, the precession of the orbit of Mercury. ---- An update earlier today changed ''static universe'' to ''steady state universe''. This seems to me potentially misleading. There is an article on the Steady State theory. This proposed that the universe was expanding, but that matter was being spontaneously created to maintain the universe's average density at a constant value. I am not certain of the situation in general relativity, but, reasoning by analogy with electromagnetism, I would hazard a guess that general relativity implicitly asserts the law of conservation of mass-energy in the same way that Maxwell's equations implicitly assert the law of conservation of charge. -- User:Alan Peakall 17:49 Feb 20, 2003 (UTC) ---- A small correction: nothing in ''special'' relativity implies that spacetime be non-Euclidean: indeed, the paradigmatic geometrical interpretation of special relativity, Minkowski spacetime, is Euclidean; it is sometimes called complex-Euclidean just because differently-moving observers map space and time axes onto it differently. But for any given coordinate system parallel lines never converge. In ''general'' relativity they ''can'' converge--spacetime is curved--and that's where Non-Euclidean geometry enters the picture. I also agree with above comments that this article seems unable to decide whether it's written for physics majors who don't know relativity yet, or for laymen who don't know physics. ---- Michio Kaku's book on M-Theory, 2nd ed. spells vielbein as 'vierbein' as in 'eins' 'zwei' 'drei' 'vier', or 1 2 3 4. Ref: Kaku p.560, eqns. A.2.23 :I've seen both spellings, and not knowing German, I have no idea which is right. User:Phys 11:36, 23 Aug 2003 (UTC) Vier means four and viel means many --User:Dmr2 11:02, 21 Sep 2004 (UTC) ---- Explanation to User:62.211.229.30 for removing ''GR is inconsistent...'' General relativity is inconsistent in several respects: :Do you mean ''internally inconsistent'' or ''inconsistent with other aspects of physics''? It claims that a physical action can result from a 'subject' (i.e. space-time) which has no physical reality but exists only as an idealized, mathematical concept; :All of modern physics assumes that physical reality has a one-to-one correspondence with idealized, mathematical models, but that at any given time, the favoured models are a limit (mathematics) of some deeper, more complex mathematical model. You are providing an argument against conventional philosophy of science in general, not against GR. Although physical forces are frequently described by gradients of some potential function, this is in principle not acceptable as the fundamental form for the interaction as it implies a non-local nature (a gradient can not be defined through a point); :A gradient is a limit (mathematics). It can perfectly well be defined at (or ''towards'' is probably better) a point. There is no reason why a motion due to gravitational forces should be described by a different concept than those for electrostatic interaction for instance; however for the latter the force does not depend on the mass (whereas the resultant acceleration does), therewith invalidating the concept of space-time curvature as an objective and unique quantity for describing the motion of objects in force field (mathematics)s; :You are saying that both electrostatic interaction and gravitation should be described by the same concept. This is a desire, not an inconsistency. See e.g. GUT or i guess supersymmetry or brane theory for attempts to unify all the forces. Einstein claims that the alleged space-time curvature around massive objects will affect the path of light rays as well. This is an unallowed generalization as the concept was derived to describe the gravitational interaction, but electromagnetic waves are immaterial and massless physical objects. Effects that apparently confirm this prediction of General Relativity could well be explained by other mechanisms. : EM waves may be 'massless', but they do possess energy, and by E=mc ^2 they will respond to a gravitational field (i.e., they will be affected by spacetime curvature). :This is not an inconsistency. On the contrary, if massless objects did not respond to ''alleged'' geometry in the same way that massive objects do, then there would be an inconsistency in GR. BTW, the observations of gravitational lensing in galaxy cluster are very nicely explained by GR. :In fact, the analogy that photons have equivalent mass is not so great. It works OK for the redshift/blueshift in a gravitational field (Pound/Rebka experiment) but simplistic attempts to get the deflection of light correct give half the right answer. Eventually, one has to face the fact that spacetime has a structure, which allows for timelike geodesics ("freely moving" particles, i.e. subject only to gravity,) null geodesics (light rays), spacelike geodesics (representing, for example a tightly stretched weightless string), and other timelike curves such as the world-lines of particles under electromagnetic or nuclear forces. User:Pdn 17:00, 27 Mar 2005 (UTC) Of course, if you wish to start a page on alternatives to general relativity, please do so - there's been a lot of experimental work to try to find alternatives to GR - e.g. http://relativity.livingreviews.org/Articles/lrr-2001-4/node9.html - but please first read and understand the pages on calculus - with wikipedia it's much more efficient than in the pre-web era, but you do have to spend some time clarifying your intuition, searching out and replacing the fuzzy bits, and even, just maybe, doing some hand calculations with pen and paper, as well as computer-aided stuff. User:Boud 13:37, 7 Nov 2003 (UTC) ---- :''... its origins go back to the axioms of Euclidean geometry.'' ?? Does that make sense? It appears to be based only on the fact that general relativity relies on a ''non''-Euclidean geometry in which one of Euclid's axioms does not hold. Is that fact enough to justify this assertion? User:Michael Hardy 23:13, 22 Nov 2003 (UTC) :More than one, actually. Remember we're really dealing with a pseudoRiemannian manifold here... User:Phys 18:30, 28 Nov 2003 (UTC) :There were attempts to prove it from the other axioms back in Euclid's time, implying that they did not believe that it was valid as an axiom(not sufficiently obvious), but thats about as far as the link goes User:67.123.41.95 So a chunk of mass-energy distorts space-time around it, and any other chunk passing by would have its path changed in a manner we call gravity. So, what if we have two chunks that are stationary, where they would each set up space-time distortion. I think that two chunks would have so-called "gravitional attraction" towards each other, but why? Neither chunk had an initial motion. Or does the passage of time count as a motion in this case (which kick-starts the space-motion "attraction")? Or does every particle since the universe began have an inheirent motion (so the initial stationary assumption can never happen)? :I am not a physicist, but I'll give this a try. By stationary, I'll assume that you mean that the two objects are in an inertial state and have the initial condition that the distance between them is not changing (some exterior force has been keeping them stationary and has just released them). The curvature of space and time is such that for them to stay in their inertial states they will start moving towards each other. --User:Edwinstearns 15:47, 24 Sep 2004 (UTC) ---- The article states: "A continuing unsolved challenge of modern physics is the question of how to correctly combine general relativity with quantum mechanics, thus applying it also to the smallest scales of time and space." Would such a combination necessarily constitute a theory of everything? If so, perhaps that should be noted. --User:LostLeviathan 15:34, 18 Nov 2004 (UTC) ==1919 confirmation: bending of starlight during a solar eclipse== The fact that light is bent by gravity is not particular confirmation of general relativity: assuming Newtonian gravitational mechanics applies to light particles like everthing else also predicts bending. The issue is the amount of bending and the difference between the two predictions is a testable factor of two. But I thought something strange happened in 1919. I remember reading that there were three attempts to measure the degree of bending: one was clouded out, one was close to Newtonian predictions and one was close to General Relativity; Eddington decide that the third was better technically than the second - and later measurements have confirmed this. --User:Henrygb 23:27, 19 Nov 2004 (UTC) == The Sagnac Effect == User:Cleon Teunissen 12:01, 15 Jan 2005 (UTC) [http://www.mathpages.com/rr/s2-07/2-07.htm Sagnac Effect] It seems to me an article on General Relativity should take account of the Sagnac effect. The Sagnac effect is demonstrated by the experimental setup called ring interferometry. You can split a beam of light, have the light go around a circuit in both opposite directions, and then you allow this light to create an interference pattern. For example, you can make the light take a square path by setting up mirrors on the corners of a square. This setup measures absolute rotation. One of the first experimentors to conduct this type of experiment was called Sagnac, he conducted his experiment in 1913, and the effect is now called the Sagnac effect. According to the sources I studied the Sagnac effect is a genuine physics phenomenon. According to the sources I studied both special and General relativity imply that absolute rotation can be measured. In the article it is stated: ''The fundamental idea in relativity is that we cannot talk of the physical quantities of velocity or acceleration without first defining a reference frame, and that a reference frame is defined by choosing particular matter as the basis for its definition.'' It seems that ring interferometry doesn't measure rotation with respect to chosen particular matter. It measures absolute rotation. [http://www.phys.canterbury.ac.nz/research/laser/ring_2000.shtml A ring interferometry experiment in New Zealand] Problem: Yes, in simple cases one can discuss absolute rotation; in fact, with respect to what would a Kerr black hole rotate otherwise (ans: asymptotic spatial infinity). That argument points up that to define absolute rotation you have to go to infinite distance, asymptotically. Look at the confirmation of the Lense-Thirring effect using satellites recently, and in progress with Gravity Probe B. Locally, you can define a "nonrotating" frame with your ring laser (why bother? Use a couple of gyroscopes! Gyroscope technology came long before ring lasers.) Anyway, this local frame you just found does not tie in to a nonrotating frame defined by distant stars, quasars, etc. So if you believe that one, you are stuck. If you do not believe that frame based on distant obects is the nonrotating one, you have to explain how stars and galaxies many thousands of light years away are all orchestrated to move as they seem to. User:Pdn 19:12, 23 Mar 2005 (UTC) == Laws of physics are always formulated in one frame of reference == User:Cleon Teunissen 15:08, 21 Jan 2005 (UTC) It is often stated: :"Laws of physics must be formulated in such a way that they are independent of the frame of reference of the observer." It seems to me that for clarity it is better to phrase the condition above as follows:. :"To do physics it is necessary to have transformations available for transforming between frames of reference. In newtonian dynamics, a velocity is transformed from one inertial reference frame to another by adding the velocity vectors. The newtonian laws of motion are ''formulated'' in just one frame of reference; independency of reference frame is provided by the assurance that in all calculations velocities can always be transformed. In the 19th century, it became apparent that if one assumes that the Maxwell equations are correct, and that the newtonian transformations apply, then it should be possible to measure velocity absolutely. Einstein recognized that if one assumes that the Lorentz transformations are the appropriate transformations, then all inertial reference frames are indistinguishable. The Maxwell equations are formulated in just one reference frame, it's the physicists choice of appropriate transformation that determines whether any law of physics has effective independency of reference frame. A calculation is performed in the one reference frame that a law of physics is formulated in. If and only if the approppriate transformations are available, observers can scientifically agree. Their observations can come out differently, they can subsequently transform their results to the frame of reference of the other observer, and find agreement. Einstein didn't reformulate any laws of physics individually: by providing the right transformations, all formulations of laws of physics were provided with extension into relativistic inertial frame indepence. (As it turned out, for example a new relativistic momentum had to be found, in order to have a momentum that displays conservation of momentum.) In newtonian dynamics, it is relatively straightforward to transform between an inertial reference frame and an accelerating reference frame: linear addition of vectors. The acceleration vector (usually a function of time and/or spatial coordinates) is added to the velocity vector (also a function). For the reverse transformation, the same acceleration vector is used, with the sign reversed. So newtonian dynamics has transformations for non-inertial frames of reference. Einstein's effort to develop General Relativity was not a program to redesign the formulation of all laws of dynamics, it was a program with two goals: to find the appropriate transformations involving non-inertial reference frames, and to find a new theory of gravity in which gravity travels through space at lightspeed. The two goals turned out to be even more profoundly connected than anticipated: to an accelerating observer, space-time appears to be distorted; with gravity, space-time is. User:Cleon Teunissen 15:08, 21 Jan 2005 (UTC) =="Dynamic Universe"== *Tuomo Suntola, [http://www.sci.fi/~suntola/ Theoretical Basis of the Dynamic Universe], 2004. ISBN 9525502104. A highly promising new model of the universe. I removed this from the article. From what I can find on the web, it is a replacement for GR that is based around the concepts of absolute space and absolute time. As far as I can tell, very few people take it seriously, as it hasn't yet been verified that it explains everything GR does, much less make new, testable predictions (in particular, one back-of-the-envelope calculation shows it getting the orbit of Mercury wrong; another says that it doesn't handle the orbital decay of binary pulsars). --User:Carnildo 00:59, 4 Feb 2005 (UTC) == This article is not good. == I do not like this article at all, and will rewrite it when I get a chance. 1) The central principle of GR is the General Principle of Relativity, which states that the laws of physics are the same in all frames of reference. The local uniformity of phyical constants is a consequence of the General Principle, NOT the Equivalance Principle. 2) The central tenant of GR is that spacetime is curved due to the presense of mass/energy/momentum within it as described by the Einstein Field Equations. This should be mentioned up front, instead of being left until later. 3) GR uses several other principles which are not mentioned: The principle of general covariance (the laws of nature are independent of the coordinate system), the principle of geodesic motion (inertial motion occurs along timelike geodesics), and local Lorentz Invariance (the rules of Special Relativity apply locally in all frames of reference). 4) The Equivalence Principle (EP) is best presented as a rule for determining whether one is in an intertial frame of reference. (The definition presented in this article is correct, but not comprehensive.) Historically, the EP is the jumping-off point for Einstein's derivation of GR. However, it is only a part of GR and is not the best place to start a popular article on the subject in my opinion. : please do the rewrite. there are lotsa reviewers here that will scrutinize it, and if it's good (and accurate) your work will not go to waste. i am solely a spectator about the subject and am looking forward to learning some of the fundamentals. i dunno if it will help but [http://arxiv.org/pdf/gr-qc/0103044] and [http://pancake.uchicago.edu/~carroll/notes/grtinypdf.pdf] were somewhat useful to me. anything you can do to add to or elucidate that is welcome. also, i recommend that you get yourself a wikipedia identity. User:Rbj 17:47, 22 Mar 2005 (UTC) == More on rewrite == The requested ID has been obtained, and I have started drafting the changes in my sandbox. However, I request that you do not hold your breath waiting for the rewrite. I am going to take my time and be very deliberate about it before doing the replacement. I may not like the current article, but I do not want to replace it with something that is almost as bad if not worse. The time that I can devote to this is also limited, but I very much want to produce an article that gives people a sense of what GR is really about. :ain't holding my breath. i would suggest that you sign your comments to "Talk:" pages with four tildes " ~ ~ ~ ~ ". then your wikipedia ID with the date and time are stamped on your comments. are you cool with the Tex editing? you might want to check out Wikipedia:How_to_edit_a_page or Help:Formula if you haven't yet. good luck, and you have any encouragement from me. User:Rbj 17:55, 23 Mar 2005 (UTC) == [A speculative response] == In reference to the null result of the Michelson-Morley experiment in the section on 'Foundations' (and other results ?) it says, '...Einstein explained these results in his theory of special relativity.' I'm not convinced he 'explained' the null result, but rather he used it as an assumption in SR. Then he developed a theory of mechanics. As a little aside, I'm not sure we really know why the speed of light is constant in all inertial reference frames, apart from the fact that otherwise there would arise theoretical contradictions - but to explain it physically is still a mystery (I think). I suppose it's a bit like asking why (physically) does the existence of matter cause spacetime to curve. What's the exact mechanism ? Food for thought .... : i think i have a feel for why the speed of E&M propagation should be the same for all inertial reference frames. it really just comes from Maxwell's Eqs. and the knowledge that there is no ether medium that E&M is propagated in. i mean, how do we tell the difference between a moving vacuum and a stationary vacuum? if we can't, if there really is no difference between a moving vacuum and a stationary vacuum, that such a concept is really meaningless, then whether the light that you are measuring originated from a flashlight mounted on a rocket moving past you at or from a stationary flashlight, how does that change the fact that a changing E field is causing a changing B field which is causing a changing E field, etc.? that propagation of an E field and B field disturbance, which has velocity ? how is it different? whether you are holding the flashlight or moving past it at high velocity, Maxwell's Eqs. say the same thing regarding the nature of E&M in the vacuum.User:Rbj 05:28, 24 Mar 2005 (UTC) Yes, the EM argument is a good (convincing) one. Now for the next question: why does matter cause spacetime curvature ? (lol, only joking). == Lightspeed, etc. == The constancy of the speed of light arises from the metric nature of spacetime. The Minknowski metric, whose line item is (in units where ) demands it quite nicely. However, this only leads to other "why"'s. I suggest that the purpose of Wikipedia be respected, which as I understand it is to report on the current state of knowledge, and hopefully to do so in a way that is accessible to the average person. So what is important here is the "what" and not the underlying "why". EMS I did say, 'as a little aside...' (lol) == A Convention == May I suggest that we try to use a consistent convention for the value of the speed of light ? After reading many textbooks/research papers etc... which put and don't tell us this, I think it might be better to just write c. Putting in equations confuses many people when they try to check units. It's especially annoying when they don't tell you this like in the 'vierbein formulation' part (which I have subsequently amended). Putting can be quite elegant in some formulae (esp. Maxwell's equations), but I think that for anyone (esp. beginners/newcomers) reading an encyclopedia it is better to have clarity rather than elegance. Also, if it's said that the speed of light is taken to be unity, you have to flap around with the formulae to see where it goes (and is it just or or , like in some gravitational radiation formulae ? ). Please let's try to keep in our formulae. == modifications to article == I've moved a few things around and included some new sections to make the article a little clearer; a lot of work still needs to be done. The 'well-known and popular metrics' have been moved to Einstein field equation. Should the maths of GR be moved to a separate article ? The statements "The fundamental idea in relativity is that we cannot talk of the physical quantities of velocity or acceleration without first defining a reference frame, and that a reference frame is defined by choosing particular matter as the basis for its definition. " are incorrect. An ordinary accelerometer measures acceleration. Of course, you can say the accelerometer is stationary in some reference frame, and so, in a sense, it locally defines a reference frame, but the question of how to extend that reference meaningfully outside the world-line of the accelerometer will lead you into a morass if you are not expert, and into a lot of digressions if you are. One asks why someone is writing a new book on relativity here, when there are so many already. There are good old books by P G Bergmann and Steve Weinberg that can be mined for descriptions, and newer books too, e.g. by Robert M. Wald. As for the second statement it was already critiqued. A reference frame can be identified by imagining a swarm of massless observers, who define the coordinate gridpoints. They need not have mass, i.e. be material; they can be hypothetical. Only requirements are that their worldlines by timelike and form a smooth family - i.e. they do not intersect. There is a maths term for that - probably "manifold" but let someone with more maths settle that. User:Pdn 06:26, 16 Apr 2005 (UTC) == Let's sort out this article. == I think it's about time this article had a serious facelift. The quantum mechanics article puts this one to shame. I've made a few changes: new introduction; removed a paragraph on curvature which used very loose language; replaced that with a more rigorous version. Don't want to remove large chunks, as some of the existing text has useful descriptions (and It'd be treading on other peoples' toes). Need to sift through it carefully. Moved image of spacetime curvature to start of article (grabs attention). Discussion of constancy of speed of light is already in special relativity. User:Mpatel :i want to encourage those of you who understand GR to do exactly this. usually wiki articles help me break through the ice and my understanding of a topic has been increased as a result. sadly, i cannot say this about this article. maybe the material is just too hard, or i am missing something. i understand classical mechanics, a smattering of QM, SR, and a little bit of the Equivalence Principle (the man in an elevator descending at 9.8 m/s^2 is in the same instantaneous situation as other in weightless space or the man in a rocket accelerating at 9.8 m/s^2 has the same experience as one standing on the surface of the earth). is there some way that you guys can start with the EP, and bring us to something like Einstein's Field Equation? or to an equivalent statement like in the Baez and Bunn paper that is cited? User:Rbj 15:48, 20 Apr 2005 (UTC) I know a fair bit about GR; believe me, the (non-mathematical) material is NOT hard - GR is probably the most intuitively pleasing theory in physics to date. The problem is, firstly, I don't want to suddenly remove a huge chunk of other people's work and, secondly, there is a lot to GR (EP, covariance principle, mathematical formulation, two-body problem etc.) - basically, the question is, what's appropriate for an encyclopedia article entitled 'general relativity' ? I think: (1) the maths should be on a totally separate page. (2) the unique role of GR as a theory which determines the geometrical background in which objects move should be emphasised. (3) the nonlinearity of GR should be emphasised, and the consequences of this discussed (again, another major difference between other dynamical equations of physics - e.g. Maxwell's, Schrodinger's). (4) Some of the intuitive descriptions present in the article are OK, but others are confusing. I'm chipping away at this article to try and achieve these objectives. User:Mpatel 16:19, 20 Apr 2005 (UTC) == Sorting out article. == OK, I've made a start in seriously modifying this article. I've deleted, swapped and changed loads of stuff. I propose: (1) In Description of Theory, we talk about how curvature arises through the use of non-inertial reference frames. Then talk about the principle of general relativity and the Equivalence Principle (and maybe covariance- but that might be better in the maths section). (2) Then discuss some of the juicy effects of GR (light bending, grav. waves, evolution of universe etc...). (3) Something on nonlinearity (probably in 'relationship with other physics theories' section). (4) Something on the history of Einstein's discovery of GR. (5) It might be OK to mention the field equation but not state it on this page (as elegant as it is) - I think it belongs in 'Mathematical formulation of GR', as should the geodesic equation; talking of which, deriving the equations of motion from the field equations might be worth a mention. I await comments :) User:Mpatel 08:38, 21 Apr 2005 (UTC) :made some changes and then did not notice I was logged out by accident (dunno why or how). Further changes by 69.244.72.110 this morning were mine. User:Pdn 12:31, 21 Apr 2005 (UTC) == More modific's == Included a subsection on topology of spacetime; might link in nicely with a brief discussion of black holes, wormholes etc. Is the section on foundations needed ? I think it's a little lengthy and possibly completely unnecessary - should it be moved somewhere else ? User:Mpatel 11:33, 22 Apr 2005 (UTC) Perhaps it could be integrated to some other main subtopic. The overal distribution of the article is a bit weird to me. It seems like a bunch of separated articles one after another, the continuity is a bit strange IMHO. However as of yet, I haven't figured out how to improve this. I'd like to ask also for a deeper explanation on how GR rises from SR. User:Nihil 01:12, 23 Apr 2005 (UTC) : Agreed. I just made a start in improving the article. The more modifications that are made to this article by more people, the better. User:Mpatel 09:23, 23 Apr 2005 (UTC) ==GR SR connection== The best way so far as I know to grasp the connection is to understand that a GR spacetime consists of a patching-together of a continuum of inifintesimal local Lorentzian (SR) pieces. Think of a soccer ball with those little pentagons. Make them smaller and smaller, and as they are so small that they approach flatness, extend each patch as a small section of an infinite plane. When you apply the Equivalence Principle all you are doing is saying that, in principle, if you could live in that (tangent) plane, you would be in Minkowski (SR) spacetime and everything would be as usual in SR. (Be careful on notation - "tangent space" is a mathematical construct that includes, as I understand it, lots of other vectors besided displacements and velocities - I think it has E&M vectors in it, too.) Of course, all these vectors can be imagined to lie in that extended plane I just described, too. How is this conceptualization applied to some poor chap standing in Dallas, TX and feeling the force of gravity pulling him downwards? Well, this discussion is all in four dimensions, and those little soccer ball patches all exist in a sequence of spacetime sections falling, in free fall, past this person. The patches have an inclination of their time axes to his that can be zero, if we make them by dropping them just like a lead sinker that he drops from rest, because if at rest when they meet him, the time axes are (instantaneously) aligned. If you want to extend these little patches above his head, I think you have to use ones with the time axes slanted, as if he threw up a sinker (or a clock) and then it passed by him again on the way down. But the point is that he is accelerated in regards to any of these coordinate patches that slip past him, and that is why he feels gravity. If you could extend the little patches to mate smoothly over a region larger than first order in the differentials, you would have found a local Minkowski space - hard to do in GR. It would exist inside a massive spherical shell, but not in very many other places I can think of, if matter is present. OK, nested shells, hollow at the center, that works. The patches can be just bent into a curved surface, or they can be more like vanes on a windmill, not mating smoothly. That is what happens in rotating systems; the patches that represent, for example, small regions on the Earth's surface are set up like vanes on a centrifugal fan. see: "Cylindrical Cardboard Model for a Rotating System in Special Relativity," Amer. J. Phys., 47, pp. 218‑223 . That's for special relativity, not GR, but it carries over to GR for rotating systems. User:Pdn 16:19, 23 Apr 2005 (UTC) ==Complain!== This article is much too unwieldy and unorganized. I think this (and perhaps some related articles) need to be rewritten from scratch as as set of more focused articles, following the Wikiprinciple of passing from the general to the specific. Suggestion: I see some stuff on "the meaning of curvature". That's important, but its really about geometry, not gtr per se, and should be incorporated into pages on Riemannian geometry (if it's not already there). Another suggestion: there's much too much historical material here. Much of this could be moved to a separate article on the historical development of gtr. User:Hillman 29 May 2005 : My advice is to go for it. I looked into doing this myself, thinking that another project of mine was winding down, but it has not and I can't do much for now. : I agree with your complaint about the history section even though I wrote it. What little was there before was pathetic and misleading. So I put that section together, knowing that it almost is a first draft of the seperate article. My own feeling is that the math and the talk about the final development of the EFE should be off-loaded ASAP. I just want it to be done in the context of a fuller article on that issue. : Wikipedia is something that is going to grow in a step-like fashion as more and more people who care about these subjects and have the requisite expertise step up to the plate and add to it. Choose your battles here, realizing that you will need to build a foundation on which your GR article improvements are to rest. I myself am still grappling with the fact that the supporting articles that an improved GR article needs to reference (or which this one does) are often in need of work themselves. Often it is better to make the incremental imporvements than to do the big project, although that day must come. : --User:Ems57fcva | User_talk:ems57fcva 04:24, 30 May 2005 (UTC) : P.S. If you are who I now think you are (and I don't know of many entities named Hillman who can't figure out if they are human or not), then I very much look forward to your contributions. My advice is to start with the tensor and mathematics of general relativity pages. If you don't want to work on the math-of-GR article at first then at least look at my talk:mathematics of general relativity on it. I may work on that article soon and the comments include my intended outline. : --User:Ems57fcva | User_talk:ems57fcva 04:45, 30 May 2005 (UTC) == History of GR == Easier to move the history chunk to the article The development of general relativity (which I've done) and make modifications to that article (and the GR article) as appropriate. User:Mpatel 15:46, 30 May 2005 (UTC) : You didn't do the second half of that job, namely cutting the fat out of the GR article's history section. I have now done that. The new article also could use some elaboration and expansion, but that job I will leave mostly to others. --User:Ems57fcva | User_talk:ems57fcva 00:05, 31 May 2005 (UTC) == Suggestion on cutting down on 'EP' == The Equivalence Principle (EP) section appears to be larger than necessary, as there is a separate page for the EP. I suggest that any valuable bits in the EP section of the GR article be moved to the equivalence principle page (if they're not already there) and the current section be reduced accordingly. I think that only the gist of the EP needs to be mentioned in the GR article. Responses appreciated. User:Mpatel 15:52, 2 Jun 2005 (UTC) : No objection here. All that I ask is that the 1907 Einstein quote be retained. Beyond that I agree that it can be a lot shorter. The first sentence of the last paragraph should also apprear in the final product, but the rest of that last paragraph needs to be ditched. : Do go ahead and look at the equivalence principle page, but myself and Joke137 have put a lot of work into it, and I doubt that you will find any need to transfer data from this page to that one. Instead it may be more of an issue of making the GR section on the EP small and consistent with the EP page. : --User:Ems57fcva | User_talk:ems57fcva 19:29, 2 Jun 2005 (UTC) == Resolved == Hi, EMS and MP, thanks for the kind words. I am very glad to see you are both doing your bit (or more) to upgrade the gr articles here! I already have compiled a long list of articles I want to (re)-write here on gr topics. While, I haven't yet found the energy/time/courage to start in on the gr article itself, I -did- rewrite the article on Brans/Dicke theory! :-/ Looks like we all agree that ideally the main gr article should feature the briefest possible summaries of various broad topics, including * the dramatic players (gravitation, matter) and the stage (spacetime) as a player, * Einstein's motivation, desiderata, and heroic search for GR, * role of diffeomorphism covariance, * equivalence principle, * Newtonian limit, * geometric/physical meaning of the EFE, nonlinearity, * global versus local distinction, * conformal/causal structure, horizons, * role of boundary conditions, smoothness, * role of approximations (linearization/weak-field, far-field, slow motion), * gravitational radiation, * reformulations of GTR (ADM, Regge), * relationship to other gravitation theories, PPN parameters, * tests of GTR (past, present, future). At the end of each brief summary, a link could point interested readers to a longer article devoted to this particular aspect, which can be written from scratch, perhaps using the best of what is already present in various Wikipedia articles. Right now, the only one of these topics which appeals to me is the meaning of the EFE. As things stand, I think that even the list of references which I entered is fairly unwieldy. Is there any wikiprecedent for putting a list of printed refrences in a separate page? Maybe only the two on-line tutorial articles should be in the gr article itself--- maybe a very brief reference section could include these two and then link to a longer page containing all the other references? FWIW, some much easier projects I'd like to carry out include: * add suitable references to all the longer articles, and put any existing references into a uniform (wikitemplated) format, * improve various of the less unwieldy articles, * add suitable figures (e.g. to the Regge calculus and Penrose diagram articles). In the near future, I'd like to rewrite the weak-field theory article, add an article on multipole moments, add more pp-wave related articles, add an article on the Neugebauer/Meinel disk solution, and write articles on the Weyl and Ernst families of vacuum solutions. We'll see. --User:Hillman : Chris - : First of all, thanks for the outline. This is something that people can and may well work towards. I myself a few months ago mentioned a set of principles that the article of the time did not address. Now they are addressed, mostly due to the work of others. If you feel comfortable with addressing the physical meaning of the EFE, then go ahead and write it up. Just be aware that the EFE has its own article, and that much the same (but in more detail) should also be there. : As for moving the full list of references to another page: I know of no precedent, but an article on the available printed and web resources on GR is not inappropriate. Normally there is not such a wealth of resources available on a topic such that a special page is needed. I don't know that I would remove all references from the GR page itself. Instead I would keep 4-6 (including the web tutorials) and then have a prominent link ("For addition references ... " perhaps) to the full bibliography/references page. : Beyond that I repeat my prior advice: Choose your battles. There is so much that can and needs to be done, including fixing up many of the existing articles. As you already see, Wikipedia is living growing resource that over time is constantly improving due to the efforts of its contributors. That does not mean that you are not needed. In fact part of what is happenning is that as Wikipedia improves so does the quality of the contributors. So hopefully in a few more years the GR part of Wikipedia will be high quality text guarded and maintained by some of the better people in the field. For now we are a band of mostly dedicated amateurs with a few professionals in the mix, but your presense is a sign that the mix is changing. : --User:Ems57fcva | User_talk:ems57fcva 15:42, 8 Jun 2005 (UTC) ==Geometric physical theory== What is this supposed to mean? Why is it important to non-logged-in editor 81.218.238.113 to have this particular language? This editor keeps reverting to this with no explanation. User:WCFrancis 17:09, 10 Jun 2005 (UTC) * This user is a Wikipedia:Vandalism. They're modifying this and a handful of other pages to reflect their own unorthodox views of relativity and cosmology. I added the user to Wikipedia:Vandalism in progress a day or two ago, so hopefully their crusade will be curtailed in the not too distant future. --User:Christopher Thomas 20:22, 10 Jun 2005 (UTC) ==The spacetime myth== Ok i see this is some kind of religion. Well i respect your religion but don't be surprised when someone will finally contradict your bizzare space-time theory. Space-time is a joke. It tells us nothing about motion, nor does it tell us anything about weight and gravitation. -- User:81.218.238.113 11:39, 11 Jun 2005 (UTC) : That comment is so full of ignorance, it doesn't even deserve a response --- User:Mpatel 11:41, 11 Jun 2005 (UTC) Sorry but you are the ignorant. Gravity has nothing to do with spacetime curvature[http://users.adelphia.net/~lilavois/Crackpots/notorious.htm]. Spacetime is a geometric construct with no counterpart in nature (see physical space). -- User:81.218.238.113 13:42, 11 Jun 2005 (UTC) :Ok, you've asked for it now. :* 'spacetime is a geometric construct with no counterpart in nature' - you sure about that? - if it were true, then you can use the same argument to conclude that space doesn't exist (same for time) - because we use geometric constructs to model space (3-D euclidean, usually) and time (1-D euclidean) individually. The constructs are mathematical and we can visualise them. :* 'spacetime tells us nothing about motion' - that's not true, as by drawing a spacetime diagram (STD) you can conclude a lot about motion. A straight worldline in a STD can represent, for example, a particle travelling at a constant speed (relative to a given reference frame) - if you've done any physics or maths at high school level, you'll realise that what you said is incorrect, as you draw a STD every time you draw simple space-time graphs of an accelerating car (it's a 2-D STD) - curved lines represent acceleration, straight lines mean zero acceleration (sound familiar ????). :* I think you're perhaps confused about the idea of spacetime curvature. In a given physical situation, the spacetime is given. Only if there is any change in the dynamical state of that system does spacetime change in any way. Modelling the motion of a planet around the Sun (and treating the planet as a point particle), for example, doesn't mean that spacetime changes (as spacetime is fixed) - but if you were to draw a STD for that planet, then the worldline would look like a spiral (see the diagram in spacetime). I repeat, the spacetime is fixed and nothing moves in spacetime (in a STD nothing moves - that's obvious, but you can still talk about a car moving along a road during a certain time interval and represent that on a STD). In GR, the geometry of spacetime is not flat, but it is curved (if you were to take timelike slices, then you would not have 3D euclidean hypersurfaces). If my interpretation is correct, the geometry of spacetime only changes when the physical system in question changes it's dynamical state (for example, if a star were to suddenly supernova, then clearly the local geometry would change - any planets orbiting the star would get flung out or destroyed). In oversimplified language, when we say that spacetime is curved, we mean: space is curved, therefore this thing that we call spacetime (= space + time) must also be curved. :* The idea of gravity as a geometric phenomena is better (meaning experimentally and aesthetically) than any other idea at present - just take a look at the results of experimental tests of GR. I hope that clears up any misunderstandings you have about gravity being curved spacetime and motion in spacetime. --- User:Mpatel 15:02, 11 Jun 2005 (UTC) :*RE: The problem with differential geometry is that it deals with abstract metric spaces. Structures are easier to visualize but what does it tell us about physical processes (such as nuclear fusion) or the energy levels of the electron? Also if particles are absolute, why the hell do they need a reference frame to be relative to? When large group of hydrogen molecules in space attract each other to produce stars, it seems more of a quantum interaction than molecules warping spacetime. Molecules in intergalactic space attracting other molecules by exchanging graviton particles just seems right. My conclusion is that physics cannot be done using abstract geometry. We can only use elements, particles and the interaction processes between them. I wish I could be more enlightening, but it seems that current knowledge levels are too low to produce anything more than just postulates. --User:81.218.238.113 15:45, 11 Jun 2005 (UTC) :Wikipedia doesn't do original research, so your conclusions are out of scope here. You can publish or promote them at other places, your own WWW page or the USENET, I suggest. Wikipedia has to report the current scientific consensus, including relevant minority viewpoints, if verfieable sources can be produced. --User:Pjacobi 20:07, 2005 Jun 11 (UTC) :----------------- : I'm sorry if this sounds rude, but one whose knowledge level is low is yours. GR, though a combination of spacetime curvature and the principle of geodesic motion does explain the observed motion of objects. : Think that you cannot see GR in action? Then drop something. Nothing is pushing on it, yet it accelerates downward, the same as it would from your point of view if you in a giant centrifuge being pushed against the walls. : GR easily explains the equivalence of inertial and gravitational mass. Does your graviton exchange model do that? If so, then what is the math be which you prove it? : In addition, GR :* predicts the observed non-Newtonian perihelion precession Mercury, :* predicts the observed bending of light passing close to the Sun being twice that of the Newtonian prediction. :* predicts the time delay of signals going deeper into a gravitaional field, :* predicts the time dilation effects that the GPS needed to account for in order to function properly, :* and corresponds to Newtonian physics in the weak field limit. : Does your model do all that, and if so the what is the math? : In your defense, I will note the GR is a highly non-intuitive theory which many people find hard to grasp. The spacetime of GR is a curved, four-dimensional manifold in which one of the dimensions involved in the curvature is time. When Einstein started to work on the thery Max Plank told him "you will never succeed, and if you do noone will believe you". He was wrong on both counts, but to this day there are a lot of people who would rather not believe him than either deal with the math or admit their own failings. :--User:Ems57fcva | User_talk:ems57fcva 02:53, 12 Jun 2005 (UTC) Max Planck was ineed wrong but not because he rejected relativity. Quantum mechanics fails to describe the gravitational interaction. Both quantum mechanics and relativity are wrong in ignoring very weak interactions[http://www.physicsforums.com/showthread.php?t=75197]. -- User:81.218.230.86 01:53, 13 Jun 2005 (UTC) : I have looked at your link, and all that I can do is hold my nose at what I read. Perhaps the worst offense is that statment that "GR is not fully compatible with Newtonian theory". Indeed it is not, and is not intended to be (except in the weak field limit). However, '''Einstein's GR works when Newton's theory does not!''' : Be advised that I have walked in your shoes. So I will warn you now: :# You do not have a theory at this point. Instead all that you have is a speculation. It is an unfortunate attribute of -uh- "independent researchers" that they often do not realize this at first. :# This is not the place to discuss your non-thoery. : I am now done with this thread. I do wish you luck, but you will not find it here. --User:Ems57fcva | User_talk:ems57fcva 03:42, 13 Jun 2005 (UTC) : P.S. I just felt that you might like to know that I liked your last edit, and agree with it's contents. However, it is totally lacking in NPOV. Therefore, ''I refuse to place anything like that in the GR page, and will revert any such content that I am the first to find there''. A page dedicated to objections to the black hole, dark matter, and dark energy may actually be quite useful. There actually is a lot of objection to those in the field. However, before you get started do realize that it is the objections and misgivings of prominent scientists such as Einstein and Hawking that need to be documented. Your feelings have no place here, nor on this issue do mine (which along with the level of research required are the reasons that I will not do that article). : Do be advised that inappropriate articles are deleted here, sometimes rapidly. So don't try anything. Your work can be tracked, and will be dealt with. I may sympathize with your view, but ''I am not your friend''. --User:Ems57fcva | User_talk:ems57fcva 05:13, 13 Jun 2005 (UTC) I am not a friend of yours either and i don't need/want any permission from you. You don't own wikipedia and neither do i. As long as we'll construct a QFT version of gravitational interactions, general relativity is disqualified as a physical model of nature and gravitation becomes just like the other forces. Peace -- User:81.218.230.86 20:42, 13 Jun 2005 (UTC) :uh, oh. Some misunderstanding about scientific theories and models again. Even Newtonion gravitation is still a valid model and theory of gravition, as it proofs useful for description and calculation of a wide range of phenomena. Of course by now we know, where its usefullness breaks down and GR delivers better predictions. There is a widespread belief, that GR will break down at "Planck scale", but neither are details clear nor will this change anything on its range of usefull applications. --User:Pjacobi Hallo Pjacobi, AFAIK general relativity breaks down when space-time becomes infinitely curved. Unfornately we will never reach Planck scale but we should be able to construct a QFT version of gravitational interactions. -- User:81.218.230.86 22:38, 13 Jun 2005 (UTC) : Pjacobi & others - All that answering this person is doing is giving him a soapbox to stand on. : He has admited that he cares not for GR, and has an almost religous belief that a QFT will solve all of the ills of GR. :: And this comes from the same idiot who thinks that gravity is space-time curvature. You fascists cannot let go of old ideas. Btw i reverted your edits about the time and physical space article. -- User:81.218.230.86 16:29, 14 Jun 2005 (UTC) ::: Edit of time re-reverted, but your link to dimension was kept. (That at least was a good idea/edit.) --User:Ems57fcva | User_talk:ems57fcva 19:07, 14 Jun 2005 (UTC) : Never mind that Wikipedia is not the place for original research or personal speculative opinions. I suggest that we leave him be, except to revert his edits to articles as needed and if deserved. --User:Ems57fcva | User_talk:ems57fcva 02:25, 14 Jun 2005 (UTC) == The development of GR page has been moved == It is now called the "History of general relativity". That is its topic anyway as a practical matter. Maybe a seperate page on the development phase will be done later. For now, I wish to call a spade a spade. --User:Ems57fcva | User_talk:ems57fcva 02:55, 12 Jun 2005 (UTC) == Reflections of Relativity link. == On , an anonymous user placed in the article: : It is out of date (says black holes are not proven to exist) and errs in saying quantum states are preserved on null geodesics (violates inverse square law of optics). Mixes up photons and other bosons. First of all, black holes indeed are not proven to exist. The black hole is a theorem of GR, and it is also true that astronomers have found concentrations of matter so massive and dense such that if GR is correct then they must be black holes. However, all observations involving these concentrations of matter are indirect, and many astronomer do not consider it to be a given that these objects are in fact black holes. Many think that these may be quark stars instead, and point to certain observations as evidence of this. Do note that under GR, quark stars only exist for a fraction of a second as a star collapses into a black hole. Stable quark stars, if they exist (and that has not been proven either) would be a serious blow to GR. == Non anonymous, not wrong == It was I who placed the material you find objectionable, and I had signed in. Black holes are proven to exist: There is one at the center of our Galaxy. See recent papers by Schoedel, Genzel, Ekhart and others. There is a movie which with some calculations establishes a massive black hole ar Sag A: [http://www.astro.ucla.edu/~jlu/gc/pictures/orbitsMovie.shtml] The way the argument runs is that while earlier, people tried to mimic the strong gravity of a black hole by assuming a very dense star cluster or a ball of massive neutrinos, the new observations go in so close that neither of these configurations could be stable. Everybody trying to explain the motions of stars near Sag A* with anything but a black hole gave up about 2 years ago. The Max Planck page at [http://www.mpe.mpg.de/ir/GC/team.php?lang=en] explains more - two groups UCLA and Max Planck have established the black hole is there. Also look on the web under Fulvio Melia who has given several talks on the analysis and implications. There are also proven black holes in some X-ray binaries, which can be shown from the flicker period at the inner edge of the disk. Fish a bit on the Web. --your next complaint-- As for the other comments: I fail to see how quantum states would not be preserved along null geodesics (since they have no passage of proper time). (With the neutrinos, their quantum state apparently not being preserved is evidence that they are massive.) I would also like to see citations of where photons and other bosons are mixed up, as well as for the other criticized portions of that text. :Quantum States - Well maybe I was too sticky there. It seems to me, however, that because the light cone is 3-dimensional, a bundle of rays on it must spread, so its density matrix decreases. That is the inverse square law, which holds classically and in QM. There is also some work showing polarization change in a ray's passing a region of strong gravity, I believe - but hard to look up so if you want, delete that part. -- the boson challenge-- :Bosons: Here is the offending sentence: "In fact, the presence of one boson in a particular quantum state actually enhances the probability of another photon entering that state." from the page: [http://www.mathpages.com/rr/s2-01/2-01.htm] As to other problems, I am tired of reading that turgid attempt of someone's to put her/his own stamp on relativity. The writer is unidentified, and the discourse ranges from dilatory to heavily laden with equations, often derived in a cumbersome way, with detours. User:Pdn 16:07, 16 Jun 2005 (UTC) Once that data is provided, a decision can be made as to whether to keep as-is, add a warning to, or remove outright this web reference. If it indeed has significant errors, I would lean towards removing it, but I don't feel that the case for that has been proven. So for now I feel that the link should be kept without warnings. --User:Ems57fcva | User_talk:ems57fcva 15:13, 16 Jun 2005 (UTC) ---- There can be no doubt that Sag A* is a gravitationally collapsed object, and that if GR is correct it is a black hole. The same also applies to the other super-massive objects in the centers of galaxies. I just don't think that there is a consensus that these really are black holes, at least amongst astronomers. However, that said, I will also admit that any scenario explaining how these objects could be something else is speculative. (I don't believe in black holes myself, btw. Even so, I also admit that GR is the best theory we have at this time. I just want the record to be straight in that I am not alone in not liking or accepting the black hole as physical reality.) That said, I will concede that if the text is saying that nothing that ceratinly is a black hole (if GR is correct) is known, that is not correct. For the quantum state business, I will point out that an expanding light sphere is composed of numerous photons. My focus is on each one. As for the boson/photon business, I need more context to be sure of the mix-up, but the offending sentence does indict itself. Beyond that, I think that the greatest indictment is in your last paragraph about the work as a whole. This seems to be an ancient reference, predating Chris Hillman's reworking of things. Finally, it is good to see that the "culprit" is you. However, my feeling is that either we keep this reference or we don't. There are plenty of good resources out there. We don't need to reference an inadequate one. --User:Ems57fcva | User_talk:ems57fcva 17:31, 16 Jun 2005 (UTC) == removal of threads == Dear "CyclopsX", The "Spacetime Myth" thread is a part of this record for better or worse. If you find it embarassing, then so be it. My advice is to leave it alone, and stop calling attention to it. --User:Ems57fcva | User_talk:ems57fcva 03:28, 17 Jun 2005 (UTC)
Relativity cosmology Gravity
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General relativity
General relativity (GR) or general relativity theory (GRT) is a fundamental physical theory of gravitation which corrects and extends gravity, especially at the macroscopic level of stars or planets. General relativity may be regarded as an extension of special relativity, this latter theory correcting Newtonian mechanics at high velocities. General relativity has a unique role amongst physical theories in the sense that it interprets the gravitational field as a geometric phenomenon. More specifically, it assumes that any object possessing mass curves the 'space' in which it exists, this curvature being equated to gravity. To conceptualize this equivalence, it is helpful to think, as several author-physicists have suggested, in terms of gravity not causing or being caused by spacetime curvature, but rather that gravity is spacetime curvature. It deals with the motion of bodies in such 'curved spaces' and has survived every experimental test performed on it since its formulation by Albert Einstein in 1915. General relativity forms the basis for modern studies in fields such as astronomy, cosmology and astrophysics. It describes with great accuracy and precision many phenomena where classical physics fails, such as the perihelion motion of planets (classical physics cannot fully account for the perihelion shift of Mercury, for example) and the bending of starlight by the Sun (again, classical physics can only account for half the experimentally observed bending). It also predicts phenomena such as the existence of gravitational waves, black holes and the expansion of the universe. In fact, even Einstein himself initially believed that the universe cannot be expanding, but experimental observations of distant galaxies by Edwin Hubble finally forced Einstein to concede. It is believed that Einstein developed the general relativity from the simple but elegant consideration that no "action at a distance", like the effect of Newtonian gravitation, can propagate through space-time instantaneously. The speed of propagation is limited by the velocity of light, as required by his Special relativity. Unlike the other revolutionary physical theory, quantum mechanics, general relativity was essentially formulated by one man—Albert Einstein. However, Einstein required the help of one of his friends, Marcel Grossmann, to help him with the mathematics of curved manifolds. == Physical Description of the Theory == In relativity theory, physical phenomena are described by observers making measurements in reference frames. In general relativity, these reference frames are arbitrarily moving relative to each other (unlike in special relativity, where the reference frames are assumed to be inertial). Consider two such reference frames, for example, one situated on Earth (the 'Earth-frame'), and another in orbit around the Earth (the 'orbit-frame'). An observer (O) in the orbit-frame will feel weightless as they 'fall' towards the Earth. In Newtonian gravitation, O's motion is explained by the action at a distance (physics) formulation of gravity, where it is assumed that a force between the Earth and O causes O to move around the Earth. General relativity views the situation in a different manner, namely, by demonstrating that the Earth modifies ('warps') the geometry in its vicinity and O will naturally follow the curves (geodesics) in this geometry unless O applies accelerative force (e.g. rockets). More precisely, the presence of matter determines the geometry of spacetime, the physical arena in which all events take place. This is a profound innovation in physics, all other physical theories assuming the structure of the spacetime in advance. It is important to note that a given matter distribution will fix the spacetime once and for all. There are a few caveats here: (1) the spacetime within which the matter is distributed cannot be properly defined without the matter, so most solutions require special assumptions, such as symmetries, to allow the relativist to concoct a candidate spacetime, then see where the matter must lie, then require its properties be "reasonable" and so on. (2) Initial and boundary conditions can also be a problem, so that gravitational waves may violate the idea of the spacetime being fixed once and for all. More specifically, let us ask how the nearly circular path on which the Earth travels can be a geodesic, which we always thought looked more like a straight line. But in the four dimensions of relativity, the principal motion of the Earth is into the future. Consider the situation in four dimensions, but for simplicity assume the Earth's velocity is perpendicular to the Z axis. Considering the time axis vertical, the Earth's path is a spiral (helix) about the t-axis, and not a tightly wound one at that. In one complete turn of the spiral, one year has elapsed, so the coordinate ct has increased one light year, but the Earth is moving in the x-y plane much more slowly, having gone only 2 astronomical units in a year; i.e. the slope of the helix is c divided by the orbital velocity, or about ten thousand. The motion of the observer O in orbit is rather like a ping-pong ball being forced to follow the 'dent' or depression created in a trampoline by a relatively massive object like a medicine ball. The geometry is determined by the medicine ball, the relatively light ping-pong ball causing no significant change in the local geometry. Thus, general relativity provides a simpler and more natural description of gravity than Newton's action at a distance formulation. An oft-quoted analogy used in visualising spacetime curvature is to imagine a universe of one-dimensional beings living in one dimension of space and one dimension of time. Each piece of matter is not a point on any imaginable curved surface, but a world line showing where that point moves as it goes from the past to the future. The precise means of calculating the geometry of spacetime given the matter distribution is encapsulated in Einstein's field equation. === The Equivalence Principle === :''(For more detailed information about the equivalence principle, see equivalence principle)'' Inertial reference frames, in which bodies maintain a uniform state of motion unless acted upon by another body, are distinguished from non-inertial frames, in which freely moving bodies have an acceleration deriving from the reference frame itself. In non-inertial frames there is a perceived force which is accounted for by the acceleration of the frame, not by the direct influence of other matter. Thus we feel acceleration when cornering on the roads when we use a car as the physical base of our reference frame. Similarly there are coriolis effect and centrifugal forces when we define reference frames based on rotating matter (such as the Earth or a child's roundabout). In Newtonian mechanics, the coriolis and centrifugal forces are regarded as non-physical ones, arising from the use of a rotating reference frame. In General Relativity there is no way, locally, to define these "forces" as distinct from those arising through the use of any non-inertial reference frame. The principle of equivalence in general relativity states that there is no local experiment to distinguish non-rotating free fall in a gravitational field from uniform motion in the absence of a gravitational field. In short there is no gravity force in a reference frame in free fall other than tidal gravity forces, which can deform objects but not accelerate them. Indeed, attempts to detect gravitational waves depend on just those tidal forces. From this perspective the observed gravity at the surface of the Earth is the force observed in a reference frame defined from matter at the surface which is not free, but is prevented from falling by the matter below (on and within the Earth, including the continents, furniture, etc.,) and is analogous to the acceleration felt in a car. In the process of discovering GR, Einstein used a fact that was known since the time of Galileo, namely, that the inertial and gravitational masses of an object happen to be the same. He used this as the basis for the principle of equivalence, which describes the effects of gravitation and acceleration as different perspectives of the same thing (at least locally), and which he stated in 1907 as: :''We shall therefore assume the complete physical equivalence of a gravitational field and the corresponding acceleration of the reference frame. This assumption extends the principle of special relativity to the case of uniformly accelerated motion of the reference frame.'' In other words, he postulated that no experiment can locally distinguish between a uniform gravitational field and a uniform acceleration. The meaning of the ''Principle of Equivalence'' has gradually broadened, in consonance with Einstein's further writings, to include the concept that no physical measurement within a given unaccelerated reference system can determine its state of motion. This implies that it is impossible to measure, and therefore virtually meaningless to discuss, changes in fundamental physical constants, such as the rest masses or electrical charges of elementary particles in different states of relative motion. Any measured change in such a constant would represent either experimental error or a demonstration that the theory of relativity was wrong or incomplete. The equivalence principle explains the experimental observation that inertial and gravitational mass are equivalent. Moreover, the principle implies that some frames of reference must obey a non-Euclidean geometry: that spacetime is curvature (by matter and energy), and gravity can be seen purely as a result of this geometry. This yields many predictions such as gravitational redshifts and light bending around stars, black holes, time slowed by gravitational fields, and slightly modified laws of gravitation even in weak gravitational fields. However, it should be noted that the equivalence principle does not uniquely determine the field equations of curved spacetime, and there is a parameter known as the cosmological constant which can be adjusted. === The Covariance Principle === :''(For more detailed information about the covariance principle, see the article principle of general covariance)'' Following on from the spirit of special relativity, the principle of general covariance states that all coordinate systems are equivalent for the formulation of the general laws of nature. Mathematically, this suggests that the laws of physics should be tensor equations. == Geometric Foundations == For a long time, it was believed that the universe obeyed the axioms of Euclidean geometry, including Euclid's parallel postulate. In crude terms, 'space is Euclidean' seemed to be the general rule. Although the development of non-euclidean geometry by Nikolai_Ivanovich_Lobachevsky, Janos Bolyai, Carl Friedrich Gauss and others, opened up a new field of research, the general consensus was still that space is Euclidean. Early on, Gauss decided to test this assumption and found (with experiments using the crude equipment of that age) that the sum of the angles of a triangle was 180 degrees, affirming that to available precision, physical space obeyed the parallel postulate and was Euclidean. Modern experiments are capable of detecting the non-Euclidean geometry of space-time directly. For example, the Pound-Rebka experiment (1959) detected the change in wavelength of light from a cobalt source rising 22.5 meters against gravity in a shaft in the Jefferson Physical Laboratory at Harvard University, and the rate of atomic clocks in Global Positioning System satellites orbiting the Earth has to be "corrected" for the effect of gravity, in order to synchronize these clocks with earth-bound ones. In so "correcting" a clock, of course, one tweaks it so as to be an imperfect or nonstandard clock from the standpoint of the equivalence principle. In other words, in order to establish a more or less global time standard, one has to adjust or modify clocks originally of standard construction and operation so as to, in a sense, violate the equivalence principle. In 1854, Gauss' student Bernhard Riemann gave a famous lecture in which he developed the general mathematics of non-euclidean geometry. In the lecture, he defined what is nowadays called an n-dimensional Riemannian manifold and defined the curvature tensor, a fundamental mathematical object in GR. He also inquired as to the dimension of the space of reality (the dimension of our world's space), as well as wondering about the actual geometry of the world. In retrospect, Riemann's lecture was ahead of its time, it finding fruition when Einstein developed GR. In fact, Einstein began with physical concepts to develop GR and knew that he needed the mathematics of curved spaces to formulate his theory. The required mathematics was precisely that developed by Riemann, the modern designation called manifold theory. == Predictions of GR == :''(For more detailed information about tests and predictions of general relativity, see Tests of general relativity)'' Like any good scientific theory, general relativity makes predictions which can be tested. Some of the predictions of general relativity include the perihelion shifts of planetary orbits (particularly that of Mercury (planet)), bending of light by massive objects, and the existence of gravitational waves. The first two of these tests have been verified to a high degree of accuracy and precision. Most researchers believe in the existence of gravitational waves, but more accurate experiments are needed to raise this prediction to the status of the other two, if one demands direct detection of the waves. Nevertheless, indirect effects of gravitational wave emission have been observed for a binary system of orbiting neutron stars, as described in Tests of general relativity. Other predictions include the expansion of the universe, the existence of black holes and possibly the existence of wormholes. The existence of black holes is generally accepted, but the existence of wormholes is still very controversial, many researchers believing that wormholes may exist only in the presence of exotic matter. The existence of white holes is very speculative, as they appear to contradict the second law of thermodynamics. Many other quantitative predictions of general relativity have since been confirmed by astronomical observations. One of the most recent, the discovery in 2003 of PSR J0737-3039, a binary neutron star in which one component is a pulsar and where the Apsis Precession 16.88° per year (or about 140,000 times faster than the precession of Mercury's perihelion), enabled the most precise experimental verification yet of the effects predicted by general relativity. [http://skyandtelescope.com/news/article_1124_1.asp] [http://skyandtelescope.com/news/article_1473_1.asp]. == Mathematics of GR == :''(For more detailed information about the mathematics of general relativity, see mathematics of general relativity)'' The mathematics of general relativity involves heavy use of tensor calculus. The use of tensors in relativity greatly simplifies many calculations and serves to reflect the fact that all observers are equivalent for the description of physical laws. An important tensor in relativity is the Riemann tensor, which is a matrix of numbers that essentially measures the deviation of a vector that is moved along a curve parallel to itself when a round trip is made. In flat space, the vector returns to the same orientation (the Riemann tensor is zero), but in a curved space it generally does not (in general, a non-zero Riemann tensor). In spaces of two dimensions, the Riemann tensor is a matrix (i.e. just a real number) called the Gaussian or scalar curvature. Curvature can be measured entirely within a surface, and similarly within higher-dimensional manifolds such as space or spacetime. The dynamics of general relativity are incorporated in the Einstein field equation, a tensor equation that describes how matter affects the geometry of spacetime, and the geodesic equation, which describes how objects move in the resulting geometry. Often, approximations are made in working with both these equations. An important feature of the Einstein field equations is that they are a set of nonlinear partial differential equations for the metric. As such, this distinguishes the field equations of general relativity from some of the other important field equations in physics, such as Maxwell's equations (which are linear in the electric and magnetic fields) and Schrodinger's equation (which is linear in the wavefunction). This constitutes another major difference between general relativity and other physical theories. == Relationship to other physical theories == === Special and general relativity === In relativity theory, all events are referred to one or more reference frames. A reference frame is defined by choosing particular matter as the basis for its definition. Thus, all motion is defined and quantified relative to other matter. In the special theory of relativity it is assumed that reference frames can be extended indefinitely in all directions in space and time. The theory of special relativity concerns itself with reference frames that move at a constant velocity with respect to each other (i.e. inertial reference frames), whereas general relativity deals with all frames of reference. In the general theory it is recognised that we can only define local frames to given accuracy for finite time periods and finite regions of space (similarly we can draw flat maps of regions of the surface of the earth but we cannot extend them to cover the whole surface without distortion). The Special relativity (1905) modified the equations used in comparing the measurements made by differently moving bodies, in view of the constant value of the speed of light, i.e. its observed invariance in reference frames moving uniformly relative to each other. This had the consequence that physics could no longer treat space and time separately, but only as a single four-dimensional system, "space-time," which was divided into "time-like" and "space-like" directions differently depending on the observer's motion. The general theory added to this that the presence of matter "warped" the local space-time environment, so that apparently "straight" lines through space and time have the properties we think of "curved" lines as having. Thus Newton's first law is replaced by the law of geodesic motion. There are no known experimental results that suggest that a non-quantum theory of gravity radically different from general relativity is necessary. For example, the Allais effect was initially speculated to demonstrate "gravitational shielding," but was subsequently explained by conventional phenomena. === Quantum mechanics and general relativity === There are good theoretical reasons for considering general relativity to be incomplete. General relativity does not include quantum mechanics, and this causes the theory to break down at sufficiently high energies. A continuing unsolved challenge of modern physics is the question of how to correctly combine general relativity with quantum mechanics, thus applying it also to the smallest scales of time and space. Most scientists consider this unifying theory's leading candidates to be M-theory and loop quantum gravity. This unification would achieve Einstein's dream of a grand unification theory, combining the strong, electroweak, and gravitational forces into one force, as well as successfully creating one set of equations that do not break down under any conditions. === Other theories === The Brans-Dicke theory and the Rosen bi-metric theory are modifications of general relativity and cannot be ruled out by current experiments. See Einstein-Cartan theory for an extension of general relativity to include torsion. There have been attempts to formulate consistent theories which combine gravity and electromagnetism, some of the first being the Kaluza-Klein theory and Weyl's gauge theory. == History == ''Full article: History of general relativity''
''See also: Tests of general relativity'' General relativity was developed by Einstein in a process that began in 1907 with the publication of an article by Einstein on the influence of gravity and acceleration on the behaviour of light in special relativity. Most of this work was done in the years 1911–1915, beginning with the publication a second article of the effect of gravitation on light. By 1912, Einstein was actively seeking a theory in which gravitation was explained as a geometric phenomenon. In 1915, these efforts culminated in the publication of the Einstein field equations, which are a set of differential equations. Since 1915, the development of general relativity has focused on solving the field equations for various cases. This generally means finding metrics which correspond to realistic physical scenarios. The interpretation of the solutions and their possible experimental and observational testing also constitutes a large part of research in GR. The expansion of the universe created an interesting episode for general relativity. In 1922, Alexander Friedmann found a solution in which the universe may expand or contract, and later Georges Lemaître derived a solution for an expanding universe. Einstein did not believe in an expanding universe, and so he added a cosmological constant to the field equations to permit the creation of static universe solutions. In 1929, Edwin Hubble found evidence that the universe is expanding. This resulted in Einstein dropping the cosmological constant, referring to it as "the biggest blunder in my career". Progress in solving the field equations and understanding the solutions has been ongoing. Notable solutions have included the Schwarzschild solution (1916), the Reissner-Nordström solution and the Kerr solution. Observationally, general relativity has a history too. The perihelion precession of Mercury was the first evidence that general relativity is correct. Eddington's 1919 expedition in which he confirmed Einstein's prediction for the deflection of light by the Sun helped to cement the status of general relativity as a likely true theory. Since then, many observations have confirmed the predictions of general relativity. These include studies of binary pulsars, observations of radio signals passing the limb of the Sun, and even the GPS system. For more information, see the Tests of general relativity article. ==Quotes== :''Spacetime grips mass, telling it how to move, and mass grips spacetime, telling it how to curve'' - John Archibald Wheeler. :''The theory appeared to me then, and still does, the greatest feat of human thinking about nature, the most amazing combination of philosophical penetration, physical intuition, and mathematical skill. But its connections with experience were slender. It appealed to me like a great work of art, to be enjoyed and admired from a distance.'' —Max Born ==References== This reading list is loosely based on ===Popular Books=== * Leisurely pace, provides superb intuition for Schwarzschild geometry. * Covers much more ground, while remaining concise and readable. * A delightful romp through the physics of black holes. Features many personal anecdotes from the author's distinguished career. ===Textbooks=== ====Introductory==== * Clearly written, short and sweet; covers less ground than the others but much cheaper. * Readable, well illustrated, fairly comprehensive without becoming encyclopedic--- what's not to love? * Features an outstanding treatment of tensor calculus and the matter tensor, a key topic which beginners often have trouble grasping. The treatment of linearized gravitational waves and stellar models is also outstanding. * Clear and very well organized. Features excellent treatment of far-field and weak-field expansions and linearized gravitational waves, including multipole moments. Offers more on solution techniques than other introductory textbooks. * In contrast to other introductions, these authors use an exceptionally clear comparison of linearized general relativity with electromagnetism to motivate Einstein's field equations. Superb treatment of observational tests and of gravitational lensing. Should be useful for students wishing to master the textbook by Weinberg. ====Advanced==== * Readable, up-to-date. Features an outstanding treatment of the mass, charge, and spin of isolated objects, plus an elementary introduction to quantum field theory on curved spacetimes and Hawking radiation. Further essential material is concisely explained in valuable appendices. [http://pancake.uchicago.edu/~carroll/grbook/ Book website]. * A unique textbook straddling the modern and pre-modern eras in general relativity, this offers a dual introduction to Maxwell's theory of electromagnetism and Einstein's theory of gravitation. Noteworthy topics include a good treatment of multipole moments and background material needed for the BKL conjecture. * A classic general relativity textbook. Features a unique two-track organization, with numerous boxes, tables, figures, and citations. In general, this book focuses more on developing physical and geometrical intuition than the textbook by Wald. * Demanding but full of valuable physical insight and techniques. No pictures, in marked contrast to the textbook by Misner, Thorne & Wheeler. Excellent treatment of topics related to PPN formalism, weak field approximations, gravitons, as well as applications of particle physics to cosmology. No exercises. * Often cited as the definitive graduate level textbook. Features an outstanding introduction to tensors (with a clear distinction between ''abstract indices'' and particular indices, overlooked by most other authors), as well as the basic singularity, stability, and uniqueness theorems, quantum field theory on curved spacetimes, and black hole thermodynamics. Much valuable material is clearly explained in a series of superb appendices. In general, this book focuses more on developing insight into mathematical formalism and techniques than on developing physical insight. ====Special Topics==== * A collection of excellent problems, with sketch solutions in the back. Text your skills! * Don't be fooled by the subtitle; this book explains many key concepts and techniques which are needed by ''all'' contemporary graduate students, but are not adequately explained elsewhere. Essential topics covered here include congruences (expansion, vorticity, and shear), optical scalars, junction conditions for matching interior solutions to exterior solutions, thin shells (including null shells), spatial hyperslices, and energy conditions. * Not easy to read, but one of the few textbooks to offer an introduction to the important Newman/Penrose formalism. Also features much material on gravitational waves. * This book is billed as an introductory textbook, but has no exercises and may be hard to read. Unique features include a chapter on measurement theory for general relativity, plus an introduction to tetrad formalism. ==External Links== ===Online Tutorials=== * Baez, John & Bunn, Ted; This superb expository paper explains the meaning of the field equation in terms of the motion of a cloud of free falling test particles. *Carroll, Sean M.; A concise but very readable overview. ===Webcourses=== * Rappoport, Saul; An elementary introduction to relativistic physics, including a smattering of gtr. * Bertschinger, Edmund; An introduction to general relativity at the level of Misner, Thorne & Wheeler. * Brown,Kevin; An idiosyncratic work, providing in-depth discussions of various aspects of special and general relativity. The subjects are treated exceptionally thoroughly. The book is written for people who already have a firm grasp of relativity. * van Putten, Maurice; An topics course on gravitational wave detectors, featuring the draft of the instructor's forthcoming textbook. General relativity Theories vi:Lý thuyết tương đối rộng
General relativity
For the purposes of readability perhaps the sentence "Early on, Gauss decided to test this assumption and found (with experiments using the crude equipment of that age)." should be modified to include what he found :) I don't have the knowledge to update and thought I would mention it here so that someone more informed in the area could execute the update. Steve. ---- I put in some links and rescued the field equation from the previous version. I think we also need to explain the differences between Newton's and Einstein's theory a bit, for instance as they relate to :black holes. --AxelBoldt ---- The current text mentions 2 things as fundamental in general Relativity: # You need a reference frame to describe motion # Reference frames can only be defined with respect to material objects; the text seems to imply that these are gravitating and therefore G.R. is a theory of gravitation too. I do not believe the 2nd assumption is true, and esp. not its implication. I have a different perspective: suppose that the principle of General Relativity can be formulated as follows: "Laws of physics must be formulated in such a way that they are independent of the frame of reference of the observer." So G.R. is a theory about theories of physics, as much as a theory of the physical universe itself. It is a recipe for making good theories, which may or may not be consistent with the universe as we actually observe it. The popularity of thought experiments in G.R. demonstrates that its focus is on how we should describe the world, rather than how we actually observe it. The theories work only as far as the universe itself is consistent, understandable, and can be described by logic and mathematics - and there is no a priori reason that it is this way. But to the extent that the universe can be described by theories, the principle formulated above gives an important property of a "good" theory. Implications for the theory of G.R. based on this principle: # Light has a constant velocity. It is well known that Einstein was troubled by the description of induction in a coil in a variable magnetic field: depending if you are in the coil or in the magnetic field, the one generates the other depending from you perspective. Indeed, the Maxwell-Heavyside equations do not require different formulae: exactly the same equations can be used and applied in your local frame of reference, and the results are identical if you go to the other frame. So this is a "good" theory. Now from these equations the velocity of light can be computed, and it is a constant, independent of your frame of reference. Of course an absolute velocity that is not relative to observers is in conflict with Galilean dynamics. Einstein drew the ultimate consequence, and chose to adjust the geometry of space rather than the theory. The Lorentz transformations immediately follow from this choice, and are the only solution consistent with this choice. # Gravity == acceleration. In a thought experiment, you can play billiard in a train that moves with constant velocity, and not notice that it moves. If it accelerates however, you will notice because the inertial mass of the balls will drive them to one end of the table (your local frame of reference). Now exactly the same will happen if the train moves up a slope with constant velocity: they will roll downhill because gravity pulls on their gravitational mass. However, you are unable to distinguish this event from the previous one -- iff inertial mass is identical to gravitational mass. So a "good" theory would describe both events with the same equations. : Now in another thought experiment you are in an elevator that is accelerated, and a beam of light is sent through one of the sides. Because light has a finite velocity, its path in the elevator case (your local frame of reference) is curved. Now from the previous thought experiment, we require that our theory does not distinguish this situation from the situation that the elevator moves with constant velocity in a gravitational field. Therefore a "good" theory of G.R. predicts (requires!) that light is deflected by a gravitational field - and this has been actually observed. -- User:Tompeters ---- I am not a physicist, so I consider myself a good example of the intended audience for this article. Is it fair to say that the theory of General Relativity asserts that one can and should represent gravity and acceleration in the same terms? Parts of the artical seem to suggest this, but in very indirect and wordy ways. I realize that not being a phycisist I may be misunderstanding the article. Whether my supposition is right or wrong, either way it seems to me that this article could be clearer (and I do not mean to diminish the work of specialists who have already done much to put this in accessible prose) User:Slrubenstein : Yes. This is called the principle of equivalence (of Inertial mass and gravitational mass). The problem is "how to design an experiment to distinguish the effects of these posited features". Thus, the use of an eclipse to detect the bending of starlight. Or, the precession of the orbit of Mercury. ---- An update earlier today changed ''static universe'' to ''steady state universe''. This seems to me potentially misleading. There is an article on the Steady State theory. This proposed that the universe was expanding, but that matter was being spontaneously created to maintain the universe's average density at a constant value. I am not certain of the situation in general relativity, but, reasoning by analogy with electromagnetism, I would hazard a guess that general relativity implicitly asserts the law of conservation of mass-energy in the same way that Maxwell's equations implicitly assert the law of conservation of charge. -- User:Alan Peakall 17:49 Feb 20, 2003 (UTC) ---- A small correction: nothing in ''special'' relativity implies that spacetime be non-Euclidean: indeed, the paradigmatic geometrical interpretation of special relativity, Minkowski spacetime, is Euclidean; it is sometimes called complex-Euclidean just because differently-moving observers map space and time axes onto it differently. But for any given coordinate system parallel lines never converge. In ''general'' relativity they ''can'' converge--spacetime is curved--and that's where Non-Euclidean geometry enters the picture. I also agree with above comments that this article seems unable to decide whether it's written for physics majors who don't know relativity yet, or for laymen who don't know physics. ---- Michio Kaku's book on M-Theory, 2nd ed. spells vielbein as 'vierbein' as in 'eins' 'zwei' 'drei' 'vier', or 1 2 3 4. Ref: Kaku p.560, eqns. A.2.23 :I've seen both spellings, and not knowing German, I have no idea which is right. User:Phys 11:36, 23 Aug 2003 (UTC) Vier means four and viel means many --User:Dmr2 11:02, 21 Sep 2004 (UTC) ---- Explanation to User:62.211.229.30 for removing ''GR is inconsistent...'' General relativity is inconsistent in several respects: :Do you mean ''internally inconsistent'' or ''inconsistent with other aspects of physics''? It claims that a physical action can result from a 'subject' (i.e. space-time) which has no physical reality but exists only as an idealized, mathematical concept; :All of modern physics assumes that physical reality has a one-to-one correspondence with idealized, mathematical models, but that at any given time, the favoured models are a limit (mathematics) of some deeper, more complex mathematical model. You are providing an argument against conventional philosophy of science in general, not against GR. Although physical forces are frequently described by gradients of some potential function, this is in principle not acceptable as the fundamental form for the interaction as it implies a non-local nature (a gradient can not be defined through a point); :A gradient is a limit (mathematics). It can perfectly well be defined at (or ''towards'' is probably better) a point. There is no reason why a motion due to gravitational forces should be described by a different concept than those for electrostatic interaction for instance; however for the latter the force does not depend on the mass (whereas the resultant acceleration does), therewith invalidating the concept of space-time curvature as an objective and unique quantity for describing the motion of objects in force field (mathematics)s; :You are saying that both electrostatic interaction and gravitation should be described by the same concept. This is a desire, not an inconsistency. See e.g. GUT or i guess supersymmetry or brane theory for attempts to unify all the forces. Einstein claims that the alleged space-time curvature around massive objects will affect the path of light rays as well. This is an unallowed generalization as the concept was derived to describe the gravitational interaction, but electromagnetic waves are immaterial and massless physical objects. Effects that apparently confirm this prediction of General Relativity could well be explained by other mechanisms. : EM waves may be 'massless', but they do possess energy, and by E=mc ^2 they will respond to a gravitational field (i.e., they will be affected by spacetime curvature). :This is not an inconsistency. On the contrary, if massless objects did not respond to ''alleged'' geometry in the same way that massive objects do, then there would be an inconsistency in GR. BTW, the observations of gravitational lensing in galaxy cluster are very nicely explained by GR. :In fact, the analogy that photons have equivalent mass is not so great. It works OK for the redshift/blueshift in a gravitational field (Pound/Rebka experiment) but simplistic attempts to get the deflection of light correct give half the right answer. Eventually, one has to face the fact that spacetime has a structure, which allows for timelike geodesics ("freely moving" particles, i.e. subject only to gravity,) null geodesics (light rays), spacelike geodesics (representing, for example a tightly stretched weightless string), and other timelike curves such as the world-lines of particles under electromagnetic or nuclear forces. User:Pdn 17:00, 27 Mar 2005 (UTC) Of course, if you wish to start a page on alternatives to general relativity, please do so - there's been a lot of experimental work to try to find alternatives to GR - e.g. http://relativity.livingreviews.org/Articles/lrr-2001-4/node9.html - but please first read and understand the pages on calculus - with wikipedia it's much more efficient than in the pre-web era, but you do have to spend some time clarifying your intuition, searching out and replacing the fuzzy bits, and even, just maybe, doing some hand calculations with pen and paper, as well as computer-aided stuff. User:Boud 13:37, 7 Nov 2003 (UTC) ---- :''... its origins go back to the axioms of Euclidean geometry.'' ?? Does that make sense? It appears to be based only on the fact that general relativity relies on a ''non''-Euclidean geometry in which one of Euclid's axioms does not hold. Is that fact enough to justify this assertion? User:Michael Hardy 23:13, 22 Nov 2003 (UTC) :More than one, actually. Remember we're really dealing with a pseudoRiemannian manifold here... User:Phys 18:30, 28 Nov 2003 (UTC) :There were attempts to prove it from the other axioms back in Euclid's time, implying that they did not believe that it was valid as an axiom(not sufficiently obvious), but thats about as far as the link goes User:67.123.41.95 So a chunk of mass-energy distorts space-time around it, and any other chunk passing by would have its path changed in a manner we call gravity. So, what if we have two chunks that are stationary, where they would each set up space-time distortion. I think that two chunks would have so-called "gravitional attraction" towards each other, but why? Neither chunk had an initial motion. Or does the passage of time count as a motion in this case (which kick-starts the space-motion "attraction")? Or does every particle since the universe began have an inheirent motion (so the initial stationary assumption can never happen)? :I am not a physicist, but I'll give this a try. By stationary, I'll assume that you mean that the two objects are in an inertial state and have the initial condition that the distance between them is not changing (some exterior force has been keeping them stationary and has just released them). The curvature of space and time is such that for them to stay in their inertial states they will start moving towards each other. --User:Edwinstearns 15:47, 24 Sep 2004 (UTC) ---- The article states: "A continuing unsolved challenge of modern physics is the question of how to correctly combine general relativity with quantum mechanics, thus applying it also to the smallest scales of time and space." Would such a combination necessarily constitute a theory of everything? If so, perhaps that should be noted. --User:LostLeviathan 15:34, 18 Nov 2004 (UTC) ==1919 confirmation: bending of starlight during a solar eclipse== The fact that light is bent by gravity is not particular confirmation of general relativity: assuming Newtonian gravitational mechanics applies to light particles like everthing else also predicts bending. The issue is the amount of bending and the difference between the two predictions is a testable factor of two. But I thought something strange happened in 1919. I remember reading that there were three attempts to measure the degree of bending: one was clouded out, one was close to Newtonian predictions and one was close to General Relativity; Eddington decide that the third was better technically than the second - and later measurements have confirmed this. --User:Henrygb 23:27, 19 Nov 2004 (UTC) == The Sagnac Effect == User:Cleon Teunissen 12:01, 15 Jan 2005 (UTC) [http://www.mathpages.com/rr/s2-07/2-07.htm Sagnac Effect] It seems to me an article on General Relativity should take account of the Sagnac effect. The Sagnac effect is demonstrated by the experimental setup called ring interferometry. You can split a beam of light, have the light go around a circuit in both opposite directions, and then you allow this light to create an interference pattern. For example, you can make the light take a square path by setting up mirrors on the corners of a square. This setup measures absolute rotation. One of the first experimentors to conduct this type of experiment was called Sagnac, he conducted his experiment in 1913, and the effect is now called the Sagnac effect. According to the sources I studied the Sagnac effect is a genuine physics phenomenon. According to the sources I studied both special and General relativity imply that absolute rotation can be measured. In the article it is stated: ''The fundamental idea in relativity is that we cannot talk of the physical quantities of velocity or acceleration without first defining a reference frame, and that a reference frame is defined by choosing particular matter as the basis for its definition.'' It seems that ring interferometry doesn't measure rotation with respect to chosen particular matter. It measures absolute rotation. [http://www.phys.canterbury.ac.nz/research/laser/ring_2000.shtml A ring interferometry experiment in New Zealand] Problem: Yes, in simple cases one can discuss absolute rotation; in fact, with respect to what would a Kerr black hole rotate otherwise (ans: asymptotic spatial infinity). That argument points up that to define absolute rotation you have to go to infinite distance, asymptotically. Look at the confirmation of the Lense-Thirring effect using satellites recently, and in progress with Gravity Probe B. Locally, you can define a "nonrotating" frame with your ring laser (why bother? Use a couple of gyroscopes! Gyroscope technology came long before ring lasers.) Anyway, this local frame you just found does not tie in to a nonrotating frame defined by distant stars, quasars, etc. So if you believe that one, you are stuck. If you do not believe that frame based on distant obects is the nonrotating one, you have to explain how stars and galaxies many thousands of light years away are all orchestrated to move as they seem to. User:Pdn 19:12, 23 Mar 2005 (UTC) == Laws of physics are always formulated in one frame of reference == User:Cleon Teunissen 15:08, 21 Jan 2005 (UTC) It is often stated: :"Laws of physics must be formulated in such a way that they are independent of the frame of reference of the observer." It seems to me that for clarity it is better to phrase the condition above as follows:. :"To do physics it is necessary to have transformations available for transforming between frames of reference. In newtonian dynamics, a velocity is transformed from one inertial reference frame to another by adding the velocity vectors. The newtonian laws of motion are ''formulated'' in just one frame of reference; independency of reference frame is provided by the assurance that in all calculations velocities can always be transformed. In the 19th century, it became apparent that if one assumes that the Maxwell equations are correct, and that the newtonian transformations apply, then it should be possible to measure velocity absolutely. Einstein recognized that if one assumes that the Lorentz transformations are the appropriate transformations, then all inertial reference frames are indistinguishable. The Maxwell equations are formulated in just one reference frame, it's the physicists choice of appropriate transformation that determines whether any law of physics has effective independency of reference frame. A calculation is performed in the one reference frame that a law of physics is formulated in. If and only if the approppriate transformations are available, observers can scientifically agree. Their observations can come out differently, they can subsequently transform their results to the frame of reference of the other observer, and find agreement. Einstein didn't reformulate any laws of physics individually: by providing the right transformations, all formulations of laws of physics were provided with extension into relativistic inertial frame indepence. (As it turned out, for example a new relativistic momentum had to be found, in order to have a momentum that displays conservation of momentum.) In newtonian dynamics, it is relatively straightforward to transform between an inertial reference frame and an accelerating reference frame: linear addition of vectors. The acceleration vector (usually a function of time and/or spatial coordinates) is added to the velocity vector (also a function). For the reverse transformation, the same acceleration vector is used, with the sign reversed. So newtonian dynamics has transformations for non-inertial frames of reference. Einstein's effort to develop General Relativity was not a program to redesign the formulation of all laws of dynamics, it was a program with two goals: to find the appropriate transformations involving non-inertial reference frames, and to find a new theory of gravity in which gravity travels through space at lightspeed. The two goals turned out to be even more profoundly connected than anticipated: to an accelerating observer, space-time appears to be distorted; with gravity, space-time is. User:Cleon Teunissen 15:08, 21 Jan 2005 (UTC) =="Dynamic Universe"== *Tuomo Suntola, [http://www.sci.fi/~suntola/ Theoretical Basis of the Dynamic Universe], 2004. ISBN 9525502104. A highly promising new model of the universe. I removed this from the article. From what I can find on the web, it is a replacement for GR that is based around the concepts of absolute space and absolute time. As far as I can tell, very few people take it seriously, as it hasn't yet been verified that it explains everything GR does, much less make new, testable predictions (in particular, one back-of-the-envelope calculation shows it getting the orbit of Mercury wrong; another says that it doesn't handle the orbital decay of binary pulsars). --User:Carnildo 00:59, 4 Feb 2005 (UTC) == This article is not good. == I do not like this article at all, and will rewrite it when I get a chance. 1) The central principle of GR is the General Principle of Relativity, which states that the laws of physics are the same in all frames of reference. The local uniformity of phyical constants is a consequence of the General Principle, NOT the Equivalance Principle. 2) The central tenant of GR is that spacetime is curved due to the presense of mass/energy/momentum within it as described by the Einstein Field Equations. This should be mentioned up front, instead of being left until later. 3) GR uses several other principles which are not mentioned: The principle of general covariance (the laws of nature are independent of the coordinate system), the principle of geodesic motion (inertial motion occurs along timelike geodesics), and local Lorentz Invariance (the rules of Special Relativity apply locally in all frames of reference). 4) The Equivalence Principle (EP) is best presented as a rule for determining whether one is in an intertial frame of reference. (The definition presented in this article is correct, but not comprehensive.) Historically, the EP is the jumping-off point for Einstein's derivation of GR. However, it is only a part of GR and is not the best place to start a popular article on the subject in my opinion. : please do the rewrite. there are lotsa reviewers here that will scrutinize it, and if it's good (and accurate) your work will not go to waste. i am solely a spectator about the subject and am looking forward to learning some of the fundamentals. i dunno if it will help but [http://arxiv.org/pdf/gr-qc/0103044] and [http://pancake.uchicago.edu/~carroll/notes/grtinypdf.pdf] were somewhat useful to me. anything you can do to add to or elucidate that is welcome. also, i recommend that you get yourself a wikipedia identity. User:Rbj 17:47, 22 Mar 2005 (UTC) == More on rewrite == The requested ID has been obtained, and I have started drafting the changes in my sandbox. However, I request that you do not hold your breath waiting for the rewrite. I am going to take my time and be very deliberate about it before doing the replacement. I may not like the current article, but I do not want to replace it with something that is almost as bad if not worse. The time that I can devote to this is also limited, but I very much want to produce an article that gives people a sense of what GR is really about. :ain't holding my breath. i would suggest that you sign your comments to "Talk:" pages with four tildes " ~ ~ ~ ~ ". then your wikipedia ID with the date and time are stamped on your comments. are you cool with the Tex editing? you might want to check out Wikipedia:How_to_edit_a_page or Help:Formula if you haven't yet. good luck, and you have any encouragement from me. User:Rbj 17:55, 23 Mar 2005 (UTC) == [A speculative response] == In reference to the null result of the Michelson-Morley experiment in the section on 'Foundations' (and other results ?) it says, '...Einstein explained these results in his theory of special relativity.' I'm not convinced he 'explained' the null result, but rather he used it as an assumption in SR. Then he developed a theory of mechanics. As a little aside, I'm not sure we really know why the speed of light is constant in all inertial reference frames, apart from the fact that otherwise there would arise theoretical contradictions - but to explain it physically is still a mystery (I think). I suppose it's a bit like asking why (physically) does the existence of matter cause spacetime to curve. What's the exact mechanism ? Food for thought .... : i think i have a feel for why the speed of E&M propagation should be the same for all inertial reference frames. it really just comes from Maxwell's Eqs. and the knowledge that there is no ether medium that E&M is propagated in. i mean, how do we tell the difference between a moving vacuum and a stationary vacuum? if we can't, if there really is no difference between a moving vacuum and a stationary vacuum, that such a concept is really meaningless, then whether the light that you are measuring originated from a flashlight mounted on a rocket moving past you at or from a stationary flashlight, how does that change the fact that a changing E field is causing a changing B field which is causing a changing E field, etc.? that propagation of an E field and B field disturbance, which has velocity ? how is it different? whether you are holding the flashlight or moving past it at high velocity, Maxwell's Eqs. say the same thing regarding the nature of E&M in the vacuum.User:Rbj 05:28, 24 Mar 2005 (UTC) Yes, the EM argument is a good (convincing) one. Now for the next question: why does matter cause spacetime curvature ? (lol, only joking). == Lightspeed, etc. == The constancy of the speed of light arises from the metric nature of spacetime. The Minknowski metric, whose line item is (in units where ) demands it quite nicely. However, this only leads to other "why"'s. I suggest that the purpose of Wikipedia be respected, which as I understand it is to report on the current state of knowledge, and hopefully to do so in a way that is accessible to the average person. So what is important here is the "what" and not the underlying "why". EMS I did say, 'as a little aside...' (lol) == A Convention == May I suggest that we try to use a consistent convention for the value of the speed of light ? After reading many textbooks/research papers etc... which put and don't tell us this, I think it might be better to just write c. Putting in equations confuses many people when they try to check units. It's especially annoying when they don't tell you this like in the 'vierbein formulation' part (which I have subsequently amended). Putting can be quite elegant in some formulae (esp. Maxwell's equations), but I think that for anyone (esp. beginners/newcomers) reading an encyclopedia it is better to have clarity rather than elegance. Also, if it's said that the speed of light is taken to be unity, you have to flap around with the formulae to see where it goes (and is it just or or , like in some gravitational radiation formulae ? ). Please let's try to keep in our formulae. == modifications to article == I've moved a few things around and included some new sections to make the article a little clearer; a lot of work still needs to be done. The 'well-known and popular metrics' have been moved to Einstein field equation. Should the maths of GR be moved to a separate article ? The statements "The fundamental idea in relativity is that we cannot talk of the physical quantities of velocity or acceleration without first defining a reference frame, and that a reference frame is defined by choosing particular matter as the basis for its definition. " are incorrect. An ordinary accelerometer measures acceleration. Of course, you can say the accelerometer is stationary in some reference frame, and so, in a sense, it locally defines a reference frame, but the question of how to extend that reference meaningfully outside the world-line of the accelerometer will lead you into a morass if you are not expert, and into a lot of digressions if you are. One asks why someone is writing a new book on relativity here, when there are so many already. There are good old books by P G Bergmann and Steve Weinberg that can be mined for descriptions, and newer books too, e.g. by Robert M. Wald. As for the second statement it was already critiqued. A reference frame can be identified by imagining a swarm of massless observers, who define the coordinate gridpoints. They need not have mass, i.e. be material; they can be hypothetical. Only requirements are that their worldlines by timelike and form a smooth family - i.e. they do not intersect. There is a maths term for that - probably "manifold" but let someone with more maths settle that. User:Pdn 06:26, 16 Apr 2005 (UTC) == Let's sort out this article. == I think it's about time this article had a serious facelift. The quantum mechanics article puts this one to shame. I've made a few changes: new introduction; removed a paragraph on curvature which used very loose language; replaced that with a more rigorous version. Don't want to remove large chunks, as some of the existing text has useful descriptions (and It'd be treading on other peoples' toes). Need to sift through it carefully. Moved image of spacetime curvature to start of article (grabs attention). Discussion of constancy of speed of light is already in special relativity. User:Mpatel :i want to encourage those of you who understand GR to do exactly this. usually wiki articles help me break through the ice and my understanding of a topic has been increased as a result. sadly, i cannot say this about this article. maybe the material is just too hard, or i am missing something. i understand classical mechanics, a smattering of QM, SR, and a little bit of the Equivalence Principle (the man in an elevator descending at 9.8 m/s^2 is in the same instantaneous situation as other in weightless space or the man in a rocket accelerating at 9.8 m/s^2 has the same experience as one standing on the surface of the earth). is there some way that you guys can start with the EP, and bring us to something like Einstein's Field Equation? or to an equivalent statement like in the Baez and Bunn paper that is cited? User:Rbj 15:48, 20 Apr 2005 (UTC) I know a fair bit about GR; believe me, the (non-mathematical) material is NOT hard - GR is probably the most intuitively pleasing theory in physics to date. The problem is, firstly, I don't want to suddenly remove a huge chunk of other people's work and, secondly, there is a lot to GR (EP, covariance principle, mathematical formulation, two-body problem etc.) - basically, the question is, what's appropriate for an encyclopedia article entitled 'general relativity' ? I think: (1) the maths should be on a totally separate page. (2) the unique role of GR as a theory which determines the geometrical background in which objects move should be emphasised. (3) the nonlinearity of GR should be emphasised, and the consequences of this discussed (again, another major difference between other dynamical equations of physics - e.g. Maxwell's, Schrodinger's). (4) Some of the intuitive descriptions present in the article are OK, but others are confusing. I'm chipping away at this article to try and achieve these objectives. User:Mpatel 16:19, 20 Apr 2005 (UTC) == Sorting out article. == OK, I've made a start in seriously modifying this article. I've deleted, swapped and changed loads of stuff. I propose: (1) In Description of Theory, we talk about how curvature arises through the use of non-inertial reference frames. Then talk about the principle of general relativity and the Equivalence Principle (and maybe covariance- but that might be better in the maths section). (2) Then discuss some of the juicy effects of GR (light bending, grav. waves, evolution of universe etc...). (3) Something on nonlinearity (probably in 'relationship with other physics theories' section). (4) Something on the history of Einstein's discovery of GR. (5) It might be OK to mention the field equation but not state it on this page (as elegant as it is) - I think it belongs in 'Mathematical formulation of GR', as should the geodesic equation; talking of which, deriving the equations of motion from the field equations might be worth a mention. I await comments :) User:Mpatel 08:38, 21 Apr 2005 (UTC) :made some changes and then did not notice I was logged out by accident (dunno why or how). Further changes by 69.244.72.110 this morning were mine. User:Pdn 12:31, 21 Apr 2005 (UTC) == More modific's == Included a subsection on topology of spacetime; might link in nicely with a brief discussion of black holes, wormholes etc. Is the section on foundations needed ? I think it's a little lengthy and possibly completely unnecessary - should it be moved somewhere else ? User:Mpatel 11:33, 22 Apr 2005 (UTC) Perhaps it could be integrated to some other main subtopic. The overal distribution of the article is a bit weird to me. It seems like a bunch of separated articles one after another, the continuity is a bit strange IMHO. However as of yet, I haven't figured out how to improve this. I'd like to ask also for a deeper explanation on how GR rises from SR. User:Nihil 01:12, 23 Apr 2005 (UTC) : Agreed. I just made a start in improving the article. The more modifications that are made to this article by more people, the better. User:Mpatel 09:23, 23 Apr 2005 (UTC) ==GR SR connection== The best way so far as I know to grasp the connection is to understand that a GR spacetime consists of a patching-together of a continuum of inifintesimal local Lorentzian (SR) pieces. Think of a soccer ball with those little pentagons. Make them smaller and smaller, and as they are so small that they approach flatness, extend each patch as a small section of an infinite plane. When you apply the Equivalence Principle all you are doing is saying that, in principle, if you could live in that (tangent) plane, you would be in Minkowski (SR) spacetime and everything would be as usual in SR. (Be careful on notation - "tangent space" is a mathematical construct that includes, as I understand it, lots of other vectors besided displacements and velocities - I think it has E&M vectors in it, too.) Of course, all these vectors can be imagined to lie in that extended plane I just described, too. How is this conceptualization applied to some poor chap standing in Dallas, TX and feeling the force of gravity pulling him downwards? Well, this discussion is all in four dimensions, and those little soccer ball patches all exist in a sequence of spacetime sections falling, in free fall, past this person. The patches have an inclination of their time axes to his that can be zero, if we make them by dropping them just like a lead sinker that he drops from rest, because if at rest when they meet him, the time axes are (instantaneously) aligned. If you want to extend these little patches above his head, I think you have to use ones with the time axes slanted, as if he threw up a sinker (or a clock) and then it passed by him again on the way down. But the point is that he is accelerated in regards to any of these coordinate patches that slip past him, and that is why he feels gravity. If you could extend the little patches to mate smoothly over a region larger than first order in the differentials, you would have found a local Minkowski space - hard to do in GR. It would exist inside a massive spherical shell, but not in very many other places I can think of, if matter is present. OK, nested shells, hollow at the center, that works. The patches can be just bent into a curved surface, or they can be more like vanes on a windmill, not mating smoothly. That is what happens in rotating systems; the patches that represent, for example, small regions on the Earth's surface are set up like vanes on a centrifugal fan. see: "Cylindrical Cardboard Model for a Rotating System in Special Relativity," Amer. J. Phys., 47, pp. 218‑223 . That's for special relativity, not GR, but it carries over to GR for rotating systems. User:Pdn 16:19, 23 Apr 2005 (UTC) ==Complain!== This article is much too unwieldy and unorganized. I think this (and perhaps some related articles) need to be rewritten from scratch as as set of more focused articles, following the Wikiprinciple of passing from the general to the specific. Suggestion: I see some stuff on "the meaning of curvature". That's important, but its really about geometry, not gtr per se, and should be incorporated into pages on Riemannian geometry (if it's not already there). Another suggestion: there's much too much historical material here. Much of this could be moved to a separate article on the historical development of gtr. User:Hillman 29 May 2005 : My advice is to go for it. I looked into doing this myself, thinking that another project of mine was winding down, but it has not and I can't do much for now. : I agree with your complaint about the history section even though I wrote it. What little was there before was pathetic and misleading. So I put that section together, knowing that it almost is a first draft of the seperate article. My own feeling is that the math and the talk about the final development of the EFE should be off-loaded ASAP. I just want it to be done in the context of a fuller article on that issue. : Wikipedia is something that is going to grow in a step-like fashion as more and more people who care about these subjects and have the requisite expertise step up to the plate and add to it. Choose your battles here, realizing that you will need to build a foundation on which your GR article improvements are to rest. I myself am still grappling with the fact that the supporting articles that an improved GR article needs to reference (or which this one does) are often in need of work themselves. Often it is better to make the incremental imporvements than to do the big project, although that day must come. : --User:Ems57fcva | User_talk:ems57fcva 04:24, 30 May 2005 (UTC) : P.S. If you are who I now think you are (and I don't know of many entities named Hillman who can't figure out if they are human or not), then I very much look forward to your contributions. My advice is to start with the tensor and mathematics of general relativity pages. If you don't want to work on the math-of-GR article at first then at least look at my talk:mathematics of general relativity on it. I may work on that article soon and the comments include my intended outline. : --User:Ems57fcva | User_talk:ems57fcva 04:45, 30 May 2005 (UTC) == History of GR == Easier to move the history chunk to the article The development of general relativity (which I've done) and make modifications to that article (and the GR article) as appropriate. User:Mpatel 15:46, 30 May 2005 (UTC) : You didn't do the second half of that job, namely cutting the fat out of the GR article's history section. I have now done that. The new article also could use some elaboration and expansion, but that job I will leave mostly to others. --User:Ems57fcva | User_talk:ems57fcva 00:05, 31 May 2005 (UTC) == Suggestion on cutting down on 'EP' == The Equivalence Principle (EP) section appears to be larger than necessary, as there is a separate page for the EP. I suggest that any valuable bits in the EP section of the GR article be moved to the equivalence principle page (if they're not already there) and the current section be reduced accordingly. I think that only the gist of the EP needs to be mentioned in the GR article. Responses appreciated. User:Mpatel 15:52, 2 Jun 2005 (UTC) : No objection here. All that I ask is that the 1907 Einstein quote be retained. Beyond that I agree that it can be a lot shorter. The first sentence of the last paragraph should also apprear in the final product, but the rest of that last paragraph needs to be ditched. : Do go ahead and look at the equivalence principle page, but myself and Joke137 have put a lot of work into it, and I doubt that you will find any need to transfer data from this page to that one. Instead it may be more of an issue of making the GR section on the EP small and consistent with the EP page. : --User:Ems57fcva | User_talk:ems57fcva 19:29, 2 Jun 2005 (UTC) == Resolved == Hi, EMS and MP, thanks for the kind words. I am very glad to see you are both doing your bit (or more) to upgrade the gr articles here! I already have compiled a long list of articles I want to (re)-write here on gr topics. While, I haven't yet found the energy/time/courage to start in on the gr article itself, I -did- rewrite the article on Brans/Dicke theory! :-/ Looks like we all agree that ideally the main gr article should feature the briefest possible summaries of various broad topics, including * the dramatic players (gravitation, matter) and the stage (spacetime) as a player, * Einstein's motivation, desiderata, and heroic search for GR, * role of diffeomorphism covariance, * equivalence principle, * Newtonian limit, * geometric/physical meaning of the EFE, nonlinearity, * global versus local distinction, * conformal/causal structure, horizons, * role of boundary conditions, smoothness, * role of approximations (linearization/weak-field, far-field, slow motion), * gravitational radiation, * reformulations of GTR (ADM, Regge), * relationship to other gravitation theories, PPN parameters, * tests of GTR (past, present, future). At the end of each brief summary, a link could point interested readers to a longer article devoted to this particular aspect, which can be written from scratch, perhaps using the best of what is already present in various Wikipedia articles. Right now, the only one of these topics which appeals to me is the meaning of the EFE. As things stand, I think that even the list of references which I entered is fairly unwieldy. Is there any wikiprecedent for putting a list of printed refrences in a separate page? Maybe only the two on-line tutorial articles should be in the gr article itself--- maybe a very brief reference section could include these two and then link to a longer page containing all the other references? FWIW, some much easier projects I'd like to carry out include: * add suitable references to all the longer articles, and put any existing references into a uniform (wikitemplated) format, * improve various of the less unwieldy articles, * add suitable figures (e.g. to the Regge calculus and Penrose diagram articles). In the near future, I'd like to rewrite the weak-field theory article, add an article on multipole moments, add more pp-wave related articles, add an article on the Neugebauer/Meinel disk solution, and write articles on the Weyl and Ernst families of vacuum solutions. We'll see. --User:Hillman : Chris - : First of all, thanks for the outline. This is something that people can and may well work towards. I myself a few months ago mentioned a set of principles that the article of the time did not address. Now they are addressed, mostly due to the work of others. If you feel comfortable with addressing the physical meaning of the EFE, then go ahead and write it up. Just be aware that the EFE has its own article, and that much the same (but in more detail) should also be there. : As for moving the full list of references to another page: I know of no precedent, but an article on the available printed and web resources on GR is not inappropriate. Normally there is not such a wealth of resources available on a topic such that a special page is needed. I don't know that I would remove all references from the GR page itself. Instead I would keep 4-6 (including the web tutorials) and then have a prominent link ("For addition references ... " perhaps) to the full bibliography/references page. : Beyond that I repeat my prior advice: Choose your battles. There is so much that can and needs to be done, including fixing up many of the existing articles. As you already see, Wikipedia is living growing resource that over time is constantly improving due to the efforts of its contributors. That does not mean that you are not needed. In fact part of what is happenning is that as Wikipedia improves so does the quality of the contributors. So hopefully in a few more years the GR part of Wikipedia will be high quality text guarded and maintained by some of the better people in the field. For now we are a band of mostly dedicated amateurs with a few professionals in the mix, but your presense is a sign that the mix is changing. : --User:Ems57fcva | User_talk:ems57fcva 15:42, 8 Jun 2005 (UTC) ==Geometric physical theory== What is this supposed to mean? Why is it important to non-logged-in editor 81.218.238.113 to have this particular language? This editor keeps reverting to this with no explanation. User:WCFrancis 17:09, 10 Jun 2005 (UTC) * This user is a Wikipedia:Vandalism. They're modifying this and a handful of other pages to reflect their own unorthodox views of relativity and cosmology. I added the user to Wikipedia:Vandalism in progress a day or two ago, so hopefully their crusade will be curtailed in the not too distant future. --User:Christopher Thomas 20:22, 10 Jun 2005 (UTC) ==The spacetime myth== Ok i see this is some kind of religion. Well i respect your religion but don't be surprised when someone will finally contradict your bizzare space-time theory. Space-time is a joke. It tells us nothing about motion, nor does it tell us anything about weight and gravitation. -- User:81.218.238.113 11:39, 11 Jun 2005 (UTC) : That comment is so full of ignorance, it doesn't even deserve a response --- User:Mpatel 11:41, 11 Jun 2005 (UTC) Sorry but you are the ignorant. Gravity has nothing to do with spacetime curvature[http://users.adelphia.net/~lilavois/Crackpots/notorious.htm]. Spacetime is a geometric construct with no counterpart in nature (see physical space). -- User:81.218.238.113 13:42, 11 Jun 2005 (UTC) :Ok, you've asked for it now. :* 'spacetime is a geometric construct with no counterpart in nature' - you sure about that? - if it were true, then you can use the same argument to conclude that space doesn't exist (same for time) - because we use geometric constructs to model space (3-D euclidean, usually) and time (1-D euclidean) individually. The constructs are mathematical and we can visualise them. :* 'spacetime tells us nothing about motion' - that's not true, as by drawing a spacetime diagram (STD) you can conclude a lot about motion. A straight worldline in a STD can represent, for example, a particle travelling at a constant speed (relative to a given reference frame) - if you've done any physics or maths at high school level, you'll realise that what you said is incorrect, as you draw a STD every time you draw simple space-time graphs of an accelerating car (it's a 2-D STD) - curved lines represent acceleration, straight lines mean zero acceleration (sound familiar ????). :* I think you're perhaps confused about the idea of spacetime curvature. In a given physical situation, the spacetime is given. Only if there is any change in the dynamical state of that system does spacetime change in any way. Modelling the motion of a planet around the Sun (and treating the planet as a point particle), for example, doesn't mean that spacetime changes (as spacetime is fixed) - but if you were to draw a STD for that planet, then the worldline would look like a spiral (see the diagram in spacetime). I repeat, the spacetime is fixed and nothing moves in spacetime (in a STD nothing moves - that's obvious, but you can still talk about a car moving along a road during a certain time interval and represent that on a STD). In GR, the geometry of spacetime is not flat, but it is curved (if you were to take timelike slices, then you would not have 3D euclidean hypersurfaces). If my interpretation is correct, the geometry of spacetime only changes when the physical system in question changes it's dynamical state (for example, if a star were to suddenly supernova, then clearly the local geometry would change - any planets orbiting the star would get flung out or destroyed). In oversimplified language, when we say that spacetime is curved, we mean: space is curved, therefore this thing that we call spacetime (= space + time) must also be curved. :* The idea of gravity as a geometric phenomena is better (meaning experimentally and aesthetically) than any other idea at present - just take a look at the results of experimental tests of GR. I hope that clears up any misunderstandings you have about gravity being curved spacetime and motion in spacetime. --- User:Mpatel 15:02, 11 Jun 2005 (UTC) :*RE: The problem with differential geometry is that it deals with abstract metric spaces. Structures are easier to visualize but what does it tell us about physical processes (such as nuclear fusion) or the energy levels of the electron? Also if particles are absolute, why the hell do they need a reference frame to be relative to? When large group of hydrogen molecules in space attract each other to produce stars, it seems more of a quantum interaction than molecules warping spacetime. Molecules in intergalactic space attracting other molecules by exchanging graviton particles just seems right. My conclusion is that physics cannot be done using abstract geometry. We can only use elements, particles and the interaction processes between them. I wish I could be more enlightening, but it seems that current knowledge levels are too low to produce anything more than just postulates. --User:81.218.238.113 15:45, 11 Jun 2005 (UTC) :Wikipedia doesn't do original research, so your conclusions are out of scope here. You can publish or promote them at other places, your own WWW page or the USENET, I suggest. Wikipedia has to report the current scientific consensus, including relevant minority viewpoints, if verfieable sources can be produced. --User:Pjacobi 20:07, 2005 Jun 11 (UTC) :----------------- : I'm sorry if this sounds rude, but one whose knowledge level is low is yours. GR, though a combination of spacetime curvature and the principle of geodesic motion does explain the observed motion of objects. : Think that you cannot see GR in action? Then drop something. Nothing is pushing on it, yet it accelerates downward, the same as it would from your point of view if you in a giant centrifuge being pushed against the walls. : GR easily explains the equivalence of inertial and gravitational mass. Does your graviton exchange model do that? If so, then what is the math be which you prove it? : In addition, GR :* predicts the observed non-Newtonian perihelion precession Mercury, :* predicts the observed bending of light passing close to the Sun being twice that of the Newtonian prediction. :* predicts the time delay of signals going deeper into a gravitaional field, :* predicts the time dilation effects that the GPS needed to account for in order to function properly, :* and corresponds to Newtonian physics in the weak field limit. : Does your model do all that, and if so the what is the math? : In your defense, I will note the GR is a highly non-intuitive theory which many people find hard to grasp. The spacetime of GR is a curved, four-dimensional manifold in which one of the dimensions involved in the curvature is time. When Einstein started to work on the thery Max Plank told him "you will never succeed, and if you do noone will believe you". He was wrong on both counts, but to this day there are a lot of people who would rather not believe him than either deal with the math or admit their own failings. :--User:Ems57fcva | User_talk:ems57fcva 02:53, 12 Jun 2005 (UTC) Max Planck was ineed wrong but not because he rejected relativity. Quantum mechanics fails to describe the gravitational interaction. Both quantum mechanics and relativity are wrong in ignoring very weak interactions[http://www.physicsforums.com/showthread.php?t=75197]. -- User:81.218.230.86 01:53, 13 Jun 2005 (UTC) : I have looked at your link, and all that I can do is hold my nose at what I read. Perhaps the worst offense is that statment that "GR is not fully compatible with Newtonian theory". Indeed it is not, and is not intended to be (except in the weak field limit). However, '''Einstein's GR works when Newton's theory does not!''' : Be advised that I have walked in your shoes. So I will warn you now: :# You do not have a theory at this point. Instead all that you have is a speculation. It is an unfortunate attribute of -uh- "independent researchers" that they often do not realize this at first. :# This is not the place to discuss your non-thoery. : I am now done with this thread. I do wish you luck, but you will not find it here. --User:Ems57fcva | User_talk:ems57fcva 03:42, 13 Jun 2005 (UTC) : P.S. I just felt that you might like to know that I liked your last edit, and agree with it's contents. However, it is totally lacking in NPOV. Therefore, ''I refuse to place anything like that in the GR page, and will revert any such content that I am the first to find there''. A page dedicated to objections to the black hole, dark matter, and dark energy may actually be quite useful. There actually is a lot of objection to those in the field. However, before you get started do realize that it is the objections and misgivings of prominent scientists such as Einstein and Hawking that need to be documented. Your feelings have no place here, nor on this issue do mine (which along with the level of research required are the reasons that I will not do that article). : Do be advised that inappropriate articles are deleted here, sometimes rapidly. So don't try anything. Your work can be tracked, and will be dealt with. I may sympathize with your view, but ''I am not your friend''. --User:Ems57fcva | User_talk:ems57fcva 05:13, 13 Jun 2005 (UTC) I am not a friend of yours either and i don't need/want any permission from you. You don't own wikipedia and neither do i. As long as we'll construct a QFT version of gravitational interactions, general relativity is disqualified as a physical model of nature and gravitation becomes just like the other forces. Peace -- User:81.218.230.86 20:42, 13 Jun 2005 (UTC) :uh, oh. Some misunderstanding about scientific theories and models again. Even Newtonion gravitation is still a valid model and theory of gravition, as it proofs useful for description and calculation of a wide range of phenomena. Of course by now we know, where its usefullness breaks down and GR delivers better predictions. There is a widespread belief, that GR will break down at "Planck scale", but neither are details clear nor will this change anything on its range of usefull applications. --User:Pjacobi Hallo Pjacobi, AFAIK general relativity breaks down when space-time becomes infinitely curved. Unfornately we will never reach Planck scale but we should be able to construct a QFT version of gravitational interactions. -- User:81.218.230.86 22:38, 13 Jun 2005 (UTC) : Pjacobi & others - All that answering this person is doing is giving him a soapbox to stand on. : He has admited that he cares not for GR, and has an almost religous belief that a QFT will solve all of the ills of GR. :: And this comes from the same idiot who thinks that gravity is space-time curvature. You fascists cannot let go of old ideas. Btw i reverted your edits about the time and physical space article. -- User:81.218.230.86 16:29, 14 Jun 2005 (UTC) ::: Edit of time re-reverted, but your link to dimension was kept. (That at least was a good idea/edit.) --User:Ems57fcva | User_talk:ems57fcva 19:07, 14 Jun 2005 (UTC) : Never mind that Wikipedia is not the place for original research or personal speculative opinions. I suggest that we leave him be, except to revert his edits to articles as needed and if deserved. --User:Ems57fcva | User_talk:ems57fcva 02:25, 14 Jun 2005 (UTC) == The development of GR page has been moved == It is now called the "History of general relativity". That is its topic anyway as a practical matter. Maybe a seperate page on the development phase will be done later. For now, I wish to call a spade a spade. --User:Ems57fcva | User_talk:ems57fcva 02:55, 12 Jun 2005 (UTC) == Reflections of Relativity link. == On , an anonymous user placed in the article: : It is out of date (says black holes are not proven to exist) and errs in saying quantum states are preserved on null geodesics (violates inverse square law of optics). Mixes up photons and other bosons. First of all, black holes indeed are not proven to exist. The black hole is a theorem of GR, and it is also true that astronomers have found concentrations of matter so massive and dense such that if GR is correct then they must be black holes. However, all observations involving these concentrations of matter are indirect, and many astronomer do not consider it to be a given that these objects are in fact black holes. Many think that these may be quark stars instead, and point to certain observations as evidence of this. Do note that under GR, quark stars only exist for a fraction of a second as a star collapses into a black hole. Stable quark stars, if they exist (and that has not been proven either) would be a serious blow to GR. == Non anonymous, not wrong == It was I who placed the material you find objectionable, and I had signed in. Black holes are proven to exist: There is one at the center of our Galaxy. See recent papers by Schoedel, Genzel, Ekhart and others. There is a movie which with some calculations establishes a massive black hole ar Sag A: [http://www.astro.ucla.edu/~jlu/gc/pictures/orbitsMovie.shtml] The way the argument runs is that while earlier, people tried to mimic the strong gravity of a black hole by assuming a very dense star cluster or a ball of massive neutrinos, the new observations go in so close that neither of these configurations could be stable. Everybody trying to explain the motions of stars near Sag A* with anything but a black hole gave up about 2 years ago. The Max Planck page at [http://www.mpe.mpg.de/ir/GC/team.php?lang=en] explains more - two groups UCLA and Max Planck have established the black hole is there. Also look on the web under Fulvio Melia who has given several talks on the analysis and implications. There are also proven black holes in some X-ray binaries, which can be shown from the flicker period at the inner edge of the disk. Fish a bit on the Web. --your next complaint-- As for the other comments: I fail to see how quantum states would not be preserved along null geodesics (since they have no passage of proper time). (With the neutrinos, their quantum state apparently not being preserved is evidence that they are massive.) I would also like to see citations of where photons and other bosons are mixed up, as well as for the other criticized portions of that text. :Quantum States - Well maybe I was too sticky there. It seems to me, however, that because the light cone is 3-dimensional, a bundle of rays on it must spread, so its density matrix decreases. That is the inverse square law, which holds classically and in QM. There is also some work showing polarization change in a ray's passing a region of strong gravity, I believe - but hard to look up so if you want, delete that part. -- the boson challenge-- :Bosons: Here is the offending sentence: "In fact, the presence of one boson in a particular quantum state actually enhances the probability of another photon entering that state." from the page: [http://www.mathpages.com/rr/s2-01/2-01.htm] As to other problems, I am tired of reading that turgid attempt of someone's to put her/his own stamp on relativity. The writer is unidentified, and the discourse ranges from dilatory to heavily laden with equations, often derived in a cumbersome way, with detours. User:Pdn 16:07, 16 Jun 2005 (UTC) Once that data is provided, a decision can be made as to whether to keep as-is, add a warning to, or remove outright this web reference. If it indeed has significant errors, I would lean towards removing it, but I don't feel that the case for that has been proven. So for now I feel that the link should be kept without warnings. --User:Ems57fcva | User_talk:ems57fcva 15:13, 16 Jun 2005 (UTC) ---- There can be no doubt that Sag A* is a gravitationally collapsed object, and that if GR is correct it is a black hole. The same also applies to the other super-massive objects in the centers of galaxies. I just don't think that there is a consensus that these really are black holes, at least amongst astronomers. However, that said, I will also admit that any scenario explaining how these objects could be something else is speculative. (I don't believe in black holes myself, btw. Even so, I also admit that GR is the best theory we have at this time. I just want the record to be straight in that I am not alone in not liking or accepting the black hole as physical reality.) That said, I will concede that if the text is saying that nothing that ceratinly is a black hole (if GR is correct) is known, that is not correct. For the quantum state business, I will point out that an expanding light sphere is composed of numerous photons. My focus is on each one. As for the boson/photon business, I need more context to be sure of the mix-up, but the offending sentence does indict itself. Beyond that, I think that the greatest indictment is in your last paragraph about the work as a whole. This seems to be an ancient reference, predating Chris Hillman's reworking of things. Finally, it is good to see that the "culprit" is you. However, my feeling is that either we keep this reference or we don't. There are plenty of good resources out there. We don't need to reference an inadequate one. --User:Ems57fcva | User_talk:ems57fcva 17:31, 16 Jun 2005 (UTC) == removal of threads == Dear "CyclopsX", The "Spacetime Myth" thread is a part of this record for better or worse. If you find it embarassing, then so be it. My advice is to leave it alone, and stop calling attention to it. --User:Ems57fcva | User_talk:ems57fcva 03:28, 17 Jun 2005 (UTC)
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