General relativity

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 is directly related to the energy and  of whatever matter and radiation are present.

Quotes

 * 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.


 * Einstein's general theory of relativity... was needed not because of conspicuous failures of Newton's theory... but because of inconsistencies between it and the requirements of electromagnetic theory, which Einstein had revised earlier in his special theory of relativity.
 * Peter G. Bergmann, The Riddle of Gravitation: From Newton to Einstein to Today's Exciting Theories (1968) p. 6.

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 s and the 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.
 * 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.
 * Alexander Blum, Roberto Lalli,, "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 , 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 s 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,, "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."
 * Jacob Bronowski, The Origins of Knowledge and Imagination (1978)


 * Differential geometry originally sneaked into theoretical physics through Einstein's theory of general relativity.


 * 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.


 * General relativity was considered by Einstein as his most important discovery... a new theory of gravitation bringing in a very powerful kind of symmetry. This symmetry is of importance in physics only where gravitational fields occur, while the symmetry previously... of special relativity, is of importance in all physics. So that this further symmetry... although it is such a wonderful mathematical theory, does not have the big effect on physics.
 * P. A. M. Dirac Speaking with Friedrich Hund on Symmetry in Relativity, Quantum mechanics and Physics of Elementary Particles (Göttingen, 1982) Filmdokumente zur Zeitgeschichte, G209; Youtube link title: "Interview, Göttingen 1982". See also Friedrich Hund.


 * I might say that my recent work has been very much concerned with Einstein’s general relativity, and I believe that the times and the distances which are to be used in Einstein’s general relativity are not the same as the times and distances which would be provided by atomic clocks. There are good theoretical reasons for believing that that is so and for believing that gravitational forces are getting weaker, compared to electric forces, as the world gets older.
 * P. A. M. Dirac, Interview, Göttingen 1982.

One thing at least is certain, light has weight One thing is certain, and the rest debate— Light rays, when near the Sun, do not go straight.
 * Oh leave the Wise our measures to collate
 * Arthur Eddington, as quoted by Allie Vibert Douglas, The Life of Sir Arthur Eddington (1956) p. 44.


 * 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 [ ] 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.
 * Albert Einstein, "Cosmological Considerations in the General Theory of Relativity," Königlich Preußische Akademie der Wissenschaften (1917) 142-152, as quoted in The Collected Papers of Albert Einstein Vol. 6: The Berlin Years: Writings, 1914-1917 p. 431-432

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.
 * 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.
 * Albert Einstein, "Einstein Expounds His New Theory," New York Times (Dec. 3, 1919) p. 19.


 * 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.
 * , 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.


 * A scientific theory is usually felt to be better than its predecessors not only in the sense that it is a better instrument for discovering and solving puzzles but also because it is somehow a better representation of what nature is really like. One often hears that successive theories grow ever closer to, or approximate more and more closely to, the truth. Apparently generalizations like that refer not to the puzzle-solutions and the concrete predictions derived from a theory but rather to its ontology, to the match, that is, between the entities with which the theory populates nature and what is “really there.” Perhaps there is some other way of salvaging the notion of ‘truth’ for application to whole theories, but this one will not do. There is, I think, no theory-independent way to reconstruct phrases like ‘really there’; the notion of a match between the ontology of a theory and its “real” counterpart in nature now seems to me illusive in principle. Besides, as a historian, I am impressed with the implausability of the view. I do not doubt, for example, that Newton’s mechanics improves on Aristotle’s and that Einstein’s improves on Newton’s as instruments for puzzle-solving. But I can see in their succession no coherent direction of ontological development. On the contrary, in some important respects, though by no means in all, Einstein’s general theory of relativity is closer to Aristotle’s than either of them is to Newton’s.
 * Thomas Kuhn, The Structure of Scientific Revolutions, 3rd ed. (1996), Postscript—1969


 * 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.
 * Lev Landau and Evgeny Lifshitz, The Classical Theory of Fields (4th ed., 1975)


 * The number of those actively engaged in research in general relativity ... remain[ed] small in the 1930s, 1940s, and early 1950s. ... 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... decided to study the relative influence of nuclear and gravitational influences in s. ...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 ... In this paper, the foundations are laid for a general relativistic theory of . ...Half a year later, the paper... by Oppenheimer and  came out... Thus began the physics of s...
 * 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.
 * Wolfgang Pauli, Theory of Relativity (1921)


 * 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 Einstein: Philosopher-Scientist, ed. Paul Arthur Schlipp.


 * Einstein asked himself a question... how can the sun and the Earth "attract" each other without touching..? ...[H]e imagined that the sun and the Earth each modified the space and time that surrounded them, just as a body in water displaces the water... This modification of the structure of time influences in turn the movement of the bodies, causing them to "fall" toward one another. ...The Earth is a large mass and slows down time in its vicinity. ...If things fall, it is due to this slowing of time. ...Where time passes uniformly, in interplanetary space, things do not fall. ...[H]ere on ...our planet, the movement of things inclines naturally toward where time passes more slowly, as when we run ...into the sea and the resistance of the water on our legs makes us fall headfirst... [T]ime passes more slowly for your feet than it does for your head.
 * Carlo Rovelli, The Order of Time (2018) p. 11.


 * Despite the weakness of the early experimental evidence for general relativity, Einstein’s theory became the standard textbook theory of gravitation in the 1920s and retained that position from then on, even while the various eclipse expeditions of the 1920s and 1930s were reporting at best equivocal evidence for the theory. … Perhaps all of us were just gullible and lucky, but I do not think that is the real explanation. I believe that the general acceptance of general relativity was due in large part to the attractions of the theory itself—in short, to its beauty.
 * Steven Weinberg, Dreams of a Final Theory (1992), Chap. 5 : Tales of Theory and Experiment


 * ... I don’t see any reason why anyone today would take Einstein’s general theory of relativity seriously as the foundation of a quantum theory of gravitation, if by Einstein’s theory is meant the theory with a Lagrangian density given by just the term $${\sqrt{g} R / 16 \pi G}$$. It seems to me there’s no reason in the world to suppose that the Lagrangian does not contain all the higher terms with more factors of the curvature and/or more derivatives, all of which are suppressed by inverse powers of the Planck mass, and of course don’t show up at any energy far below the Planck mass, much less in astronomy or particle physics. Why would anyone suppose that these higher terms are absent?
 * Steven Weinberg, (quote from p. 9)


 * 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 Approach to General Relativity." ...[which] outlined a very elegant and streamlined technique for solving certain problems in general relativity. ...Later that summer ... ...[put] the finishing touches on his Ph.D. thesis ..."Mach's Principle and a Varying Gravitational Constant." ...[which] presented the equations for ...an alternative to Einstein's ...a "scaler-tensor" theory of gravity ...[eventually] known as the.
 * , Was Einstein Right?: Putting General Relativity To The Test (1993) Ch. 1. The Renaissance of General Relativity.


 * Thomas Matthews and 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 ""... It was a remarkable year for general relativity, because it contained all the signs that a renaissance was about to begin. ...an era in which general relativity would become an active and exciting branch of physics, after almost a half century in the backwaters.
 * , Was Einstein Right?: Putting General Relativity To The Test (1993) Ch. 1. The Renaissance of General Relativity.


 * GTR has an extreme inner beauty and elegance; the construction of the GTR required the introduction of only one constant—the constant of gravitation. ...GTR produces the following: (1) Newton's law of gravitation, itself; (2) a foundation that enables one to apply Newton's law to the interaction of bodies surrounded by infinitely expanding matter; and (3) Friedmann's nonstationary cosmological model, including the prediction of the Hubble redshift for the spectra of distant objects. Only secondarily do we cite the three famous tests...—the precession of Mercury's perihelion, the deflection of a light beam passin near the Sun, and the variation of the frequency of light in a gravitational field.
 * ,, Relativistic Astrophysics (1971) Vol. 1, also published by Dover as Stars and Relativity (1996)

Also see

 * Albert Einstein
 * Relativity Simply Explained
 * Special relativity
 * Theory of relativity