General relativity

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General relativity (GR, also known as the general theory of relativity or GTR) is the geometric theory of gravitation published by Albert Einstein in 1915 and the current description of gravitation in modern physics. General relativity generalizes special relativity and Newton's law of universal gravitation, providing a unified description of gravity as a geometric property of space and time, or spacetime. In particular, the spacetime curvature is directly related to the energy and momentum of whatever matter and radiation are present.


  • Although Einstein's general theory of relativity predicts that there can exist... a singularity in our past, it provides no reason why... a creation out of nothing should occur. ...There are ways of avoiding... a past singularity. If gravity were ever to become a repulsive... force in the distant past then the Universe need not have experienced a singular beginning.
    • John D. Barrow, Theories of Everything: The Quest for Ultimate Explanation (1991) p. 26.
  • In the early 1960s general relativity experienced a sudden revival in connection with astrophysical discoveries far removed from its original domain, which had essentially been confined to the solar system.
    The physicist Clifford Will coined the phrase “Renaissance of General Relativity” to describe the process through which general relativity became an internationally visible, highly active field of research in which theoretical explorations went hand in hand with new astrophysical discoveries such as quasars and the cosmic microwave background radiation. The systematic exploration of exact solutions, and the understanding of space-time singularities and of the physical reality of gravitational waves, all came only after the low-water-mark period, in the wake of the renaissance of general relativity.
    • Alexander Blum, Roberto Lalli, Jürgen Renn, "The Reinvention of General Relativity: A Historiographical Framework for Assessing One Hundred Years of Curved Space-time," Isis, Vol. 106, No. 3 (Sept. 2015), pp. 598-620, citing Clifford Martin Will, Was Einstein Right? Putting General Relativity to the Test (1986).
  • The theoretical developments involving general relativity in the period prior to the renaissance made use of central principles of Einstein’s theory and of his heuristics and methodology; the physicists who pursued these developments mostly did so, however, not to explore general relativity for its own sake but, rather, from an ulterior motive—the construction of some sort of successor theory. This goal they did not achieve. They did not consider general relativity itself to be a theory fundamental enough to warrant detailed theoretical study, nor did they believe that it held much empirical potential beyond what was already known. There was one central exception to this latter belief, and that is cosmology.
    • Alexander Blum, Roberto Lalli, Jürgen Renn, "The Reinvention of General Relativity: A Historiographical Framework for Assessing One Hundred Years of Curved Space-time," Isis, Vol. 106, No. 3 (Sept. 2015), pp. 598-620.
  • If I were giving this lecture fifty years from now, the word "gravitation" would be as old-fashioned as the word "phlogiston" is to us. Relativity has certainly demoted gravitation as a real explanation, just as Priestley's and Lavoisier's analyses and decoding of chemical reactions destroyed the word "phlogiston."
  • Up to the early 1950s, general relativity was a little-frequented subject, amongst physicists—a theory that had to be praised, but that could be safely ignored. ...Its supporting evidence was sparse, questionable, and unstable: essentially it reduced to the changing experimental verdicts on the three notorious tests.
    • Marco Marnane Capria, Physics Before and After Einstein (2005)
  • There was difficulty reconciling the Newtonian theory of gravitation with its instantaneous propagation of forces with the requirements of special relativity; and Einstein working on this difficulty was led to a generalization of his relativity—which was probably the greatest scientific discovery that was ever made.
    • P. A. M. Dirac, quoted in Chandrasekhar, S. "On the “Derivation” of Einstein's Field Equations." American Journal of Physics 40.2 (1972): 224-234.
  • The theoretical view of the actual universe, if it is in correspondence to our reasoning, is the following. The curvature of space is variable in time and place, according to the distribution of matter, but we may roughly approximate it by means of a spherical space. ...this view is logically consistent, and from the standpoint of the general theory of relativity [is most obvious] lies nearest at hand; whether, from the standpoint of present astronomical knowledge, it is tenable, will not be discussed here. In order to arrive at this consistent view, we admittedly had to introduce an extension of the field equations of gravitation, which is not justified by our actual knowledge of gravitation. It is to be emphasized, however, that a positive curvature of space is given by our results, even if the supplementary term [cosmological constant] is not introduced. The term is necessary only for the purpose of making possible a quasi-static distribution of matter, as required by the fact of the small velocity of the stars.
  • To begin with the difference between my conception and Newton's law of gravitation: Please imagine the earth removed, and in its place suspended a box as big as a room or a whole house and inside a man naturally floating in the centre, there being no for force whatever pulling him. Imagine, further, this box being, by a rope or other contrivance, suddenly jerked to one side, which is scientifically termed 'difform motion,' as opposed to 'uniform motion.' The person would then naturally reach bottom on the opposite side. The result would consequently be the same as if he obeyed Newton's law of gravitation, while, in fact, there is no gravitation exerted whatever, which proves that difform motion will in every case produce the same effects as gravitation.
    I have applied this new idea to every kind of difform motion and have thus developed mathematical formulas which I am convinced give more precise results than those based on Newton's theory. Newton's formulas, however, are such close approximations that it was difficult to find by observation any obvious disagreement with experience.
  • The other constraint in our choice of concepts... lies in Einstein's call for frugality and simplicity. ...the aim of any good theoretical system is "the greatest possible sparsity of the logically independent elements (basic concepts and axioms)." Any redundancy or elaboration must be avoided, for "it is the grand object of all theory to make these irreducible elements as simple and as few in number as possible." For example, it was, in his view, "an unsatisfactory feature of classical mechanics that in its fundamental laws the same mass appears in two different roles, namely as an inertial mass in the laws of motion, and as a gravitational mass in the law of gravitation." The equivalence of these two interpretations of mass signaled to him a truth which needed to be stated as a basic axiom (in General Relativity Theory), rather than saddling the theory with a proliferation which did not seem to be inherent in phenomena.
    • Gerald Holton, The Advancement of Science, and its Burdens (1986) quoting Albert Einstein from, respectively, "Autobiographical notes" in Albert Einstein: Philosopher-scientist, The Library of Living Philosophers (1949) p.13, and from Ideas and Opinions (1954) Tr. Sonja Bargmann, p. 293.
  • The theory of gravitational fields, constructed on the basis of the theory of relativity, is called the general theory of relativity. It was established by Einstein (and finally formulated by him in 1915), and represents probably the most beautiful of all existing physical theories. It is remarkable that it was developed by Einstein in a purely deductive manner and only later was substantiated by astronomical observations.
  • The number of those actively engaged in research in general relativity ... remain[ed] small in the 1930s, 1940s, and early 1950s. ...Peter Bergmann once said to me, 'You only had to know what your six best friends were doing and you would know what was happening in general relativity.' ...However, in the 1930s a new element... briefly attracted attention, then stayed... quiescent for a quarter of a century. ...J. Robert Oppenheimer and... Robert Serber decided to study the relative influence of nuclear and gravitational influences in neutron stars. ...Their work attracted... Richard Chase Tolman. ...there appeared in 1939, a pair of papers, one by Tolman on the static solution of Einstein's field equations for fluid spheres... and one... by Oppenheimer and George Volkoff... In this paper, the foundations are laid for a general relativistic theory of stellar structure. ...Half a year later, the paper... by Oppenheimer and Hartland Snyder came out... Thus began the physics of black holes...
    • Abraham Pais, Subtle is the Lord: The Science and the Life of Albert Einstein (2005) pp. 268-269.
  • It thus characterizes not only the gravitational field but also the behaviour of measuring rods and clocks, i.e. the metric of the four-dimensional world which contains the geometry of ordinary three-dimensional space as a special case. This fusion of two previously quite disconnected subjects—metric and gravitation—must be considered as the most beautiful achievement of the general theory of relativity.
  • The great triumph of the theory of relativity lies in its absorbing the universal force of gravitation into one geometric structure... Einstein's achievements would be substantially as great even though it were not for... observational tests.
    • Howard P. Robertson, "Geometry as a Branch of Physics," (1949) from Albert Einstien: Philosopher-Scientist, ed. Paul Arthur Schlipp.
  • September 1959 to September 1960—a year with great portents for Einstein's general theory of relativity. ...a paper by Robert V. Pound and Glen A. Rebka, Jr. ...entitled "Apparent Weight of Photons"... described the first successful laboratory measurement of the... gravitational red shift of light... A few months later, in June 1960... there appeared a paper by... Roger Penrose... "A Spinor Approach to General Relativity." ...[which] outlined a very elegant and streamlined technique for solving certain problems in general relativity. ...Later that summer ...Carl H. Brans ...[put] the finishing touches on his Ph.D. thesis ..."Mach's Principle and a Varying Gravitational Constant." ...[which] presented the equations for alternative to Einstein's ...a "scaler-tensor" theory of gravity ...[eventually] known as the Brans–Dicke theory.
    • Clifford Martin Will, Was Einstein Right?: Putting General Relativity To The Test (1993) Ch. 1. The Renaissance of General Relativity.
  • Thomas Matthews and Allan Sandage prepared to... make some observations of a radio source they denoted 3C48... interested in... [the] visible light... on the night of September 26, 1960 they took a photographic plate of the area... Conventional wisdom... told them that they would find a cluster of galaxies... Instead... subsequent observations... and throughout 1961 showed... its spectrum of colors was highly unusual... its brightness and luminosity varied widely and rapidly... it was only "quasi" stellar. Hence the name quasi stellar radio source or "quasar"... It was a remarkable year for general relativity, because it contained all the signs that a renaissance was about to begin. era in which general relativity would become an active and exciting branch of physics, after almost a half century in the backwaters.
    • Clifford Martin Will, Was Einstein Right?: Putting General Relativity To The Test (1993) Ch. 1. The Renaissance of General Relativity.

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