Equivalence principle

718: 48: 2419: 7573: 6713: 731: 29: 972: 2094: 1899: 2414:{\displaystyle \eta (A,B)=2{\frac {\left({\frac {m_{{\textrm {p}}ass}}{m_{{\textrm {i}}nert}}}\right)_{A}-\left({\frac {m_{{\textrm {p}}ass}}{m_{{\textrm {i}}nert}}}\right)_{B}}{\left({\frac {m_{{\textrm {p}}ass}}{m_{{\textrm {i}}nert}}}\right)_{A}+\left({\frac {m_{{\textrm {p}}ass}}{m_{{\textrm {i}}nert}}}\right)_{B}}}.} 6257: 5364:

Kimura, M.; Aghion, S.; Amsler, C.; Ariga, A.; Ariga, T.; Belov, A.; Bonomi, G.; Bräunig, P.; Bremer, J.; Brusa, R. S.; Cabaret, L.; Caccia, M.; Caravita, R.; Castelli, F.; Cerchiari, G.; Chlouba, K.; Cialdi, S.; Comparat, D.; Consolati, G.; Demetrio, A.; Derking, H.; Di Noto, L.; Doser, M.; Dudarev,

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The strong equivalence principle applies the same constraints as the Einstein equivalence principle, but allows the freely falling bodies to be massive gravitating objects as well as test particles. Thus this is a version of the equivalence principle that applies to objects that exert a gravitational

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in 1907, when he observed that identical physical laws are observed in two systems, one subject to a constant gravitational field causing acceleration and the other subject to constant acceleration like a rocket far from any gravitational field. Since the physical laws are the same, Einstein assumed

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Touboul, Pierre; Métris, Gilles; Rodrigues, Manuel; André, Yves; Baghi, Quentin; Bergé, Joël; Boulanger, Damien; Bremer, Stefanie; Carle, Patrice; Chhun, Ratana; Christophe, Bruno; Cipolla, Valerio; Damour, Thibault; Danto, Pascale; Dittus, Hansjoerg; Fayet, Pierre; Foulon, Bernard; Gageant, Claude;

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Very careful experiments have shown that the inertial mass on the left side and gravitational mass on the right side are numerically equal and independent of the material composing the masses. The equivalence principle is the hypothesis that this numerical equality of inertial and gravitational mass

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Guidotti, Pierre-Yves; Hagedorn, Daniel; Hardy, Emilie; Huynh, Phuong-Anh; Inchauspe, Henri; Kayser, Patrick; Lala, Stéphanie; Lämmerzahl, Claus; Lebat, Vincent; Leseur, Pierre; Liorzou, Françoise; et al. (2017). "MICROSCOPE Mission: First Results of a Space Test of the Equivalence Principle".

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conjectured that any complete and consistent theory of gravity that embodies the weak equivalence principle implies the Einstein equivalence principle; the conjecture can't be proven but has several plausibility arguments in its favor. Nonetheless, the two principles are tested with very different

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This assumption of exact physical equivalence makes it impossible for us to speak of the absolute acceleration of the system of reference, just as the usual theory of relativity forbids us to talk of the absolute velocity of a system; and it makes the equal falling of all bodies in a gravitational

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Newton, Isaac; "Philosophiae Naturalis Principia Mathematica" , translated by Andrew Motte, revised by Florian Cajori, Berkeley, California: University of California Press, 1934; Newton, Isaac; "The Principia: Mathematical Principles of Natural Philosophy", translated by I. Bernard Cohen and Anne

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of a violation would be just as profound a result as discovery of a violation. Non-discovery of equivalence principle violation in this range would suggest that gravity is so fundamentally different from other forces as to require a major reevaluation of current attempts to unify gravity with the

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alone determines all of the effects of gravity. If an observer measures a patch of space to be flat, then the strong equivalence principle suggests that it is absolutely equivalent to any other patch of flat space elsewhere in the universe. Einstein's theory of general relativity (including the

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The weak equivalence principle, also known as the universality of free fall or the Galilean equivalence principle can be stated in many ways. The strong equivalence principle, a generalization of the weak equivalence principle, includes astronomic bodies with gravitational self-binding energy.

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Newton, just 50 years after Galileo, developed the idea that gravitational and inertial mass were different concepts and compared the periods of pendulums composed of different materials to verify that these masses are the same. This form of the equivalence principle became known as "weak

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The breakthrough came suddenly one day. I was sitting on a chair in my patent office in Bern. Suddenly a thought struck me: If a man falls freely, he would not feel his weight. I was taken aback. This simple thought experiment made a deep impression on me. This led me to the theory of

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Stubbs, Christopher W.; Adelberger, Eric G.; Heckel, Blayne R.; Rogers, Warren F.; Swanson, H. Erik; Watanabe, R.; Gundlach, Jens H.; Raab, Frederick J. (1989). "Limits on Composition-Dependent Interactions Using a Laboratory Source: Is There a "Fifth Force" Coupled to Isospin?".

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Tests of the weak equivalence principle are those that verify the equivalence of gravitational mass and inertial mass. An obvious test is dropping different objects and verifying that they land at the same time. Historically this was the first approach, though probably not by

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as part of his program to test general relativity. Two new principles were suggested, the so-called Einstein equivalence principle and the strong equivalence principle, each of which assumes the weak equivalence principle as a starting point. These are discussed below.

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Testing local Lorentz invariance amounts to testing special relativity, a theory with vast number of existing tests. Nevertheless, attempts to look for quantum gravity require even more precise tests. The modern tests include looking for directional variations in the

980: 979: 3812:, translated by Masahiro Morikawa from the text recorded in Japanese by Jun Ishiwara, Association of Asia Pacific Physical Societies (AAPPS) Bulletin, Vol. 15, No. 2, pp. 17–19, April 2005. Einstein recalls events of 1907 in a talk in Japan on 14 December 1922. 3363:

With the first successful production of antimatter, in particular anti-hydrogen, a new approach to test the weak equivalence principle has been proposed. Experiments to compare the gravitational behavior of matter and antimatter are currently being developed.

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Adelberger, Eric G.; Stubbs, Christopher W.; Heckel, Blayne R.; Su, Y.; Swanson, H. Erik; Smith, G. L.; Gundlach, Jens H.; Rogers, Warren F. (1990). "Testing the equivalence principle in the field of the Earth: Particle physics at masses below 1 μeV?".

1015:"... in a uniform gravitational field all objects, regardless of their composition, fall with precisely the same acceleration." "The weak equivalence principle implicitly assumes that the falling objects are bound by non-gravitational forces." 5537:

Webb, John K.; Murphy, Michael T.; Flambaum, Victor V.; Dzuba, Vladimir A.; Barrow, John D.; Churchill, Chris W.; Prochaska, Jason X.; Wolfe, Arthur M. (2001). "Further Evidence for Cosmological Evolution of the Fine Structure Constant".

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the outcome of any local, non-gravitational test experiment is independent of the experimental apparatus' velocity relative to the gravitational field and is independent of where and when in the gravitational field the experiment is

2616: 2521: 1400: 1297: 3458:, where nuclear reactions similar to ones we observe today have been shown to have occurred underground approximately two billion years ago. These reactions are extremely sensitive to the values of the fundamental constants. 2751: 4562:

Galilei, Galileo; "Discorsi e Dimostrazioni Matematiche Intorno a Due Nuove Scienze", Leida: Appresso gli Elsevirii, 1638; "Discourses and Mathematical Demonstrations Concerning Two New Sciences", Leiden: Elsevier Press,

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The Einstein equivalence principle has been criticized as imprecise, because there is no universally accepted way to distinguish gravitational from non-gravitational experiments (see for instance Hadley and Durand).

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is a consequence of nature. The weak form, known for centuries, relates to masses of any composition in free fall taking the same trajectories and landing at identical times. The extended form by

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Baeßler, Stefan; Heckel, Blayne R.; Adelberger, Eric G.; Gundlach, Jens H.; Schmidt, Ulrich; Swanson, H. Erik (1999). "Improved Test of the Equivalence Principle for Gravitational Self-Energy".

1894:{\displaystyle {\frac {M_{0}^{\mathrm {act} }M_{1}^{\mathrm {pass} }}{r^{2}m_{1}^{\mathrm {inert} }}}={\frac {M_{0}^{\mathrm {act} }M_{2}^{\mathrm {pass} }}{r^{2}m_{2}^{\mathrm {inert} }}}} 3407:

In addition to the tests of the weak equivalence principle, the Einstein equivalence principle requires testing the local Lorentz invariance and local positional invariance conditions.

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Some of the tests of the equivalence principle use names for the different ways mass appears in physical formulae. In nonrelativistic physics three kinds of mass can be distinguished:

799:. The strong form requires Einstein's form to work for stellar objects. Highly precise experimental tests of the principle limit possible deviations from equivalence to be very small. 1452: 1031:

Uniformity of the gravitational field eliminates measurable tidal forces originating from a radial divergent gravitational field (e.g., the Earth) upon finite sized physical bodies.

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In other words, passive gravitational mass must be proportional to inertial mass for objects, independent of their material composition if the weak equivalence principle is obeyed.

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We have seen that the various formulations of the equivalence principle form hierarchy (or rather, a nested sequence of statements narrowing down the type of gravitational theory),

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Schlamminger, Stephan; Choi, Ki-Young; Wagner, Todd A.; Gundlach, Jens H.; Adelberger, Eric G. (2008). "Test of the Equivalence Principle Using a Rotating Torsion Balance".

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Three main forms of the equivalence principle are in current use: weak (Galilean), Einsteinian, and strong. Some studies also create finer divisions or slight alternative.

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under uniform motion. An observer in a windowless room cannot distinguish between being on the surface of the Earth and being in a spaceship in deep space accelerating at 1

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A tight bound on the effect of nearby gravitational fields on the strong equivalence principle comes from modeling the orbits of binary stars and comparing the results to

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Like the Einstein equivalence principle, the strong equivalence principle requires gravity is geometrical by nature, but in addition it forbids any extra fields, so the

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and variation of the fundamental constants. Heuristic arguments suggest that the magnitude of these equivalence principle violations could be in the 10 to 10 range.

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Since Einstein developed general relativity, there was a need to develop a framework to test the theory against other possible theories of gravity compatible with

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The strong equivalence principle can be tested by 1) finding orbital variations in massive bodies (Sun-Earth-Moon), 2) variations in the gravitational constant (

1526: 6628: 5963:, 3349 (1959). Explains the value of research on gravitation and distinguishes between the strong (later renamed "Einstein") and weak equivalence principles. 6653: 762: 6048:"...Physicists in Germany have used an atomic interferometer to perform the most accurate ever test of the equivalence principle at the level of atoms..." 4607:

Smith, G. L.; Hoyle, C. D.; Gundlach, J. H.; Adelberger, E. G.; Heckel, B. R.; Swanson, H. E. (1999). "Short-range tests of the equivalence principle".

3545:) depending on nearby sources of gravity or on motion, or 3) searching for a variation of Newton's gravitational constant over the life of the universe 795:

to also hold in free fall and requires the weak equivalence to be valid everywhere. This form was a critical input for the development of the theory of

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The two additional constraints added to the weak principle to get the Einstein form − (1) the independence of the outcome on relative velocity (local

1071:. Theories of gravity that obey the Einstein equivalence principle must be "metric theories", meaning that trajectories of freely falling bodies are 5261: 141: 5302:. Gravitation and Cosmology: 2nd Mexican Meeting on Mathematical and Experimental Physics, AIP Conference Proceedings. Vol. 758. p. 95. 5196:

Touboul, P., Métris, G., Rodrigues, M., Bergé, J., Robert, A., Baghi, Q., André, Y., Bedouet, J., Boulanger, D., Bremer, S. and Carle, P. (2022).

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Wagner, Todd A.; Schlamminger, Stephan; Gundlach, Jens H.; Adelberger, Eric G. (2012). "Torsion-balance tests of the weak equivalence principle".

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Chapter 1 discusses the equivalence principle, but incorrectly, according to modern usage, states that the strong equivalence principle is wrong.

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Mass (measured with a balance) and weight (measured with a scale) are locally in identical ratio for all bodies (the opening page to Newton's

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orbiting it. The system provided them a chance to test the strong equivalence principle in a strong gravitational field with high accuracy.

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Haugen, Mark P.; Lämmerzahl, Claus (2001). "Principles of Equivalence: Their Role in Gravitation Physics and Experiments That Test Them.".

2886:{\displaystyle S_{0,1}={\frac {M_{0}^{\mathrm {act} }}{M_{0}^{\mathrm {pass} }}}-{\frac {M_{1}^{\mathrm {act} }}{M_{1}^{\mathrm {pass} }}}} 2091:

is the difference of the ratios of gravitational and inertial masses divided by their average for the two sets of test masses "A" and "B".

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Instead, the weak equivalence principle assumes falling bodies are self-bound by non-gravitational forces only (e.g. a stone). Either way:

346: 7323: 3444:. For example, Webb et al. reported detection of variation (at the 10 level) of the fine-structure constant from measurements of distant 1120:) is thought to be the only theory of gravity that satisfies the strong equivalence principle. A number of alternative theories, such as 4042: 1012:"All uncharged, freely falling test particles follow the same trajectories, once an initial position and velocity have been prescribed". 7558: 6658: 6184: 2034:{\displaystyle {\frac {M_{1}^{\mathrm {pass} }}{m_{1}^{\mathrm {inert} }}}={\frac {M_{2}^{\mathrm {pass} }}{m_{2}^{\mathrm {inert} }}}} 995:

showed that Galileo was right: acceleration is the same for all bodies subject to gravity on the Moon, even for a hammer and a feather.

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Einstein, Albert. "On the relativity principle and the conclusions drawn from it." Jahrb Radioaktivitat Elektronik 4 (1907): 411–462.

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In 1911 Einstein demonstrated the power of the equivalence principle by using it to predict that clocks run at different rates in a

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The equivalence principle can be considered an extension of the principle of relativity, the principle that the laws of physics are

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in the 1960s. The most precise measurement was done in 1976 by flying a hydrogen maser and comparing it to one on the ground. The

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Philoponus, John; "Corollaries on Place and Void", translated by David Furley, Ithaca, New York: Cornell University Press, 1987

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The present best limits on the variation of the fundamental constants have mainly been set by studying the naturally occurring

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Zeeman, Pieter (1918) "Some experiments on gravitation: The ratio of mass to weight for crystals and radioactive substances",

7267: 4106: 4052: 1407: 1018:"... in a gravitational field the acceleration of a test particle is independent of its properties, including its rest mass." 416: 5999:, Cambridge, UK: Cambridge University Press, 1993. This is the standard technical reference for tests of general relativity. 3879: 6751: 3784:

Einstein, Albert. "On the Influence of Gravitation on the Propagation of Light." Annalen der Physik 35.898–908 (1911): 906.

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Voisin, G.; Cognard, I.; Freire, P. C. C.; Wex, N.; Guillemot, L.; Desvignes, G.; Kramer, M.; Theureau, G. (1 June 2020).

5809:; et al. (4 July 2018). "Universality of free fall from the orbital motion of a pulsar in a stellar triple system". 2748:

In words, passive gravitational mass must be proportional to active gravitational mass for all objects. The difference,

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Testing local positional invariance divides in to tests in space and in time. Space-based tests use measurements of the

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in 1971. He dropped a falcon feather and a hammer at the same time, showing on video that they landed at the same time.

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Bessel, Friedrich W.; "Versuche Uber die Kraft, mit welcher die Erde Körper von verschiedner Beschaffenhelt anzieht",

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other forces of nature. A positive detection, on the other hand, would provide a major guidepost towards unification.

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Braginski, Vladimir Borisovich; Panov, Vladimir Ivanovich (1971). "Журнал Экспериментальной и Теоретической Физики".

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Orbital variations due to gravitational self-energy should cause a "polarization" of solar system orbits called the

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to give precision approaching 1 in a billion. Modern experiments have improved this by another factor of a million.

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What is now called the "Einstein equivalence principle" states that the weak equivalence principle holds, and that:

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Evidence for gravitational theories: proceedings of course 20 of the International School of Physics "Enrico Fermi"

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in a gravitational field. He connected the equivalence principle to his earlier principle of special relativity:

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cannot have varied by more than 10% since the creation of the universe. The best data comes from studies of the

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Currently envisioned tests of the weak equivalence principle are approaching a degree of sensitivity such that

1680:{\displaystyle a_{1}={\frac {F_{1}}{m_{1}^{\mathrm {inert} }}}=a_{2}={\frac {F_{2}}{m_{2}^{\mathrm {inert} }}}} 894:

the gravitational field and the acceleration were "physically equivalent". Einstein stated this hypothesis as:

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The Principle of Relativity: A Collection of Original Memoirs on the Special and General Theory of Relativity

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then, by the weak equivalence principle, they fall at the same rate (i.e. their accelerations are the same).

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which have placed limits on the differential acceleration of objects towards the Earth, the Sun and towards

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of pendulums made with different materials as an alternative test giving the first precision measurements.

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A falling object behaves exactly the same on a planet or in an equivalent accelerating frame of reference.

7595: 7181: 6915: 6900: 6437: 6396: 6340: 6189: 6114: 6013:, Princeton, New Jersey: Princeton University Press, 1983. Chapter V discusses the equivalence principle. 4995:

Baeßler, Stefan; et al. (2001). "Remarks by Heinrich Hertz (1857–94) on the equivalence principle".

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Singh, Vishwa Vijay; Müller, Jürgen; Biskupek, Liliane; Hackmann, Eva; Lämmerzahl, Claus (13 July 2023).

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Whitman, with the assistance of Julia Budenz, Berkeley, California: University of California Press, 1999

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Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics

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means that experimental setup must be small compared to variations in the gravitational field, called

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Most alternative theories of gravity predict a change in the gravity constant over time. Studies of

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timing data. In 2014, astronomers discovered a stellar triple system containing a millisecond pulsar

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Hadley, Mark J. (1997). "The Logic of Quantum Mechanics Derived from Classical General Relativity".

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Overduin, James; Everitt, Francis; Mester, John; Worden, Paul (2009). "The Science Case for STEP".

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Rocha, G; Trotta, R; Martins, C.J.A.P; Melchiorri, A; Avelino, P.P; Viana, P.T.P (November 2003).

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Gyros, Clocks, Interferometers...: Testing Relativistic Gravity in Space. Lecture Notes in Physics

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and Galileo Galilei – will test the weak equivalence principle in space, to much higher accuracy.

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experiment must be small enough so that its gravitational potential does not alter the result.

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This article is about the principle in gravitation. For the principle in electromagnetism, see

5890:"An improved test of the strong equivalence principle with the pulsar in a triple star system" 5365:

A.; Ereditato, A.; Ferragut, R.; Fontana, A.; Gerber, S.; Giammarchi, M.; et al. (2015).

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Renner, János (1935). "Kísérleti vizsgálatok a tömegvonzás és tehetetlenség arányosságáról".

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we ... assume the complete physical equivalence of a gravitational field and a corresponding

604: 5977:, New York: W. H. Freeman and Company, 1973, Chapter 16 discusses the equivalence principle. 5915: 4596: 3829:

Clifton, Timothy; Ferreira, Pedro G.; Padilla, Antonio; Skordis, Constantinos (March 2012).

3672: 3066: 2926: 7388: 7314: 7158: 6760: 6557: 6506: 6499: 6452: 6124: 6097: 5911: 5828: 5764: 5705: 5622: 5557: 5495: 5438: 5378: 5303: 5276:"The Eöt-Wash Group | Laboratory Tests of Gravitational and sub-Gravitational Physics" 5219: 5154: 5092: 5047: 5004: 4961: 4917: 4873: 4811: 4719: 4665: 4626: 4375: 4326: 4269: 4196: 4086: 4007: 3959: 3901: 3852: 3722: 3587: 3376: 1531: 1484: 1457: 1180: 1153: 1097: 917: 424: 5871:"Even Phenomenally Dense Neutron Stars Fall like a Feather – Einstein Gets It Right Again" 4353: 8: 7610: 7463: 7458: 7448: 7280: 7229: 7047: 7032: 6858: 6789: 6737: 6024: 5391: 4019: 3633: 3608: 2912: 838: 827: 619: 589: 584: 336: 7453: 5832: 5768: 5709: 5682:

Viswanathan, V; Fienga, A; Minazzoli, O; Bernus, L; Laskar, J; Gastineau, M (May 2018).

5626: 5561: 5499: 5442: 5382: 5307: 5223: 5158: 5096: 5051: 5008: 4965: 4921: 4877: 4815: 4723: 4669: 4630: 4379: 4330: 4273: 4200: 4090: 4011: 3963: 3905: 3856: 3726: 599: 569: 7528: 7428: 7352: 7210: 7191: 7185: 7136: 7078: 6987: 6905: 6823: 6800: 6768: 6520: 6404: 6380: 6224: 6107: 6102: 5935: 5901: 5852: 5818: 5788: 5754: 5723: 5695: 5638: 5612: 5581: 5547: 5519: 5485: 5454: 5428: 5243: 5209: 5178: 5144: 5116: 5082: 5020: 4616: 4365: 4315:"An amusing analogy: modelling quantum-type behaviours with wormhole-based time travel" 4295: 4259: 4227: 4186: 4174: 4124: 4112: 4076: 4023: 3997: 3925: 3891: 3842: 3628: 3384: 3191: 1511: 1064: 955: 936: 886: 823: 796: 792: 780: 669: 554: 479: 326: 231: 216: 177: 39: 5016: 4354:"Equivalence of Active and Passive Gravitational Mass Tested with Lunar Laser Ranging" 3971: 3734: 7538: 7370: 7362: 6963: 6920: 6611: 5985: 5939: 5927: 5844: 5780: 5727: 5573: 5523: 5511: 5474:"The fundamental constants and their variation: observational and theoretical status" 5473: 5247: 5235: 5170: 5108: 5024: 4977: 4933: 4889: 4841:

Keiser, George M.; Faller, James E. (1979). "New approach to the Eötvös experiment".

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predict violations of the weak equivalence principle because they contain many light

1079: 499: 274: 7408: 5856: 5585: 5120: 4338: 4299: 4116: 4027: 2611:{\displaystyle F_{0}={\frac {M_{1}^{\mathrm {act} }M_{0}^{\mathrm {pass} }}{r^{2}}}} 2516:{\displaystyle F_{1}={\frac {M_{0}^{\mathrm {act} }M_{1}^{\mathrm {pass} }}{r^{2}}}} 1395:{\displaystyle F_{2}={\frac {M_{0}^{\mathrm {act} }M_{2}^{\mathrm {pass} }}{r^{2}}}} 1292:{\displaystyle F_{1}={\frac {M_{0}^{\mathrm {act} }M_{1}^{\mathrm {pass} }}{r^{2}}}} 549: 7443: 7433: 7380: 7357: 6935: 6569: 6551: 6229: 5919: 5870: 5836: 5792: 5772: 5713: 5642: 5630: 5565: 5503: 5458: 5446: 5396: 5386: 5366: 5311: 5231: 5227: 5182: 5166: 5162: 5104: 5100: 5055: 5012: 4969: 4925: 4881: 4819: 4727: 4673: 4634: 4387: 4383: 4334: 4287: 4222: 4204: 4094: 4015: 3967: 3909: 3860: 3730: 3549: 3481: 3357: 624: 579: 559: 504: 7503: 5923: 5569: 3864: 644: 7518: 7493: 7418: 7413: 7296: 7257: 7219: 7163: 7037: 6973: 6599: 6531: 6296: 6204: 6149: 6119: 6083: 4449: 3794: 3564: 3368: 3353: 3169: 3004: 2966: 2930: 2421:

Values of this parameter are used to compare tests of the equivalence principle.

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but earlier by Simon Stevin who dropped lead balls of different masses off the

449: 7543: 7215: 7199: 7195: 7098: 7068: 6925: 6828: 6356: 6134: 6006:, Basic Books (1993). This is a popular account of tests of general relativity. 5806: 4929: 4885: 4823: 4638: 3412: 722: 689: 684: 372: 236: 5840: 5507: 5450: 4475: 939:) and in later years Einstein recalled the role of the equivalence principle: 7589: 7533: 7513: 7508: 7423: 7291: 7119: 7063: 6895: 6848: 6575: 6545: 6432: 6035: 5931: 5684:"The new lunar ephemeris INPOP17a and its application to fundamental physics" 5515: 4973: 4395: 4218: 4098: 3921: 3438: 3372: 815: 649: 564: 544: 469: 367: 246: 5198:"MICROSCOPE Mission: Final Results of the Test of the Equivalence Principle" 4827: 4654:"A Determination of the Ratio of Mass to Weight for a Radioactive Substance" 609: 7553: 7473: 7438: 6968: 6930: 6683: 6563: 5848: 5784: 5718: 5683: 5577: 5239: 5174: 5112: 4981: 4937: 4893: 4732: 4707: 4678: 4653: 4403: 4236: 3591: 3380: 3026: 2982: 2918: 1053: 867: 819: 594: 574: 6025:

Gravity and the principle of equivalence – The Feynman Lectures on Physics

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requires compensation for this redshift to give accurate position values.

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Experimental Tests of the Equivalence Principle and Newton's Law in Space

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Shapiro, Irwin I.; Counselman, III; Charles, C.; King, Robert W. (1976).

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Di Casola, Eolo; Liberati, Stefano; Sonego, Sebastiano (1 January 2015).

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Everitt, C.W.F.; Damour, T.; Nordtvedt, K.; Reinhard, R. (October 2003).

3568: 3388: 3349: 2937: 1105: 992: 871: 784: 484: 454: 5776: 5367:"Testing the Weak Equivalence Principle with an antimatter beam at CERN" 4209: 3578:, analysis of pulsars, and the lunar laser ranging data have shown that 1140:

Inertial mass intrinsic to an object, the sum of all of its mass–energy.

7548: 7114: 6958: 6953: 6693: 5490: 5401: 4291: 3330: 2424:

A similar parameter can be used to compare passive and active mass. By

1146:

Active mass, the mass that determines the objects gravitational effect.

1108:. It is much more restrictive than the Einstein equivalence principle. 935:

Immediately after completing his work on a theory of gravity (known as

863: 694: 256: 182: 114:{\displaystyle G_{\mu \nu }+\Lambda g_{\mu \nu }={\kappa }T_{\mu \nu }} 5315: 4769:, Annals of Physics, Volume 26, Issue 3, 20 February 1964, pp. 442–517 4531:, Princeton, New Jersey: Princeton University Press, 1995, pp. 117–119 4081: 3913: 6945: 5336: 4694:

Proceedings of the Koninklijke Nederlandse Akademie van Wetenschappen

3583: 2922: 1150:

By definition of active and passive gravitational mass, the force on

1072: 988: 265: 5350: 4861: 3987: 16:

The hypothesis that inertial and gravitational masses are equivalent

7488: 6838: 5906: 5823: 5700: 5214: 5149: 4621: 4370: 3514: 634: 444: 284: 28: 6052: 5759: 5433: 5087: 4860:

Niebauer, Timothy M.; McHugh, Martin P.; Faller, James E. (1987).

4314: 4191: 4002: 3896: 3847: 3556:. Up to the limit of one part in 10 there is no Nordtvedt effect. 1104:

be the same everywhere in the universe and is incompatible with a

4800:"Verification of the principle of equivalence for massive bodies" 4480: 2936:

A popular exposition of this measurement was done on the Moon by

2893:

is used to quantify differences between passive and active mass.

5681: 7168: 5037: 3560: 3518: 3445: 845:

and the laws of physics are unable to distinguish these cases.

5072: 3708: 3402: 6729: 4175:"The Confrontation between General Relativity and Experiment" 3828: 3711:"Historical perspective on testing the Equivalence Principle" 5598: 4906: 4797: 4708:"Some Experiments on the Proportionality of Mass and Weight" 4606: 4598:

Mathematische und Naturwissenschaftliche Berichte aus Ungarn

3536: 1096:

force on themselves, such as stars, planets, black holes or

7149: 6004:

Was Einstein Right?: Putting General Relativity to the Test

5418: 5133: 4351: 3452: 1143:

Passive mass, the response to gravity, the object's weight.

875: 5973:

Misner, Charles W.; Thorne, Kip S.; and Wheeler, John A.;

4767:

The equivalence of inertial and passive gravitational mass

2901: 5966:

Dicke, Robert H.; "Mach's Principle and Equivalence", in

4950: 4451:'Magic Is No Magic': The Wonderful World of Simon Stevin 3824: 3822: 3820: 3818: 2915:

and listened for the sound they made on a wooden plank.

5536: 5363: 3877: 3415:(called "clock anisotropy tests") and new forms of the 1299:

Likewise the force on a second object of arbitrary mass

1131: 885:

A version of the equivalence principle consistent with

5887: 6325:

Die Grundlagen der Einsteinschen Relativitäts-Theorie

5956:

Dicke, Robert H.; "New Research on Old Gravitation",

4444: 4319:

Journal of Optics B: Quantum and Semiclassical Optics

3983: 3981: 3815: 2754: 2626: 2529: 2434: 2097: 2062: 1909: 1695: 1561: 1534: 1514: 1487: 1460: 1410: 1313: 1210: 1183: 1156: 57: 4859: 4523: 4521: 4519: 4517: 4515: 3419:. The anisotropy measures less than one part in 10. 809:

Newton's equation of motion in a gravitational field

4765:Roll, Peter G.; Krotkov, Robert; Dicke, Robert H.; 4513: 4511: 4509: 4507: 4505: 4503: 4501: 4499: 4497: 4495: 3753:

A History of the Theories of Aether and Electricity

779:is the hypothesis that the observed equivalence of 5657:"Fundamental Physics of Space – Technical Details" 3978: 3586:of Mars, based on three successive NASA missions, 2885: 2738: 2610: 2515: 2413: 2083: 2033: 1893: 1679: 1547: 1520: 1500: 1473: 1446: 1394: 1291: 1196: 1169: 113: 6258:Investigations on the Theory of Brownian Movement 6030:Introducing The Einstein Principle of Equivalence 5805: 5743:"A millisecond pulsar in a stellar triple system" 5688:Monthly Notices of the Royal Astronomical Society 3666: 3664: 3552:. This effect has been sensitively tested by the 1034: 7587: 5292: 4759: 4492: 4421:(Facsim. ed.). Mineola (N.Y.): Dover publ. 4070: 2944:Chronology of weak equivalence principles tests 834:is a consequence of their fundamental identity. 5414: 5412: 4586:, Berlin: J. Ch. Poggendorff, 25 401–408 (1832) 1090: 6265:Relativity: The Special and the General Theory 5997:Theory and experiment in gravitational physics 4778: 3661: 6745: 6068: 4476:"Weak Equivalence Principle test on the moon" 4066: 4064: 3746: 3744: 3344:Experiments are still being performed at the 1002: 756: 5409: 5351:""GALILEO GALILEI" GG Small Mission Project" 5293:Dittus, Hansjörg; Lāmmerzahl, Claus (2005). 5260:: CS1 maint: multiple names: authors list ( 4840: 4168: 4166: 3448:. Other researchers dispute these findings. 4749:Mathematikai és Természettudományi Értesítő 4440: 4438: 4164: 4162: 4160: 4158: 4156: 4154: 4152: 4150: 4148: 4146: 3945: 3797:. United Kingdom, Dover Publications, 1923. 3755:. Vol. 2. Courier Dover Publications. 3403:Tests of the Einstein equivalence principle 3358:Satellite Test of the Equivalence Principle 1024:Philosophiæ Naturalis Principia Mathematica 6752: 6738: 6075: 6061: 4712:Proceedings of the Royal Society of London 4658:Proceedings of the Royal Society of London 4061: 3880:"Nonequivalence of equivalence principles" 3809:How I Constructed the Theory of Relativity 3741: 3462:Tests of changes in fundamental constants 2929:'s approach in 1908 used a very sensitive 2909:Galileo's Leaning Tower of Pisa experiment 763: 749: 5905: 5822: 5758: 5717: 5699: 5616: 5551: 5489: 5432: 5400: 5390: 5213: 5148: 5086: 4843:Bulletin of the American Physical Society 4731: 4677: 4651: 4620: 4419:Galileo at Work: His Scientific Biography 4369: 4281: 4263: 4226: 4208: 4190: 4080: 4001: 3946:Ghins, Michel; Budden, Tim (March 2001). 3895: 3846: 3750: 3704: 3702: 3700: 3537:Tests of the strong equivalence principle 3437:Time-based tests search for variation of 6699:Emergency Committee of Atomic Scientists 4435: 4143: 3751:Whittaker, Sir Edmund (1 January 1989). 3670: 970: 27: 6044:at Living Reviews on General Relativity 4994: 2902:Tests of the weak equivalence principle 1447:{\displaystyle F=m^{\mathrm {inert} }a} 7588: 6443:Albert Einstein World Award of Science 5741:Ransom, Scott M.; et al. (2014). 5740: 5286: 4746: 4705: 4527:Ciufolini, Ignazio; Wheeler, John A.; 4488:from the original on 21 December 2021. 4312: 4249: 4040: 4034: 3697: 1303:due to the gravitational field of mass 6733: 6056: 5982:Gravitation and Spacetime 2nd edition 5371:Journal of Physics: Conference Series 4416: 4410: 2896: 5472:Uzan, Jean-Philippe (7 April 2003). 5471: 5465: 4172: 3476:Limit on fractional change per year 1132:Active, passive, and inertial masses 900:acceleration of the reference system 7324:Tolman–Oppenheimer–Volkoff equation 7277:Friedmann–Lemaître–Robertson–Walker 6082: 4862:"Galilean test for the fifth force" 4173:Will, Clifford M. (December 2014). 4075:. Vol. 562. pp. 195–212. 13: 6472:Albert Einstein: Creator and Rebel 6185:Einstein–Infeld–Hoffmann equations 6155:Einstein relation (kinetic theory) 6042:The Einstein Equivalence Principle 6011:Foundations of Space-Time Theories 5980:Ohanian, Hans; and Ruffini, Remo; 5949: 2875: 2872: 2869: 2866: 2849: 2846: 2843: 2819: 2816: 2813: 2810: 2793: 2790: 2787: 2728: 2725: 2722: 2719: 2702: 2699: 2696: 2672: 2669: 2666: 2663: 2646: 2643: 2640: 2589: 2586: 2583: 2580: 2563: 2560: 2557: 2494: 2491: 2488: 2485: 2468: 2465: 2462: 2023: 2020: 2017: 2014: 2011: 1994: 1991: 1988: 1985: 1961: 1958: 1955: 1952: 1949: 1932: 1929: 1926: 1923: 1882: 1879: 1876: 1873: 1870: 1841: 1838: 1835: 1832: 1815: 1812: 1809: 1783: 1780: 1777: 1774: 1771: 1742: 1739: 1736: 1733: 1716: 1713: 1710: 1669: 1666: 1663: 1660: 1657: 1610: 1607: 1604: 1601: 1598: 1435: 1432: 1429: 1426: 1423: 1373: 1370: 1367: 1364: 1347: 1344: 1341: 1270: 1267: 1264: 1261: 1244: 1241: 1238: 1177:due to the gravitational field of 74: 14: 7632: 7094:Hamilton–Jacobi–Einstein equation 6333:The Einstein Theory of Relativity 6018: 3356:. Future satellite experiments – 7572: 7571: 6712: 6711: 6448:Einstein Prize for Laser Science 4047:. World Scientific. p. 82. 3831:"Modified gravity and cosmology" 3793:Lorentz, Hendrik Antoon, et al. 874:is independent of the amount of 730: 729: 716: 46: 6493:Einstein: His Life and Universe 5881: 5863: 5799: 5734: 5675: 5649: 5592: 5530: 5357: 5343: 5329: 5268: 5189: 5127: 5066: 5031: 4988: 4944: 4900: 4853: 4834: 4791: 4772: 4740: 4699: 4686: 4645: 4589: 4576: 4566: 4556: 4543: 4534: 4468: 4448:; Vanden Berghe, Guido (2008). 4345: 4306: 4243: 3939: 3456:natural nuclear fission reactor 1404:By definition of inertial mass: 855:History of gravitational theory 6901:Mass–energy equivalence (E=mc) 6759: 6115:Mass–energy equivalence (E=mc) 5601:"New constraints on varying α" 5392:10.1088/1742-6596/631/1/012047 5232:10.1103/PhysRevLett.129.121102 5167:10.1103/PhysRevLett.119.231101 5105:10.1103/PhysRevLett.100.041101 4551:De Beghinselen der Weeghconst 4388:10.1103/PhysRevLett.131.021401 4252:Foundations of Physics Letters 4020:10.1088/0264-9381/29/18/184002 3948:"The Principle of Equivalence" 3871: 3800: 3787: 3778: 3769: 3644:Unsolved problems in astronomy 3619:Einstein's thought experiments 3554:Lunar Laser Ranging Experiment 2523:must be equal and opposite to 2113: 2101: 2078: 2066: 1035:Einstein equivalence principle 966: 925:field seem a matter of course. 1: 5570:10.1103/PhysRevLett.87.091301 4997:Classical and Quantum Gravity 4584:Annalen der Physik und Chemie 3990:Classical and Quantum Gravity 3972:10.1016/S1355-2198(00)00038-1 3865:10.1016/j.physrep.2012.01.001 3735:10.1016/S0273-1177(03)90335-8 3655: 3367:Proposals that may lead to a 862:compared different materials 21:surface equivalence principle 5894:Astronomy & Astrophysics 4179:Living Reviews in Relativity 3649:Unsolved problems in physics 3278:Adelberger, Eric G.; et al. 2426:Newton's third law of motion 1091:Strong equivalence principle 7: 6916:Relativistic Doppler effect 6438:Albert Einstein Peace Prize 6215:Unsuccessful investigations 5924:10.1051/0004-6361/202038104 5635:10.1016/j.newar.2003.07.018 5060:10.1103/physrevlett.83.3585 5017:10.1088/0264-9381/18/13/301 4652:Southerns, Leonard (1910). 3884:American Journal of Physics 3639:Tests of general relativity 3601: 3596:Mars Reconnaissance Orbiter 3417:Michelson-Morley experiment 991:mission in 1971, astronaut 811:, written out in full, is: 227:Gravitational time dilation 10: 7637: 7387:In computational physics: 6911:Relativity of simultaneity 6365:Picasso at the Lapin Agile 6303:Russell–Einstein Manifesto 6175:Bose–Einstein correlations 5984:, New York: Norton, 1994, 5875:Charles Blue, Paul Vosteen 5421:Advances in Space Research 4930:10.1103/physrevlett.62.609 4886:10.1103/physrevlett.59.609 4824:10.1103/physrevlett.36.555 4706:Potter, Harold H. (1923). 4639:10.1103/PhysRevD.61.022001 4454:. WIT Press. p. 154. 3715:Advances in Space Research 2084:{\displaystyle \eta (A,B)} 1003:Weak equivalence principle 852: 848: 802: 347:Mathisson–Papapetrou–Dixon 188:Pseudo-Riemannian manifold 18: 7569: 7401: 7266: 7238: 7224:Lense–Thirring precession 7107: 7056: 7018: 6997: 6986: 6944: 6888: 6872: 6814: 6806:Doubly special relativity 6778: 6767: 6707: 6621: 6530: 6461: 6415: 6312: 6273:The Meaning of Relativity 6238: 6090: 6036:The Equivalence Principle 5841:10.1038/s41586-018-0265-1 5508:10.1103/RevModPhys.75.403 5478:Reviews of Modern Physics 5451:10.1016/j.asr.2009.02.012 4696:, Amsterdam 20(4) 542–553 4339:10.1088/1464-4266/4/4/319 4313:Durand, Stéphane (2002). 3675:The Meaning of Relativity 3671:Einstein, Albert (2003). 3442:constants and mass ratios 3432:Global positioning system 3369:quantum theory of gravity 7084:Post-Newtonian formalism 7074:Einstein field equations 7010:Mathematical formulation 6834:Hyperbolic orthogonality 6664:Albert Einstein Archives 6594:Bernhard Caesar Einstein 6341:Relics: Einstein's Brain 6289:The Evolution of Physics 6170:Bose–Einstein statistics 6165:Bose–Einstein condensate 6145:Einstein field equations 6032:from Syracuse University 4974:10.1103/physrevd.42.3267 4868:(Submitted manuscript). 4605:(Leipzig) 68 11 (1922); 4417:Drake, Stillman (2003). 4099:10.1007/3-540-40988-2_10 4044:Five-dimensional Physics 4041:Wesson, Paul S. (2006). 3624:Gauge gravitation theory 3576:Big Bang nucleosynthesis 3387:, which should generate 3346:University of Washington 3045:Friedrich Wilhelm Bessel 958:. This was developed by 807:In classical mechanics, 352:Hamilton–Jacobi–Einstein 332:Einstein field equations 155:Mathematical formulation 7621:Philosophy of astronomy 6795:Galilean transformation 6786:Principle of relativity 6674:Einstein Papers Project 6190:Einstein–de Haas effect 5916:2020A&A...638A..24V 5540:Physical Review Letters 5202:Physical Review Letters 5137:Physical Review Letters 5075:Physical Review Letters 5040:Physical Review Letters 4910:Physical Review Letters 4866:Physical Review Letters 4804:Physical Review Letters 4529:Gravitation and Inertia 4358:Physical Review Letters 3499:fine-structure constant 1128:add additional fields. 1100:. It requires that the 914:gravitational potential 6880:Lorentz transformation 6606:Thomas Martin Einstein 6514:Introducing Relativity 6486:Einstein for Beginners 6389:Einstein and Eddington 6180:Einstein–Cartan theory 5280:www.npl.washington.edu 4733:10.1098/rspa.1923.0130 4679:10.1098/rspa.1910.0078 3428:Pound–Rebka experiment 3424:gravitational redshift 2887: 2740: 2612: 2517: 2415: 2085: 2035: 1895: 1681: 1549: 1522: 1508:are the same distance 1502: 1475: 1448: 1396: 1293: 1198: 1171: 1126:Einstein-aether theory 1102:gravitational constant 1083:kinds of experiments. 1069:gravitational redshift 996: 952: 933: 910: 866:to determine that the 222:Gravitational redshift 115: 33: 7348:Weyl−Lewis−Papapetrou 7089:Raychaudhuri equation 7028:Equivalence principle 6679:Einstein refrigerator 6669:Einstein's Blackboard 6548:(second wife; cousin) 6479:Einstein and Religion 6428:Albert Einstein Medal 6423:Albert Einstein Award 6281:The World as I See It 6220:Wave–particle duality 6200:Bohr–Einstein debates 6160:Cosmological constant 6140:Equivalence principle 6130:Einstein coefficients 5605:New Astronomy Reviews 3679:. Routledge. p. 3426:, the classic is the 3314:Schlamminger, et al. 3018:Pendulum, drop tower 2888: 2741: 2613: 2518: 2416: 2086: 2036: 1896: 1682: 1550: 1548:{\displaystyle m_{0}} 1523: 1503: 1501:{\displaystyle m_{2}} 1476: 1474:{\displaystyle m_{1}} 1449: 1397: 1294: 1199: 1197:{\displaystyle M_{0}} 1172: 1170:{\displaystyle M_{1}} 1118:cosmological constant 1098:Cavendish experiments 1075:of symmetric metric. 986: 941: 922: 896: 777:equivalence principle 510:Weyl−Lewis−Papapetrou 465:Kerr–Newman–de Sitter 285:Einstein–Rosen bridge 217:Gravitational lensing 173:Equivalence principle 116: 31: 7389:Numerical relativity 7230:pulsar timing arrays 6558:Hans Albert Einstein 6507:I Am Albert Einstein 6453:Einstein Prize (APS) 6125:Photoelectric effect 6098:Theory of relativity 5877:. NRAO. 4 July 2018. 5719:10.1093/mnras/sty096 5325:on 17 December 2008. 3588:Mars Global Surveyor 3377:loop quantum gravity 3218:Lunar laser ranging 2752: 2624: 2527: 2432: 2095: 2060: 1907: 1693: 1559: 1532: 1512: 1485: 1458: 1408: 1311: 1208: 1181: 1154: 440:Einstein–Rosen waves 166:Fundamental concepts 55: 7281:Friedmann equations 7175:Hulse–Taylor binary 7137:Gravitational waves 7033:Riemannian geometry 6859:Proper acceleration 6844:Maxwell's equations 6790:Galilean relativity 6210:Thought experiments 6009:Friedman, Michael; 6002:Will, Clifford M.; 5995:Will, Clifford M.; 5833:2018Natur.559...73A 5777:10.1038/nature12917 5769:2014Natur.505..520R 5710:2018MNRAS.476.1877V 5663:on 28 November 2016 5627:2003NewAR..47..863R 5562:2001PhRvL..87i1301W 5500:2003RvMP...75..403U 5443:2009AdSpR..43.1532O 5383:2015JPhCS.631a2047K 5308:2005AIPC..758...95D 5224:2022PhRvL.129l1102T 5159:2017PhRvL.119w1101T 5097:2008PhRvL.100d1101S 5052:1999PhRvL..83.3585B 5009:2001CQGra..18.2393B 4966:1990PhRvD..42.3267A 4922:1989PhRvL..62..609S 4878:1987PhRvL..59..609N 4830:on 22 January 2014. 4816:1976PhRvL..36..555S 4724:1923RSPSA.104..588P 4670:1910RSPSA..84..325S 4631:1999PhRvD..61b2001S 4380:2023PhRvL.131b1401S 4331:2002JOptB...4S.351D 4274:1997FoPhL..10...43H 4210:10.12942/lrr-2014-4 4201:2014LRR....17....4W 4091:2001LNP...562..195H 4012:2012CQGra..29r4002W 3964:2001SHPMP..32...33G 3906:2015AmJPh..83...39D 3857:2012PhR...513....1C 3727:2003AdSpR..32.1297E 3609:Classical mechanics 3463: 3385:Compton wavelengths 2945: 2880: 2854: 2824: 2798: 2733: 2707: 2677: 2651: 2594: 2568: 2499: 2473: 2028: 1999: 1966: 1937: 1887: 1846: 1820: 1788: 1747: 1721: 1674: 1615: 1378: 1352: 1275: 1249: 878:being accelerated. 828:gravitational field 826:× intensity of the 394:Kaluza–Klein theory 280:Minkowski spacetime 232:Gravitational waves 7596:General relativity 7330:Reissner–Nordström 7248:Brans–Dicke theory 7079:Linearized gravity 6906:Length contraction 6824:Frame of reference 6801:Special relativity 6659:Things named after 6521:Subtle is the Lord 6344:(1994 documentary) 6336:(1923 documentary) 6328:(1922 documentary) 6225:Gravitational wave 6108:General relativity 6103:Special relativity 4603:Annalen der Physik 4595:R. v. Eötvös 1890 4446:Devreese, Jozef T. 4292:10.1007/BF02764119 3806:Einstein, Albert, 3629:General covariance 3461: 2943: 2897:Experimental tests 2883: 2855: 2832: 2799: 2776: 2736: 2708: 2685: 2652: 2629: 2608: 2569: 2546: 2513: 2474: 2451: 2411: 2081: 2046:The dimensionless 2031: 2000: 1974: 1938: 1912: 1891: 1859: 1821: 1798: 1760: 1722: 1699: 1677: 1646: 1587: 1545: 1518: 1498: 1471: 1444: 1392: 1353: 1330: 1289: 1250: 1227: 1194: 1167: 1122:Brans–Dicke theory 1065:Lorentz invariance 997: 956:special relativity 937:general relativity 889:was introduced by 887:special relativity 824:gravitational mass 797:general relativity 793:special relativity 723:Physics portal 495:Oppenheimer–Snyder 435:Reissner–Nordström 327:Linearized gravity 275:Spacetime diagrams 178:Special relativity 111: 40:General relativity 34: 7601:Fictitious forces 7583: 7582: 7397: 7396: 7376:Ozsváth–Schücking 6982: 6981: 6964:Minkowski diagram 6921:Thomas precession 6864:Relativistic mass 6727: 6726: 6629:Awards and honors 6612:Siegbert Einstein 6500:Einstein's Cosmos 5807:Anne M. Archibald 5753:(7484): 520–524. 5611:(8–10): 863–869. 5427:(10): 1532–1537. 5316:10.1063/1.1900510 4960:(10): 3267–3292. 4954:Physical Review D 4609:Physical Review D 4108:978-3-540-41236-6 4054:978-981-256-661-4 3914:10.1119/1.4895342 3614:Eötvös experiment 3534: 3533: 3342: 3341: 3294:Baessler, et al. 3246:Niebauer, et al. 2913:Delft churchtower 2881: 2825: 2734: 2678: 2620:It follows that: 2606: 2511: 2406: 2393: 2376: 2353: 2322: 2305: 2282: 2252: 2235: 2212: 2181: 2164: 2141: 2029: 1967: 1889: 1790: 1675: 1616: 1521:{\displaystyle r} 1390: 1287: 1080:Leonard I. Schiff 984: 916:, and light rays 773: 772: 406: 405: 292: 291: 7628: 7575: 7574: 7358:van Stockum dust 7130:Two-body problem 7048:Mach's principle 6995: 6994: 6936:Terrell rotation 6776: 6775: 6754: 6747: 6740: 6731: 6730: 6715: 6714: 6614:(distant cousin) 6608:(great-grandson) 6570:Hermann Einstein 6552:Lieserl Einstein 6230:Tea leaf paradox 6077: 6070: 6063: 6054: 6053: 5944: 5943: 5909: 5885: 5879: 5878: 5867: 5861: 5860: 5826: 5803: 5797: 5796: 5762: 5738: 5732: 5731: 5721: 5703: 5694:(2): 1877–1888. 5679: 5673: 5672: 5670: 5668: 5659:. Archived from 5653: 5647: 5646: 5620: 5618:astro-ph/0309205 5596: 5590: 5589: 5555: 5553:astro-ph/0012539 5534: 5528: 5527: 5493: 5469: 5463: 5462: 5436: 5416: 5407: 5406: 5404: 5394: 5361: 5355: 5354: 5347: 5341: 5340: 5333: 5327: 5326: 5324: 5318:. Archived from 5301: 5290: 5284: 5283: 5272: 5266: 5265: 5259: 5251: 5217: 5193: 5187: 5186: 5152: 5131: 5125: 5124: 5090: 5070: 5064: 5063: 5035: 5029: 5028: 4992: 4986: 4985: 4948: 4942: 4941: 4904: 4898: 4897: 4857: 4851: 4850: 4838: 4832: 4831: 4826:. Archived from 4795: 4789: 4788: 4776: 4770: 4763: 4757: 4756: 4744: 4738: 4737: 4735: 4718:(728): 588–610. 4703: 4697: 4690: 4684: 4683: 4681: 4664:(571): 325–344. 4649: 4643: 4642: 4624: 4593: 4587: 4580: 4574: 4570: 4564: 4560: 4554: 4547: 4541: 4538: 4532: 4525: 4490: 4489: 4472: 4466: 4465: 4442: 4433: 4432: 4414: 4408: 4407: 4373: 4349: 4343: 4342: 4325:(4): S351–S357. 4310: 4304: 4303: 4285: 4267: 4265:quant-ph/9706018 4247: 4241: 4240: 4230: 4212: 4194: 4170: 4141: 4140: 4134: 4130: 4128: 4120: 4084: 4068: 4059: 4058: 4038: 4032: 4031: 4005: 3985: 3976: 3975: 3943: 3937: 3936: 3899: 3875: 3869: 3868: 3850: 3826: 3813: 3804: 3798: 3791: 3785: 3782: 3776: 3773: 3767: 3766: 3748: 3739: 3738: 3721:(7): 1297–1300. 3706: 3695: 3694: 3678: 3668: 3634:Mach's principle 3550:Nordtvedt effect 3482:weak interaction 3464: 3460: 3322:Torsion balance 3319: 3306:Torsion balance 3303: 3301: 3286:Torsion balance 3283: 3270:Torsion balance 3267: 3251: 3235: 3233: 3215: 3210:Shapiro, et al. 3202:Torsion balance 3199: 3183:Torsion balance 3180: 3178: 3160:Torsion balance 3157: 3155: 3137: 3135: 3120:Torsion balance 3117: 3115: 3097: 3095: 3080:Torsion balance 3077: 3075: 3055: 3053: 3033: 3015: 3013: 2993: 2991: 2946: 2942: 2892: 2890: 2889: 2884: 2882: 2879: 2878: 2863: 2853: 2852: 2840: 2831: 2826: 2823: 2822: 2807: 2797: 2796: 2784: 2775: 2770: 2769: 2745: 2743: 2742: 2737: 2735: 2732: 2731: 2716: 2706: 2705: 2693: 2684: 2679: 2676: 2675: 2660: 2650: 2649: 2637: 2628: 2617: 2615: 2614: 2609: 2607: 2605: 2604: 2595: 2593: 2592: 2577: 2567: 2566: 2554: 2544: 2539: 2538: 2522: 2520: 2519: 2514: 2512: 2510: 2509: 2500: 2498: 2497: 2482: 2472: 2471: 2459: 2449: 2444: 2443: 2420: 2418: 2417: 2412: 2407: 2405: 2404: 2403: 2398: 2394: 2392: 2391: 2378: 2377: 2374: 2366: 2365: 2355: 2354: 2351: 2343: 2333: 2332: 2327: 2323: 2321: 2320: 2307: 2306: 2303: 2295: 2294: 2284: 2283: 2280: 2272: 2264: 2263: 2262: 2257: 2253: 2251: 2250: 2237: 2236: 2233: 2225: 2224: 2214: 2213: 2210: 2202: 2192: 2191: 2186: 2182: 2180: 2179: 2166: 2165: 2162: 2154: 2153: 2143: 2142: 2139: 2131: 2123: 2090: 2088: 2087: 2082: 2040: 2038: 2037: 2032: 2030: 2027: 2026: 2008: 1998: 1997: 1982: 1973: 1968: 1965: 1964: 1946: 1936: 1935: 1920: 1911: 1900: 1898: 1897: 1892: 1890: 1888: 1886: 1885: 1867: 1858: 1857: 1847: 1845: 1844: 1829: 1819: 1818: 1806: 1796: 1791: 1789: 1787: 1786: 1768: 1759: 1758: 1748: 1746: 1745: 1730: 1720: 1719: 1707: 1697: 1686: 1684: 1683: 1678: 1676: 1673: 1672: 1654: 1645: 1644: 1635: 1630: 1629: 1617: 1614: 1613: 1595: 1586: 1585: 1576: 1571: 1570: 1554: 1552: 1551: 1546: 1544: 1543: 1527: 1525: 1524: 1519: 1507: 1505: 1504: 1499: 1497: 1496: 1480: 1478: 1477: 1472: 1470: 1469: 1453: 1451: 1450: 1445: 1440: 1439: 1438: 1401: 1399: 1398: 1393: 1391: 1389: 1388: 1379: 1377: 1376: 1361: 1351: 1350: 1338: 1328: 1323: 1322: 1298: 1296: 1295: 1290: 1288: 1286: 1285: 1276: 1274: 1273: 1258: 1248: 1247: 1235: 1225: 1220: 1219: 1203: 1201: 1200: 1195: 1193: 1192: 1176: 1174: 1173: 1168: 1166: 1165: 985: 950: 931: 908: 765: 758: 751: 738: 733: 732: 725: 721: 720: 505:van Stockum dust 490:Robertson–Walker 316: 315: 206: 205: 120: 118: 117: 112: 110: 109: 97: 89: 88: 70: 69: 50: 36: 35: 7636: 7635: 7631: 7630: 7629: 7627: 7626: 7625: 7606:Albert Einstein 7586: 7585: 7584: 7579: 7565: 7393: 7297:BKL singularity 7287:Lemaître–Tolman 7262: 7258:Quantum gravity 7240: 7234: 7220:geodetic effect 7194:(together with 7164:LISA Pathfinder 7103: 7052: 7038:Penrose diagram 7020: 7014: 6989: 6978: 6974:Minkowski space 6940: 6884: 6868: 6816: 6810: 6770: 6763: 6758: 6728: 6723: 6703: 6654:Religious views 6649:Political views 6617: 6602:(granddaughter) 6600:Evelyn Einstein 6588:Robert Einstein 6582:Eduard Einstein 6526: 6463: 6457: 6411: 6381:Einstein's Gift 6315: 6308: 6249:Annus mirabilis 6234: 6205:Teleparallelism 6150:Einstein radius 6120:Brownian motion 6086: 6084:Albert Einstein 6081: 6021: 6016: 5952: 5950:Further reading 5947: 5886: 5882: 5869: 5868: 5864: 5817:(7712): 73–76. 5804: 5800: 5739: 5735: 5680: 5676: 5666: 5664: 5655: 5654: 5650: 5597: 5593: 5535: 5531: 5470: 5466: 5417: 5410: 5362: 5358: 5349: 5348: 5344: 5335: 5334: 5330: 5322: 5299: 5291: 5287: 5274: 5273: 5269: 5253: 5252: 5194: 5190: 5132: 5128: 5071: 5067: 5036: 5032: 4993: 4989: 4949: 4945: 4905: 4901: 4858: 4854: 4839: 4835: 4810:(11): 555–558. 4796: 4792: 4777: 4773: 4764: 4760: 4745: 4741: 4704: 4700: 4691: 4687: 4650: 4646: 4594: 4590: 4581: 4577: 4571: 4567: 4561: 4557: 4549:Stevin, Simon; 4548: 4544: 4539: 4535: 4526: 4493: 4484:. 18 May 2007. 4474: 4473: 4469: 4462: 4443: 4436: 4429: 4415: 4411: 4350: 4346: 4311: 4307: 4283:10.1.1.252.6335 4248: 4244: 4171: 4144: 4132: 4131: 4122: 4121: 4109: 4069: 4062: 4055: 4039: 4035: 3986: 3979: 3944: 3940: 3876: 3872: 3835:Physics Reports 3827: 3816: 3805: 3801: 3792: 3788: 3783: 3779: 3774: 3770: 3763: 3749: 3742: 3707: 3698: 3691: 3669: 3662: 3658: 3653: 3604: 3539: 3405: 3354:Galactic Center 3317: 3299: 3297: 3281: 3265: 3262:Stubbs, et al. 3249: 3231: 3229: 3226:Keiser, Faller 3213: 3197: 3176: 3174: 3168:Roll, Krotkov, 3153: 3151: 3133: 3131: 3113: 3111: 3093: 3091: 3073: 3071: 3051: 3049: 3031: 3011: 3009: 3005:Galileo Galilei 2989: 2987: 2967:John Philoponus 2931:torsion balance 2904: 2899: 2865: 2864: 2859: 2842: 2841: 2836: 2830: 2809: 2808: 2803: 2786: 2785: 2780: 2774: 2759: 2755: 2753: 2750: 2749: 2718: 2717: 2712: 2695: 2694: 2689: 2683: 2662: 2661: 2656: 2639: 2638: 2633: 2627: 2625: 2622: 2621: 2600: 2596: 2579: 2578: 2573: 2556: 2555: 2550: 2545: 2543: 2534: 2530: 2528: 2525: 2524: 2505: 2501: 2484: 2483: 2478: 2461: 2460: 2455: 2450: 2448: 2439: 2435: 2433: 2430: 2429: 2399: 2373: 2372: 2371: 2367: 2350: 2349: 2348: 2344: 2342: 2338: 2337: 2328: 2302: 2301: 2300: 2296: 2279: 2278: 2277: 2273: 2271: 2267: 2266: 2265: 2258: 2232: 2231: 2230: 2226: 2209: 2208: 2207: 2203: 2201: 2197: 2196: 2187: 2161: 2160: 2159: 2155: 2138: 2137: 2136: 2132: 2130: 2126: 2125: 2124: 2122: 2096: 2093: 2092: 2061: 2058: 2057: 2010: 2009: 2004: 1984: 1983: 1978: 1972: 1948: 1947: 1942: 1922: 1921: 1916: 1910: 1908: 1905: 1904: 1869: 1868: 1863: 1853: 1849: 1848: 1831: 1830: 1825: 1808: 1807: 1802: 1797: 1795: 1770: 1769: 1764: 1754: 1750: 1749: 1732: 1731: 1726: 1709: 1708: 1703: 1698: 1696: 1694: 1691: 1690: 1656: 1655: 1650: 1640: 1636: 1634: 1625: 1621: 1597: 1596: 1591: 1581: 1577: 1575: 1566: 1562: 1560: 1557: 1556: 1539: 1535: 1533: 1530: 1529: 1513: 1510: 1509: 1492: 1488: 1486: 1483: 1482: 1465: 1461: 1459: 1456: 1455: 1422: 1421: 1417: 1409: 1406: 1405: 1384: 1380: 1363: 1362: 1357: 1340: 1339: 1334: 1329: 1327: 1318: 1314: 1312: 1309: 1308: 1306: 1302: 1281: 1277: 1260: 1259: 1254: 1237: 1236: 1231: 1226: 1224: 1215: 1211: 1209: 1206: 1205: 1188: 1184: 1182: 1179: 1178: 1161: 1157: 1155: 1152: 1151: 1134: 1093: 1046: 1037: 1005: 971: 969: 951: 948: 932: 929: 909: 906: 891:Albert Einstein 857: 851: 805: 789:Albert Einstein 769: 728: 715: 714: 707: 706: 530: 529: 520: 519: 475:Lemaître–Tolman 420: 419: 408: 407: 399:Quantum gravity 386:Advanced theory 313: 312: 311: 294: 293: 242:Geodetic effect 203: 202: 193: 192: 168: 167: 151: 121: 102: 98: 93: 81: 77: 62: 58: 56: 53: 52: 24: 17: 12: 11: 5: 7634: 7624: 7623: 7618: 7613: 7608: 7603: 7598: 7581: 7580: 7570: 7567: 7566: 7564: 7563: 7556: 7551: 7546: 7541: 7536: 7531: 7526: 7521: 7516: 7511: 7506: 7501: 7496: 7491: 7486: 7484:Choquet-Bruhat 7481: 7476: 7471: 7466: 7461: 7456: 7451: 7446: 7441: 7436: 7431: 7426: 7421: 7416: 7411: 7405: 7403: 7399: 7398: 7395: 7394: 7392: 7391: 7384: 7383: 7378: 7373: 7366: 7365: 7360: 7355: 7350: 7345: 7336:Axisymmetric: 7333: 7332: 7327: 7321: 7310: 7309: 7304: 7299: 7294: 7289: 7284: 7275:Cosmological: 7272: 7270: 7264: 7263: 7261: 7260: 7255: 7250: 7244: 7242: 7236: 7235: 7233: 7232: 7227: 7216:frame-dragging 7213: 7208: 7203: 7200:Einstein rings 7196:Einstein cross 7189: 7178: 7177: 7172: 7166: 7161: 7156: 7143: 7133: 7132: 7127: 7122: 7117: 7111: 7109: 7105: 7104: 7102: 7101: 7099:Ernst equation 7096: 7091: 7086: 7081: 7076: 7071: 7069:BSSN formalism 7066: 7060: 7058: 7054: 7053: 7051: 7050: 7045: 7040: 7035: 7030: 7024: 7022: 7016: 7015: 7013: 7012: 7007: 7001: 6999: 6992: 6984: 6983: 6980: 6979: 6977: 6976: 6971: 6966: 6961: 6956: 6950: 6948: 6942: 6941: 6939: 6938: 6933: 6928: 6926:Ladder paradox 6923: 6918: 6913: 6908: 6903: 6898: 6892: 6890: 6886: 6885: 6883: 6882: 6876: 6874: 6870: 6869: 6867: 6866: 6861: 6856: 6851: 6846: 6841: 6836: 6831: 6829:Speed of light 6826: 6820: 6818: 6812: 6811: 6809: 6808: 6803: 6798: 6792: 6782: 6780: 6773: 6765: 6764: 6757: 6756: 6749: 6742: 6734: 6725: 6724: 6722: 6721: 6708: 6705: 6704: 6702: 6701: 6696: 6691: 6686: 6681: 6676: 6671: 6666: 6661: 6656: 6651: 6646: 6641: 6636: 6631: 6625: 6623: 6619: 6618: 6616: 6615: 6609: 6603: 6597: 6591: 6585: 6579: 6573: 6567: 6561: 6555: 6549: 6543: 6536: 6534: 6528: 6527: 6525: 6524: 6517: 6510: 6503: 6496: 6489: 6482: 6475: 6467: 6465: 6459: 6458: 6456: 6455: 6450: 6445: 6440: 6435: 6430: 6425: 6419: 6417: 6413: 6412: 6410: 6409: 6401: 6393: 6392:(2008 TV film) 6385: 6377: 6369: 6361: 6357:Young Einstein 6353: 6349:Insignificance 6345: 6337: 6329: 6320: 6318: 6310: 6309: 6307: 6306: 6300: 6297:Why Socialism? 6293: 6285: 6277: 6269: 6261: 6254: 6244: 6242: 6236: 6235: 6233: 6232: 6227: 6222: 6217: 6212: 6207: 6202: 6197: 6192: 6187: 6182: 6177: 6172: 6167: 6162: 6157: 6152: 6147: 6142: 6137: 6135:Einstein solid 6132: 6127: 6122: 6117: 6112: 6111: 6110: 6105: 6094: 6092: 6088: 6087: 6080: 6079: 6072: 6065: 6057: 6051: 6050: 6045: 6039: 6033: 6027: 6020: 6019:External links 6017: 6015: 6014: 6007: 6000: 5993: 5978: 5971: 5964: 5953: 5951: 5948: 5946: 5945: 5880: 5862: 5798: 5733: 5674: 5648: 5591: 5529: 5491:hep-ph/0205340 5484:(2): 403–455. 5464: 5408: 5356: 5342: 5328: 5285: 5267: 5208:(12): 121102. 5188: 5143:(23): 231101. 5126: 5065: 5030: 4987: 4943: 4916:(6): 609–612. 4899: 4872:(6): 609–612. 4852: 4833: 4790: 4771: 4758: 4739: 4698: 4685: 4644: 4588: 4575: 4565: 4555: 4542: 4533: 4491: 4467: 4460: 4434: 4427: 4409: 4344: 4305: 4242: 4142: 4133:|journal= 4107: 4060: 4053: 4033: 3996:(18): 184002. 3977: 3938: 3870: 3841:(1–3): 1–189. 3814: 3799: 3786: 3777: 3768: 3761: 3740: 3696: 3689: 3659: 3657: 3654: 3652: 3651: 3646: 3641: 3636: 3631: 3626: 3621: 3616: 3611: 3605: 3603: 3600: 3565:PSR J0337+1715 3538: 3535: 3532: 3531: 3528: 3525: 3522: 3511: 3510: 3507: 3504: 3501: 3495: 3494: 3491: 3488: 3485: 3478: 3477: 3474: 3471: 3468: 3413:speed of light 3404: 3401: 3340: 3339: 3336: 3333: 3328: 3324: 3323: 3320: 3315: 3312: 3308: 3307: 3304: 3295: 3292: 3288: 3287: 3284: 3279: 3276: 3272: 3271: 3268: 3263: 3260: 3256: 3255: 3252: 3247: 3244: 3240: 3239: 3238:Fluid support 3236: 3227: 3224: 3220: 3219: 3216: 3211: 3208: 3204: 3203: 3200: 3195: 3189: 3185: 3184: 3181: 3172: 3166: 3162: 3161: 3158: 3149: 3146: 3142: 3141: 3138: 3129: 3126: 3122: 3121: 3118: 3109: 3106: 3102: 3101: 3098: 3089: 3086: 3082: 3081: 3078: 3069: 3064: 3060: 3059: 3056: 3047: 3042: 3038: 3037: 3034: 3029: 3024: 3020: 3019: 3016: 3007: 3002: 2998: 2997: 2994: 2985: 2980: 2976: 2975: 2972: 2969: 2964: 2960: 2959: 2956: 2953: 2950: 2903: 2900: 2898: 2895: 2877: 2874: 2871: 2868: 2862: 2858: 2851: 2848: 2845: 2839: 2835: 2829: 2821: 2818: 2815: 2812: 2806: 2802: 2795: 2792: 2789: 2783: 2779: 2773: 2768: 2765: 2762: 2758: 2730: 2727: 2724: 2721: 2715: 2711: 2704: 2701: 2698: 2692: 2688: 2682: 2674: 2671: 2668: 2665: 2659: 2655: 2648: 2645: 2642: 2636: 2632: 2603: 2599: 2591: 2588: 2585: 2582: 2576: 2572: 2565: 2562: 2559: 2553: 2549: 2542: 2537: 2533: 2508: 2504: 2496: 2493: 2490: 2487: 2481: 2477: 2470: 2467: 2464: 2458: 2454: 2447: 2442: 2438: 2410: 2402: 2397: 2390: 2387: 2384: 2381: 2370: 2364: 2361: 2358: 2347: 2341: 2336: 2331: 2326: 2319: 2316: 2313: 2310: 2299: 2293: 2290: 2287: 2276: 2270: 2261: 2256: 2249: 2246: 2243: 2240: 2229: 2223: 2220: 2217: 2206: 2200: 2195: 2190: 2185: 2178: 2175: 2172: 2169: 2158: 2152: 2149: 2146: 2135: 2129: 2121: 2118: 2115: 2112: 2109: 2106: 2103: 2100: 2080: 2077: 2074: 2071: 2068: 2065: 2025: 2022: 2019: 2016: 2013: 2007: 2003: 1996: 1993: 1990: 1987: 1981: 1977: 1971: 1963: 1960: 1957: 1954: 1951: 1945: 1941: 1934: 1931: 1928: 1925: 1919: 1915: 1884: 1881: 1878: 1875: 1872: 1866: 1862: 1856: 1852: 1843: 1840: 1837: 1834: 1828: 1824: 1817: 1814: 1811: 1805: 1801: 1794: 1785: 1782: 1779: 1776: 1773: 1767: 1763: 1757: 1753: 1744: 1741: 1738: 1735: 1729: 1725: 1718: 1715: 1712: 1706: 1702: 1671: 1668: 1665: 1662: 1659: 1653: 1649: 1643: 1639: 1633: 1628: 1624: 1620: 1612: 1609: 1606: 1603: 1600: 1594: 1590: 1584: 1580: 1574: 1569: 1565: 1542: 1538: 1517: 1495: 1491: 1468: 1464: 1443: 1437: 1434: 1431: 1428: 1425: 1420: 1416: 1413: 1387: 1383: 1375: 1372: 1369: 1366: 1360: 1356: 1349: 1346: 1343: 1337: 1333: 1326: 1321: 1317: 1304: 1300: 1284: 1280: 1272: 1269: 1266: 1263: 1257: 1253: 1246: 1243: 1240: 1234: 1230: 1223: 1218: 1214: 1191: 1187: 1164: 1160: 1148: 1147: 1144: 1141: 1133: 1130: 1092: 1089: 1041: 1036: 1033: 1029: 1028: 1019: 1016: 1013: 1004: 1001: 968: 965: 949:Einstein, 1922 946: 930:Einstein, 1911 927: 907:Einstein, 1907 904: 882:equivalence". 864:experimentally 850: 847: 831: 830: 804: 801: 771: 770: 768: 767: 760: 753: 745: 742: 741: 740: 739: 726: 709: 708: 705: 704: 697: 692: 687: 682: 677: 672: 667: 662: 657: 652: 647: 642: 637: 632: 627: 622: 617: 612: 607: 602: 597: 592: 587: 582: 577: 572: 567: 562: 557: 552: 547: 542: 537: 531: 527: 526: 525: 522: 521: 518: 517: 512: 507: 502: 497: 492: 487: 482: 477: 472: 467: 462: 457: 452: 447: 442: 437: 432: 421: 415: 414: 413: 410: 409: 404: 403: 402: 401: 396: 388: 387: 383: 382: 381: 380: 378:Post-Newtonian 375: 370: 362: 361: 357: 356: 355: 354: 349: 344: 339: 334: 329: 321: 320: 314: 310: 309: 306: 302: 301: 300: 299: 296: 295: 290: 289: 288: 287: 282: 277: 269: 268: 262: 261: 260: 259: 254: 249: 244: 239: 237:Frame-dragging 234: 229: 224: 219: 214: 212:Kepler problem 204: 200: 199: 198: 195: 194: 191: 190: 185: 180: 175: 169: 165: 164: 163: 160: 159: 158: 157: 152: 150: 149: 144: 139: 133: 131: 123: 122: 108: 105: 101: 96: 92: 87: 84: 80: 76: 73: 68: 65: 61: 51: 43: 42: 15: 9: 6: 4: 3: 2: 7633: 7622: 7619: 7617: 7614: 7612: 7609: 7607: 7604: 7602: 7599: 7597: 7594: 7593: 7591: 7578: 7568: 7562: 7561: 7557: 7555: 7552: 7550: 7547: 7545: 7542: 7540: 7537: 7535: 7532: 7530: 7527: 7525: 7522: 7520: 7517: 7515: 7512: 7510: 7507: 7505: 7502: 7500: 7497: 7495: 7492: 7490: 7487: 7485: 7482: 7480: 7477: 7475: 7472: 7470: 7469:Chandrasekhar 7467: 7465: 7462: 7460: 7457: 7455: 7452: 7450: 7447: 7445: 7442: 7440: 7437: 7435: 7432: 7430: 7429:Schwarzschild 7427: 7425: 7422: 7420: 7417: 7415: 7412: 7410: 7407: 7406: 7404: 7400: 7390: 7386: 7385: 7382: 7379: 7377: 7374: 7372: 7368: 7367: 7364: 7361: 7359: 7356: 7354: 7351: 7349: 7346: 7343: 7339: 7335: 7334: 7331: 7328: 7325: 7322: 7320: 7316: 7315:Schwarzschild 7312: 7311: 7308: 7305: 7303: 7300: 7298: 7295: 7293: 7290: 7288: 7285: 7282: 7278: 7274: 7273: 7271: 7269: 7265: 7259: 7256: 7254: 7251: 7249: 7246: 7245: 7243: 7237: 7231: 7228: 7225: 7221: 7217: 7214: 7212: 7211:Shapiro delay 7209: 7207: 7204: 7201: 7197: 7193: 7190: 7187: 7183: 7180: 7179: 7176: 7173: 7170: 7167: 7165: 7162: 7160: 7157: 7155: 7154:collaboration 7151: 7147: 7144: 7142: 7138: 7135: 7134: 7131: 7128: 7126: 7123: 7121: 7120:Event horizon 7118: 7116: 7113: 7112: 7110: 7106: 7100: 7097: 7095: 7092: 7090: 7087: 7085: 7082: 7080: 7077: 7075: 7072: 7070: 7067: 7065: 7064:ADM formalism 7062: 7061: 7059: 7055: 7049: 7046: 7044: 7041: 7039: 7036: 7034: 7031: 7029: 7026: 7025: 7023: 7017: 7011: 7008: 7006: 7003: 7002: 7000: 6996: 6993: 6991: 6985: 6975: 6972: 6970: 6969:Biquaternions 6967: 6965: 6962: 6960: 6957: 6955: 6952: 6951: 6949: 6947: 6943: 6937: 6934: 6932: 6929: 6927: 6924: 6922: 6919: 6917: 6914: 6912: 6909: 6907: 6904: 6902: 6899: 6897: 6896:Time dilation 6894: 6893: 6891: 6887: 6881: 6878: 6877: 6875: 6871: 6865: 6862: 6860: 6857: 6855: 6852: 6850: 6849:Proper length 6847: 6845: 6842: 6840: 6837: 6835: 6832: 6830: 6827: 6825: 6822: 6821: 6819: 6813: 6807: 6804: 6802: 6799: 6796: 6793: 6791: 6787: 6784: 6783: 6781: 6777: 6774: 6772: 6766: 6762: 6755: 6750: 6748: 6743: 6741: 6736: 6735: 6732: 6720: 6719: 6710: 6709: 6706: 6700: 6697: 6695: 6692: 6690: 6687: 6685: 6682: 6680: 6677: 6675: 6672: 6670: 6667: 6665: 6662: 6660: 6657: 6655: 6652: 6650: 6647: 6645: 6642: 6640: 6637: 6635: 6632: 6630: 6627: 6626: 6624: 6620: 6613: 6610: 6607: 6604: 6601: 6598: 6595: 6592: 6589: 6586: 6583: 6580: 6577: 6576:Maja Einstein 6574: 6571: 6568: 6565: 6562: 6559: 6556: 6553: 6550: 6547: 6546:Elsa Einstein 6544: 6541: 6538: 6537: 6535: 6533: 6529: 6523: 6522: 6518: 6516: 6515: 6511: 6509: 6508: 6504: 6502: 6501: 6497: 6495: 6494: 6490: 6488: 6487: 6483: 6481: 6480: 6476: 6474: 6473: 6469: 6468: 6466: 6460: 6454: 6451: 6449: 6446: 6444: 6441: 6439: 6436: 6434: 6433:Kalinga Prize 6431: 6429: 6426: 6424: 6421: 6420: 6418: 6414: 6407: 6406: 6402: 6400:(2017 series) 6399: 6398: 6394: 6391: 6390: 6386: 6383: 6382: 6378: 6375: 6374: 6370: 6367: 6366: 6362: 6359: 6358: 6354: 6351: 6350: 6346: 6343: 6342: 6338: 6335: 6334: 6330: 6327: 6326: 6322: 6321: 6319: 6317: 6311: 6304: 6301: 6298: 6294: 6291: 6290: 6286: 6283: 6282: 6278: 6275: 6274: 6270: 6267: 6266: 6262: 6259: 6255: 6252: 6250: 6246: 6245: 6243: 6241: 6237: 6231: 6228: 6226: 6223: 6221: 6218: 6216: 6213: 6211: 6208: 6206: 6203: 6201: 6198: 6196: 6193: 6191: 6188: 6186: 6183: 6181: 6178: 6176: 6173: 6171: 6168: 6166: 6163: 6161: 6158: 6156: 6153: 6151: 6148: 6146: 6143: 6141: 6138: 6136: 6133: 6131: 6128: 6126: 6123: 6121: 6118: 6116: 6113: 6109: 6106: 6104: 6101: 6100: 6099: 6096: 6095: 6093: 6089: 6085: 6078: 6073: 6071: 6066: 6064: 6059: 6058: 6055: 6049: 6046: 6043: 6040: 6037: 6034: 6031: 6028: 6026: 6023: 6022: 6012: 6008: 6005: 6001: 5998: 5994: 5991: 5990:0-393-96501-5 5987: 5983: 5979: 5976: 5972: 5969: 5965: 5962: 5959: 5955: 5954: 5941: 5937: 5933: 5929: 5925: 5921: 5917: 5913: 5908: 5903: 5899: 5895: 5891: 5884: 5876: 5872: 5866: 5858: 5854: 5850: 5846: 5842: 5838: 5834: 5830: 5825: 5820: 5816: 5812: 5808: 5802: 5794: 5790: 5786: 5782: 5778: 5774: 5770: 5766: 5761: 5756: 5752: 5748: 5744: 5737: 5729: 5725: 5720: 5715: 5711: 5707: 5702: 5697: 5693: 5689: 5685: 5678: 5662: 5658: 5652: 5644: 5640: 5636: 5632: 5628: 5624: 5619: 5614: 5610: 5606: 5602: 5595: 5587: 5583: 5579: 5575: 5571: 5567: 5563: 5559: 5554: 5549: 5546:(9): 091301. 5545: 5541: 5533: 5525: 5521: 5517: 5513: 5509: 5505: 5501: 5497: 5492: 5487: 5483: 5479: 5475: 5468: 5460: 5456: 5452: 5448: 5444: 5440: 5435: 5430: 5426: 5422: 5415: 5413: 5403: 5398: 5393: 5388: 5384: 5380: 5377:(1): 012047. 5376: 5372: 5368: 5360: 5352: 5346: 5338: 5332: 5321: 5317: 5313: 5309: 5305: 5298: 5297: 5289: 5281: 5277: 5271: 5263: 5257: 5249: 5245: 5241: 5237: 5233: 5229: 5225: 5221: 5216: 5211: 5207: 5203: 5199: 5192: 5184: 5180: 5176: 5172: 5168: 5164: 5160: 5156: 5151: 5146: 5142: 5138: 5130: 5122: 5118: 5114: 5110: 5106: 5102: 5098: 5094: 5089: 5084: 5081:(4): 041101. 5080: 5076: 5069: 5061: 5057: 5053: 5049: 5045: 5041: 5034: 5026: 5022: 5018: 5014: 5010: 5006: 5002: 4998: 4991: 4983: 4979: 4975: 4971: 4967: 4963: 4959: 4955: 4947: 4939: 4935: 4931: 4927: 4923: 4919: 4915: 4911: 4903: 4895: 4891: 4887: 4883: 4879: 4875: 4871: 4867: 4863: 4856: 4848: 4844: 4837: 4829: 4825: 4821: 4817: 4813: 4809: 4805: 4801: 4794: 4786: 4782: 4775: 4768: 4762: 4754: 4750: 4743: 4734: 4729: 4725: 4721: 4717: 4713: 4709: 4702: 4695: 4689: 4680: 4675: 4671: 4667: 4663: 4659: 4655: 4648: 4640: 4636: 4632: 4628: 4623: 4618: 4615:(2): 022001. 4614: 4610: 4604: 4600: 4599: 4592: 4585: 4579: 4569: 4559: 4552: 4546: 4537: 4530: 4524: 4522: 4520: 4518: 4516: 4514: 4512: 4510: 4508: 4506: 4504: 4502: 4500: 4498: 4496: 4487: 4483: 4482: 4477: 4471: 4463: 4461:9781845643911 4457: 4453: 4452: 4447: 4441: 4439: 4430: 4428:9780486495422 4424: 4420: 4413: 4405: 4401: 4397: 4393: 4389: 4385: 4381: 4377: 4372: 4367: 4364:(2): 021401. 4363: 4359: 4355: 4348: 4340: 4336: 4332: 4328: 4324: 4320: 4316: 4309: 4301: 4297: 4293: 4289: 4284: 4279: 4275: 4271: 4266: 4261: 4257: 4253: 4246: 4238: 4234: 4229: 4224: 4220: 4216: 4211: 4206: 4202: 4198: 4193: 4188: 4184: 4180: 4176: 4169: 4167: 4165: 4163: 4161: 4159: 4157: 4155: 4153: 4151: 4149: 4147: 4138: 4126: 4118: 4114: 4110: 4104: 4100: 4096: 4092: 4088: 4083: 4082:gr-qc/0103067 4078: 4074: 4067: 4065: 4056: 4050: 4046: 4045: 4037: 4029: 4025: 4021: 4017: 4013: 4009: 4004: 3999: 3995: 3991: 3984: 3982: 3973: 3969: 3965: 3961: 3957: 3953: 3949: 3942: 3935: 3931: 3927: 3923: 3919: 3915: 3911: 3907: 3903: 3898: 3893: 3889: 3885: 3881: 3874: 3866: 3862: 3858: 3854: 3849: 3844: 3840: 3836: 3832: 3825: 3823: 3821: 3819: 3811: 3810: 3803: 3796: 3790: 3781: 3772: 3764: 3762:0-486-26126-3 3758: 3754: 3747: 3745: 3736: 3732: 3728: 3724: 3720: 3716: 3712: 3705: 3703: 3701: 3692: 3690:9781134449798 3686: 3682: 3677: 3676: 3667: 3665: 3660: 3650: 3647: 3645: 3642: 3640: 3637: 3635: 3632: 3630: 3627: 3625: 3622: 3620: 3617: 3615: 3612: 3610: 3607: 3606: 3599: 3597: 3593: 3589: 3585: 3581: 3577: 3572: 3570: 3566: 3562: 3557: 3555: 3551: 3546: 3544: 3529: 3526: 3523: 3520: 3516: 3513: 3512: 3508: 3505: 3502: 3500: 3497: 3496: 3492: 3489: 3486: 3483: 3480: 3479: 3475: 3472: 3469: 3466: 3465: 3459: 3457: 3454: 3449: 3447: 3443: 3440: 3439:dimensionless 3435: 3433: 3429: 3425: 3420: 3418: 3414: 3408: 3400: 3397: 3396:non-discovery 3392: 3390: 3386: 3382: 3381:scalar fields 3378: 3374: 3373:string theory 3370: 3365: 3361: 3359: 3355: 3351: 3347: 3337: 3334: 3332: 3329: 3326: 3325: 3321: 3316: 3313: 3310: 3309: 3305: 3296: 3293: 3290: 3289: 3285: 3280: 3277: 3274: 3273: 3269: 3264: 3261: 3258: 3257: 3253: 3248: 3245: 3242: 3241: 3237: 3228: 3225: 3222: 3221: 3217: 3212: 3209: 3206: 3205: 3201: 3196: 3193: 3190: 3187: 3186: 3182: 3173: 3171: 3167: 3164: 3163: 3159: 3150: 3147: 3144: 3143: 3139: 3130: 3127: 3124: 3123: 3119: 3110: 3107: 3104: 3103: 3099: 3090: 3087: 3084: 3083: 3079: 3070: 3068: 3067:Loránd Eötvös 3065: 3062: 3061: 3057: 3048: 3046: 3043: 3040: 3039: 3035: 3030: 3028: 3025: 3022: 3021: 3017: 3008: 3006: 3003: 3000: 2999: 2995: 2986: 2984: 2981: 2978: 2977: 2973: 2970: 2968: 2965: 2962: 2961: 2957: 2954: 2952:Investigator 2951: 2948: 2947: 2941: 2939: 2934: 2932: 2928: 2927:Loránd Eötvös 2924: 2921:measured the 2920: 2916: 2914: 2910: 2894: 2860: 2856: 2837: 2833: 2827: 2804: 2800: 2781: 2777: 2771: 2766: 2763: 2760: 2756: 2746: 2713: 2709: 2690: 2686: 2680: 2657: 2653: 2634: 2630: 2618: 2601: 2597: 2574: 2570: 2551: 2547: 2540: 2535: 2531: 2506: 2502: 2479: 2475: 2456: 2452: 2445: 2440: 2436: 2427: 2422: 2408: 2400: 2395: 2388: 2385: 2382: 2379: 2368: 2362: 2359: 2356: 2345: 2339: 2334: 2329: 2324: 2317: 2314: 2311: 2308: 2297: 2291: 2288: 2285: 2274: 2268: 2259: 2254: 2247: 2244: 2241: 2238: 2227: 2221: 2218: 2215: 2204: 2198: 2193: 2188: 2183: 2176: 2173: 2170: 2167: 2156: 2150: 2147: 2144: 2133: 2127: 2119: 2116: 2110: 2107: 2104: 2098: 2075: 2072: 2069: 2063: 2056: 2052: 2050: 2044: 2041: 2005: 2001: 1979: 1975: 1969: 1943: 1939: 1917: 1913: 1901: 1864: 1860: 1854: 1850: 1826: 1822: 1803: 1799: 1792: 1765: 1761: 1755: 1751: 1727: 1723: 1704: 1700: 1687: 1651: 1647: 1641: 1637: 1631: 1626: 1622: 1618: 1592: 1588: 1582: 1578: 1572: 1567: 1563: 1540: 1536: 1515: 1493: 1489: 1466: 1462: 1441: 1418: 1414: 1411: 1402: 1385: 1381: 1358: 1354: 1335: 1331: 1324: 1319: 1315: 1282: 1278: 1255: 1251: 1232: 1228: 1221: 1216: 1212: 1189: 1185: 1162: 1158: 1145: 1142: 1139: 1138: 1137: 1129: 1127: 1123: 1119: 1114: 1109: 1107: 1103: 1099: 1088: 1084: 1081: 1076: 1074: 1070: 1066: 1061: 1059: 1055: 1051: 1045: 1040: 1032: 1026: 1025: 1020: 1017: 1014: 1011: 1010: 1009: 1000: 994: 990: 964: 961: 957: 945: 940: 938: 926: 921: 919: 915: 903: 901: 895: 892: 888: 883: 879: 877: 873: 869: 865: 861: 856: 846: 844: 840: 835: 829: 825: 821: 817: 816:inertial mass 814: 813: 812: 810: 800: 798: 794: 790: 786: 785:inertial mass 782: 781:gravitational 778: 766: 761: 759: 754: 752: 747: 746: 744: 743: 737: 727: 724: 719: 713: 712: 711: 710: 703: 702: 698: 696: 693: 691: 688: 686: 683: 681: 678: 676: 673: 671: 668: 666: 663: 661: 658: 656: 653: 651: 648: 646: 643: 641: 640:Chandrasekhar 638: 636: 633: 631: 628: 626: 623: 621: 618: 616: 613: 611: 608: 606: 603: 601: 598: 596: 593: 591: 588: 586: 583: 581: 578: 576: 573: 571: 568: 566: 563: 561: 558: 556: 555:Schwarzschild 553: 551: 548: 546: 543: 541: 538: 536: 533: 532: 524: 523: 516: 515:Hartle–Thorne 513: 511: 508: 506: 503: 501: 498: 496: 493: 491: 488: 486: 483: 481: 478: 476: 473: 471: 468: 466: 463: 461: 458: 456: 453: 451: 448: 446: 443: 441: 438: 436: 433: 430: 426: 425:Schwarzschild 423: 422: 418: 412: 411: 400: 397: 395: 392: 391: 390: 389: 385: 384: 379: 376: 374: 371: 369: 366: 365: 364: 363: 359: 358: 353: 350: 348: 345: 343: 340: 338: 335: 333: 330: 328: 325: 324: 323: 322: 318: 317: 307: 304: 303: 298: 297: 286: 283: 281: 278: 276: 273: 272: 271: 270: 267: 264: 263: 258: 255: 253: 250: 248: 247:Event horizon 245: 243: 240: 238: 235: 233: 230: 228: 225: 223: 220: 218: 215: 213: 210: 209: 208: 207: 197: 196: 189: 186: 184: 181: 179: 176: 174: 171: 170: 162: 161: 156: 153: 148: 145: 143: 140: 138: 135: 134: 132: 130: 127: 126: 125: 124: 106: 103: 99: 94: 90: 85: 82: 78: 71: 66: 63: 59: 49: 45: 44: 41: 38: 37: 30: 26: 22: 7616:Acceleration 7559: 7253:Kaluza–Klein 7027: 7005:Introduction 6931:Twin paradox 6716: 6684:Einsteinhaus 6564:Pauline Koch 6542:(first wife) 6540:Mileva Marić 6519: 6512: 6505: 6498: 6491: 6484: 6477: 6470: 6403: 6395: 6387: 6379: 6371: 6363: 6355: 6347: 6339: 6331: 6323: 6287: 6279: 6271: 6263: 6248: 6139: 6038:at MathPages 6010: 6003: 5996: 5981: 5974: 5967: 5960: 5957: 5897: 5893: 5883: 5874: 5865: 5814: 5810: 5801: 5750: 5746: 5736: 5691: 5687: 5677: 5665:. 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4396:0031-9007 4278:CiteSeerX 4219:2367-3613 4192:1403.7377 4135:ignored ( 4125:cite book 4003:1207.2442 3930:119110646 3922:0002-9505 3897:1310.7426 3848:1106.2476 3584:ephemeris 3484:constant 3467:Constant 3192:Braginsky 3140:Pendulum 3100:Pendulum 3058:Pendulum 3036:Pendulum 2828:− 2194:− 2099:η 2064:η 1073:geodesics 989:Apollo 15 839:invariant 791:requires 620:Robertson 585:Friedmann 580:Eddington 570:Nordström 560:de Sitter 417:Solutions 342:Geodesics 337:Friedmann 319:Equations 305:Equations 266:Spacetime 201:Phenomena 107:ν 104:μ 95:κ 86:ν 83:μ 75:Λ 67:ν 64:μ 7577:Category 7454:Lemaître 7419:Einstein 7409:Poincaré 7369:Others: 7353:Taub–NUT 7319:interior 7241:theories 7239:Advanced 7206:redshift 7021:concepts 6839:Rapidity 6817:concepts 6718:Category 6644:Memorial 6590:(cousin) 6578:(sister) 6572:(father) 6566:(mother) 6464:Einstein 6299:" (1949) 6260:" (1905) 5857:49578025 5849:29973733 5785:24390352 5586:40461557 5578:11531558 5240:36179190 5175:29286705 5121:18653407 5113:18352252 4982:10012726 4938:10040283 4894:10035824 4486:Archived 4404:37505941 4300:15007947 4237:28179848 4185:(1): 4. 4117:15430387 4028:59141292 3602:See also 3567:and two 3527:quasars 3515:electron 3371:such as 3194:, Panov 2971:"small" 1124:and the 1027:, 1687). 947:— 944:gravity. 928:— 905:— 736:Category 600:Lemaître 565:Reissner 550:Poincaré 535:Einstein 480:Taub–NUT 445:Wormhole 429:interior 142:Timeline 7519:Hawking 7514:Penrose 7499:Novikov 7479:Wheeler 7424:Hilbert 7414:Lorentz 7371:pp-wave 7192:lensing 6988:General 6769:Special 6622:Related 6316:culture 6091:Physics 5958:Science 5912:Bibcode 5900:: A24. 5829:Bibcode 5793:4468698 5765:Bibcode 5706:Bibcode 5643:9280269 5623:Bibcode 5558:Bibcode 5496:Bibcode 5459:8019480 5439:Bibcode 5379:Bibcode 5304:Bibcode 5220:Bibcode 5183:6211162 5155:Bibcode 5093:Bibcode 5048:Bibcode 5005:Bibcode 4962:Bibcode 4918:Bibcode 4874:Bibcode 4812:Bibcode 4720:Bibcode 4666:Bibcode 4627:Bibcode 4481:YouTube 4376:Bibcode 4327:Bibcode 4270:Bibcode 4228:5255900 4197:Bibcode 4087:Bibcode 4008:Bibcode 3960:Bibcode 3902:Bibcode 3853:Bibcode 3723:Bibcode 3473:Method 3446:quasars 3352:in the 3148:Renner 3128:Potter 3108:Zeeman 2958:Method 1689:Hence: 870:due to 860:Galileo 849:History 803:Concept 655:Hawking 650:Penrose 625:Bardeen 615:Wheeler 545:Hilbert 540:Lorentz 500:pp-wave 137:History 7560:others 7549:Thorne 7539:Misner 7524:Taylor 7509:Geroch 7504:Ehlers 7474:Zwicky 7292:Kasner 6532:Family 6416:Prizes 6397:Genius 6305:(1955) 6292:(1938) 6284:(1934) 6276:(1922) 6268:(1916) 6253:(1905) 6251:papers 5988: 5938: 5930: 5855: 5847: 5811:Nature 5791: 5783: 5747:Nature 5726: 5641: 5584: 5576: 5522: 5514: 5457: 5246: 5238: 5181: 5173: 5119: 5111: 5023: 4980: 4936: 4892: 4849:: 579. 4787:: 873. 4755:: 569. 4458: 4425: 4402: 4394: 4298: 4280: 4235: 4225: 4217: 4115: 4105: 4051: 4026: 3928: 3920: 3759: 3687: 3594:, and 3561:pulsar 3519:proton 3001:1590? 2923:period 2049:Eötvös 1113:metric 1056:. 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