Equivalence Principle
Equivalence Principle
Equivalence Principle
In the physics of general relativity, the equivalence principle is any of several related concepts dealing with the equivalence of gravitational and inertial mass, and to Albert Einstein's observation that the gravitational "force" as experienced locally while standing on a massive body (such as the Earth) is actually the same as the pseudo-force experienced by an observer in a non-inertial (accelerated) frame of reference.
Contents
1 Einstein's statement of the equivalence principle 2 Development of gravitation theory 3 Modern usage 3.1 The weak equivalence principle 3.1.1 Active, passive, and inertial masses 3.1.2 Tests of the weak equivalence principle 3.2 The Einstein equivalence principle 3.2.1 Tests of the Einstein equivalence principle 3.3 The strong equivalence principle 3.3.1 Tests of the strong equivalence principle 4 Challenges to the equivalence principle 5 Explanations of the equivalence principle 6 Experiments 7 See also 8 Notes 9 References 10 External links
It is only when there is numerical equality between the inertial and gravitational mass that the acceleration is independent of the nature of the body. Albert Einstein, [1]
As long as we restrict ourselves to purely mechanical processes in the realm where Newton's mechanics holds sway, we are certain of the equivalence of the systems K and K'. But this view of ours will not have any deeper significance unless the systems K and K' are equivalent with respect to all physical processes, that is, unless the laws of nature with respect to K are in entire agreement with those with respect to K'. By assuming this to be so, we arrive at a principle which, if it is really true, has great heuristic importance. For by theoretical consideration of processes which take place relatively to a system of reference with uniform acceleration, we obtain information as to the career of processes in a homogeneous gravitational field. Einstein, 1911 Einstein combined (postulated) the equivalence principle with special relativity to predict that clocks run at different rates in a gravitational potential, and light rays bend in a gravitational field, even before he developed the concept of curved spacetime. So the original equivalence principle, as described by Einstein, concluded that free-fall and inertial motion were physically equivalent. This form of the equivalence principle can be stated as follows. 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 1g. This is not strictly true, because massive bodies give rise to tidal effects (caused by variations in the strength and direction of the gravitational field) which are absent from an accelerating spaceship in deep space. Although the equivalence principle guided the development of general relativity, it is not a founding principle of relativity but rather a simple consequence of the geometrical nature of the theory. In general relativity, objects in free-fall follow geodesics of spacetime, and what we perceive as the force of gravity is instead a result of our being unable to follow those geodesics of spacetime, because the mechanical resistance of matter prevents us from doing so. 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 special relativity. This was developed by Robert Dicke 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. They only differ in whether or not they apply to gravitational experiments.
Modern usage
Three forms of the equivalence principle are in current use: weak (Galilean), Einsteinian, and strong.
independent of their properties, including their rest mass.[5] All local centers of mass vacuum free fall along identical (parallel-displaced, same speed) minimum action trajectories independent of all observable properties. The vacuum world line of a body immersed in a gravitational field is independent of all observable properties. The local effects of motion in a curved space (gravitation) are indistinguishable from those of an accelerated observer in flat space, without exception. 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 Philosophi Naturalis Principia Mathematica, 1687). Locality eliminates measurable tidal forces originating from a radial divergent gravitational field (e.g., the Earth) upon finite sized physical bodies. The "falling" equivalence principle embraces Galileo's, Newton's, and Einstein's conceptualization. The equivalence principle does not deny the existence of measurable effects caused by a rotating gravitating mass (frame dragging), or bear on the measurements of light deflection and gravitational time delay made by non-local observers. Active, passive, and inertial masses By definition of active and passive gravitational mass, the force on due to the gravitational field of is:
Likewise the force on a second object of arbitrary mass2 due to the gravitational field of mass0 is:
If and are the same distance (i.e. their accelerations are the same)
from
then, by the weak equivalence principle, they fall at the same rate
Hence:
Therefore:
In other words, passive gravitational mass must be proportional to inertial mass for all objects. Furthermore by Newton's third law of motion:
It follows that:
In other words, passive gravitational mass must be proportional to active gravitational mass for all objects. The dimensionless Etvs-parameter 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."
Tests of the weak equivalence principle Tests of the weak equivalence principle are those that verify the equivalence of gravitational mass and inertial mass. An obvious test is dropping two contrasted objects in hard vacuum, e.g., inside Fallturm Bremen. Researcher Year John Philoponus Simon Stevin[6] Galileo Galilei Isaac Method Result
6th Described correctly the effect of no detectable difference century dropping balls of different masses ~1586 Dropped lead balls of different masses off the Delft churchtower no detectable difference
~1610 Rolling balls down inclined planes no detectable difference measure the period of pendulums ~1680 of different mass but identical no measurable difference
no measurable difference
measure the period of pendulums of different mass but identical no measurable difference length measure the torsion on a wire, suspending a balance beam, between two nearly identical masses under the acceleration of gravity and the rotation of the Earth Torsion balance experiment, dropping aluminum and gold test masses Dropped a falcon feather and a hammer at the same time on the Moon Torsion balance, aluminum and platinum test masses, measuring acceleration towards the sun
Lornd Etvs
1908
[7]
no detectable difference (not a rigorous experiment, but very dramatic being the first lunar one[8]) difference is less than 1 part in 1012
1971
Et-Wash group
Torsion balance, measuring acceleration of different masses 1987 towards the earth, sun and galactic center, using several different kinds of masses
[9][10]
See:[11] Year 500? 1585 1590? 1686 1832 1910 1918 1922 1923 1935 Investigator Philoponus [12] Stevin [13] Galileo [14] Newton [15] Bessel [16] Southerns [17] Zeeman [18] Etvs [19] Potter [20] Renner [21] Sensitivity Method "small" 510-2 210-2 10-3 210-5 510-6 310-8 510-9 310-6 210-9 Drop Tower Drop Tower Pendulum, Drop Tower Pendulum Pendulum Pendulum Torsion Balance Torsion Balance Pendulum Torsion Balance
Dicke,Roll,Krotkov [22] Braginsky,Panov [23] Shapiro, et al.[24] Keiser,Faller [25] Niebauer, et al.[26] Heckel, et al.[27] Adelberger, et al.[28] Baessler, et al.[29]
3x10-11 10-12 10-12 410-11 10-10 10-11 10-12 5x10-14 10-17 10-16 210-17
Torsion Balance Torsion Balance Lunar Laser Ranging Fluid Support Drop Tower Torsion Balance Torsion Balance Torsion Balance Earth Orbit Earth Orbit vacuum free fall
Experiments are still being performed at the University of Washington which have placed limits on the differential acceleration of objects towards the Earth, the sun and towards dark matter in the galactic center. Future satellite experiments[31] STEP (Satellite Test of the Equivalence Principle), Galileo Galilei, and MICROSCOPE (MICROSatellite pour l'Observation de Principe d'Equivalence) will test the weak equivalence principle in space, to much higher accuracy. The need to continue testing Einstein's theory of gravity may seem superfluous, as the theory is elegant and is compatible with observations. However, no quantum theory of gravity is known, and most suggestions violate one of the equivalence principles at some level. String theory, supergravity and even quintessence, for example, seem to violate the weak equivalence principle because they contain many light scalar fields with long Compton wavelengths. These fields should generate fifth forces and variation of the fundamental constants. There are a number of mechanisms that have been suggested by physicists to reduce these violations of the equivalence principle to below observable levels.
values such as the fine-structure constant and electron-to-proton mass ratio must not depend on where in space or time we measure them. Many physicists believe that any Lorentz invariant theory that satisfies the weak equivalence principle also satisfies the Einstein equivalence principle. Schiff's conjecture suggests that the weak equivalence principle actually implies the Einstein equivalence principle, but it has not been proven. Nonetheless, the two principles are tested with very different kinds of experiments. 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[33] and Durand[34]). Tests of the Einstein equivalence principle In addition to the tests of the weak equivalence principle, the Einstein equivalence principle can be tested by searching for variation of dimensionless constants and mass ratios. The present best limits on the variation of the fundamental constants have mainly been set by studying the naturally occurring Oklo natural nuclear fission reactor, 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. Constant fine structure constant weak interaction constant Year Method 1976 Oklo 1976 Oklo Limit on fractional change 107 102 104
proton gyromagnetic factor 1976 astrophysical 101 There have been a number of controversial attempts to constrain the variation of the strong interaction constant. There have been several suggestions that "constants" do vary on cosmological scales. The best known is the reported detection of variation (at the 105 level) of the fine-structure constant from measurements of distant quasars, see Webb et al.[35] Other researchers dispute these findings. Other tests of the Einstein equivalence principle are gravitational redshift experiments, such as the Pound-Rebka experiment which test the position independence of experiments.
themselves, such as stars, planets, black holes or Cavendish experiments. The second part is the Einstein equivalence principle (with the same definition of "local"), restated to allow gravitational experiments and selfgravitating bodies. The freely-falling object or laboratory, however, must still be small, so that tidal forces may be neglected (hence "local experiment"). This is the only form of the equivalence principle that applies to self-gravitating objects (such as stars), which have substantial internal gravitational interactions. It requires that the gravitational constant be the same everywhere in the universe and is incompatible with a fifth force. It is much more restrictive than the Einstein equivalence principle. The strong equivalence principle suggests that gravity is entirely geometrical by nature (that is, the metric alone determines the effect of gravity) and does not have any extra fields associated with it. 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 cosmological constant) is thought to be the only theory of gravity that satisfies the strong equivalence principle. A number of alternative theories, such as Brans-Dicke theory, satisfy only the Einstein equivalence principle. Tests of the strong equivalence principle The strong equivalence principle can be tested by searching for a variation of Newton's gravitational constant G over the life of the universe, or equivalently, variation in the masses of the fundamental particles. A number of independent constraints, from orbits in the solar system and studies of big bang nucleosynthesis have shown that G cannot have varied by more than 10%. Thus, the strong equivalence principle can be tested by searching for fifth forces (deviations from the gravitational force-law predicted by general relativity). These experiments typically look for failures of the inverse-square law (specifically Yukawa forces or failures of Birkhoff's theorem) behavior of gravity in the laboratory. The most accurate tests over short distances have been performed by the Et-Wash group. A future satellite experiment, SEE (Satellite Energy Exchange), will search for fifth forces in space and should be able to further constrain violations of the strong equivalence principle. Other limits, looking for much longer-range forces, have been placed by searching for the Nordtvedt effect, a "polarization" of solar system orbits that would be caused by gravitational self-energy accelerating at a different rate from normal matter. This effect has been sensitively tested by the Lunar Laser Ranging Experiment. Other tests include studying the deflection of radiation from distant radio sources by the sun, which can be accurately measured by very long baseline interferometry. Another sensitive test comes from measurements of the frequency shift of signals to and from the Cassini spacecraft. Together, these measurements have put tight limits on Brans-Dicke theory and other alternative theories of gravity.
fraction."
Experiments
University of Washington[38] Lunar Laser Ranging[39] Galileo-Galilei satellite experiment[40] Satellite Test of the Equivalence Principle (STEP)[41] MICROSCOPE[42] Satellite Energy Exchange (SEE)[43] "...Physicists in Germany have used an atomic interferometer to perform the most accurate ever test of the equivalence principle at the level of atoms..."[44]
See also
General Relativity General covariance Classical Mechanics Frame of reference Inertial frame of reference Mach's principle Equivalence principle (geometric) Brans-Dicke theory Gauge gravitation theory Self-creation cosmology Fredkin Finite Nature Hypothesis Tests of general relativity Unsolved problems in astronomy Unsolved problems in physics
Notes
1. ^ A. Einstein. How I Constructed the Theory of Relativity, 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 talk in Japan on 14 December 1922. 2. ^ Alan Macdonald (September 15, 2012). "General Relativity in a Nutshell" (http://faculty.luther.edu/~macdonal/EGR.pdf). Luther College. p. 32. Retrieved February 8, 2013. 3. ^ TA Wagner, S Schalmminger, JH Gundlach, EG Adelberger, "Torsion-balance tests of the weak equivalence principle", Class. Quantum Grav. 29, 184002 (2012); http://arXiv.org/abs/1207.2442 4. ^ J Champion, SM Ransom, P Lazarus, F Camilo, et al., Science 320(5881), 1309 (2008), http://arXiv.org/abs/0805.2396 5. ^ Paul S Wesson (2006). Five-dimensional Physics (http://books.google.com/?
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32.
id=dSv8ksxHR0oC&printsec=frontcover&dq=intitle:Five+intitle:Dimensional+intitle:Physics). World Scientific. p. 82. ISBN 981-256-661-9. ^ T. Devreese, Jozef; Vanden Berghe, Guido (2008). 'Magic Is No Magic': The Wonderful World of Simon Stevin (http://books.google.co.kr/books?isbn=1845643917). p. 154. ISBN 9781845643911. ^ P. G. Roll, R. Krotkov, R. H. Dicke, The equivalence of inertial and passive gravitational mass, Annals of Physics, Volume 26, Issue 3, 20 February 1964, Pages 442-517 ^ http://www.youtube.com/watch?v=MJyUDpm9Kvk ^ Schlamminger, S.; Choi, K.-Y.; Wagner, T.; Gundlach, J.; Adelberger, E. (2008). "Test of the Equivalence Principle Using a Rotating Torsion Balance". Physical Review Letters 100 (4). arXiv:0712.0607 (http://arxiv.org/abs/0712.0607). Bibcode:2008PhRvL.100d1101S (http://adsabs.harvard.edu/abs/2008PhRvL.100d1101S). doi:10.1103/PhysRevLett.100.041101 (http://dx.doi.org/10.1103%2FPhysRevLett.100.041101). ^ Schlamminger; Choi; Wagner; Gundlach; Adelberger (2007). "Test of the Equivalence Principle Using a Rotating Torsion Balance". Phys.Rev.Lett. 100 (4). arXiv:0712.0607 (http://arxiv.org/abs/0712.0607). Bibcode:2008PhRvL.100d1101S (http://adsabs.harvard.edu/abs/2008PhRvL.100d1101S). doi:10.1103/PhysRevLett.100.041101 (http://dx.doi.org/10.1103%2FPhysRevLett.100.041101). ^ Ciufolini & Wheeler, "Gravitation and Inertia" (Princeton University Press: Princeton, 1995) pp. 117-119 ^ Philoponus, J. "Corollaries on Place and Void" David Furley trans. (Ithaca, NY: Cornell University Press, 1987) ^ Stevin, Simon. De Beghinselen der Weeghconst "Principles of the Art of Weighing" (Leyden, 1586); Dijksterhuis, EJ. "The Principal Works of Simon Stevin" (Amsterdam 1955) ^ Galilei, Galileo. "Discorsi e Dimostrazioni Matematiche Intorno a Due Nuove Scienze" (Appresso gli Elsevirii, Leida: 1638); "Discourses and Mathematical Demonstrations Concerning Two New Sciences," (Elsevier Press, Leiden: Netherlands, 1638) ^ Newton, Isaac. "Philosophiae Naturalis Principia Mathematica" (Mathematical Principles of Natural Philosophy and his System of the World), trans. by A. Motte and revised by F. Cajori (University of California Press: Berkeley, 1934); Newton, Isaac "The Principia: Mathematical Principles of Natural Philosophy" Trans. I. Bernard Cohen and Anne Whitman, with the assistance of Julia Budenz (University of California Press: Berkeley, 1999) ^ Ann. Physik und Chemie (Poggendorff) 25 401 (1832) ^ Proc. Roy. Soc. Lond. 84 325 (1910) ^ Proc. K. Akad. Amsterdam 20(4) 542 (1918) ^ Math. Naturw. Ber. aus. Ungarn 8 65 (1889); Ann. Physik (Leipzig) 68 11 (1922); Phys. Rev. D 61(2) 022001 (1999) ^ Proc. Roy. Soc. Lond. 104 588 (1923) ^ s Termszettudomnyi rtesit 53 569 (1935) ^ Ann. Phys. (NY) 26 442 (1964) ^ Zh. Eksp. Teor. Fiz. 61 873 (1971) ^ Phys. Rev. Lett. 36 555 (1976) ^ Bull. Am. Phys. Soc. 24 579 (1979) ^ Phys. Rev. Lett. 59 609 (1987) ^ Phys. Rev. Lett. 62 609 (1989) ^ Phys. Rev. D 42 3267 (1990) ^ Class. Quantum. Grav. 18(13) 2393 (2001); Phys.Rev. Lett 83(18) 3585 (1999) ^ http://arxiv.org/abs/1206.0028 , Class. Quantum Grav. 27, 095005 (2010); http://www.cfa.harvard.edu/PAG/6%2520Presentations/Reasenberg_Q2C3_web.pdf ^ Dittus, H; C. Lmmerzahl. "Experimental Tests of the Equivalence Principle and Newtons Law in Space" (http://www.zarm.uni-bremen.de/2forschung/gravi/publications/papers/2005DittusLaemmerzahl.pdf) (PDF). GRAVITATION AND COSMOLOGY: 2nd Mexican Meeting on Mathematical and Experimental Physics. AIP Conference Proceedings 758: 95. Bibcode:2005AIPC..758...95D (http://adsabs.harvard.edu/abs/2005AIPC..758...95D). doi:10.1063/1.1900510 (http://dx.doi.org/10.1063%2F1.1900510). ^ Haugen, Mark P.; C. Lmmerzahl (2001). Principles of Equivalence: Their Role in Gravitation Physics and Experiments that Test Them. Springer. arXiv:gr-qc/0103067 (http://arxiv.org/abs/gr-qc/0103067). ISBN 978-3-
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Experiments that Test Them. Springer. arXiv:gr-qc/0103067 (http://arxiv.org/abs/gr-qc/0103067). ISBN 978-3540-41236-6. ^ Hadley (1997). "The Logic of Quantum Mechanics Derived from Classical General Relativity". Found.Phys.Lett. 10: 4360. arXiv:quant-ph/9706018 (http://arxiv.org/abs/quant-ph/9706018). Bibcode:1997FoPhL..10...43H (http://adsabs.harvard.edu/abs/1997FoPhL..10...43H). doi:10.1007/BF02764119 (http://dx.doi.org/10.1007%2FBF02764119). ^ http://stacks.iop.org/ob/4/S351 ^ Webb; Murphy; Flambaum; Dzuba; Barrow; Churchill; Prochaska; Wolfe (2000). "Further Evidence for Cosmological Evolution of the Fine Structure Constant". Phys.Rev.Lett. 87 (9). arXiv:astro-ph/0012539 (http://arxiv.org/abs/astro-ph/0012539). Bibcode:2001PhRvL..87i1301W (http://adsabs.harvard.edu/abs/2001PhRvL..87i1301W). doi:10.1103/PhysRevLett.87.091301 (http://dx.doi.org/10.1103%2FPhysRevLett.87.091301). PMID 11531558 (//www.ncbi.nlm.nih.gov/pubmed/11531558). ^ Webb; King; Murphy; Flambaum; Carswell; Bainbridge (2010). "Evidence for spatial variation of the fine structure constant". arXiv:1008.3907 (http://arxiv.org/abs/1008.3907) [astro-ph.CO (http://arxiv.org/archive/astroph.CO)]. ^ Wright, Karen (March 01, 2001). "Very Dark Energy" (http://discovermagazine.com/2001/mar/featdark#.USwYk6XmjoI). Discover Magazine. Retrieved 26 February 2013. ^ Et-Wash group (http://www.npl.washington.edu/eotwash/) ^ http://funphysics.jpl.nasa.gov/technical/grp/lunar-laser.html ^ http://eotvos.dm.unipi.it/nobili/ ^ http://einstein.stanford.edu/STEP/ ^ http://smsc.cnes.fr/MICROSCOPE/index.htm ^ http://www.phys.utk.edu/see/ ^ 16 November 2004, physicsweb: Equivalence principle passes atomic test (http://physicsworld.com/cws/article/news/2004/nov/16/equivalence-principle-passes-atomic-test)
References
R. H. Dicke, "New Research on Old Gravitation," Science 129, 3349 (1959). This paper is the first to make the distinction between the strong and weak equivalence principles. R. H. Dicke, "Mach's Principle and Equivalence," in Evidence for gravitational theories: proceedings of course 20 of the International School of Physics "Enrico Fermi", ed C. Mller (Academic Press, New York, 1962). This article outlines the approach to precisely testing general relativity advocated by Dicke and pursued from 1959 onwards. Albert Einstein, "ber das Relativittsprinzip und die aus demselben gezogene Folgerungen," Jahrbuch der Radioaktivitaet und Elektronik 4 (1907); translated "On the relativity principle and the conclusions drawn from it," in The collected papers of Albert Einstein. Vol. 2 : The Swiss years: writings, 19001909 (Princeton University Press, Princeton, NJ, 1989), Anna Beck translator. This is Einstein's first statement of the equivalence principle. Albert Einstein, "ber den Einflu der Schwerkraft auf die Ausbreitung des Lichtes," Annalen der Physik 35 (1911); translated "On the Influence of Gravitation on the Propagation of Light" in The collected papers of Albert Einstein. Vol. 3 : The Swiss years: writings, 19091911 (Princeton University Press, Princeton, NJ, 1994), Anna Beck translator, and in The Principle of Relativity, (Dover, 1924), pp 99108, W. Perrett and G. B. Jeffery translators, ISBN 0-486-60081-5. The two Einstein papers are discussed online at The Genesis of General Relativity (http://www1.kcn.ne.jp/~h-uchii/gen.GR.html). C. Brans, "The roots of scalar-tensor theory: an approximate history", arXiv:gr-qc/0506063. Discusses the history of attempts to construct gravity theories with a scalar field and the relation to the equivalence principle and Mach's principle. C. W. Misner, K. S. Thorne and J. A. Wheeler, Gravitation, W. H. Freeman and Company, New York (1973), Chapter 16 discusses the equivalence principle. Hans Ohanian and Remo Ruffini Gravitation and Spacetime 2nd edition, Norton, New York (1994). ISBN 0-39396501-5 Chapter 1 discusses the equivalence principle, but incorrectly, according to modern usage, states that the
96501-5 Chapter 1 discusses the equivalence principle, but incorrectly, according to modern usage, states that the strong equivalence principle is wrong. J. P. Uzan, "The fundamental constants and their variation: Observational status and theoretical motivations," Rev. Mod. Phys. 75, 403 (2003). arXiv:hep-ph/0205340 This technical article reviews the best constraints on the variation of the fundamental constants. C. M. Will, Theory and experiment in gravitational physics, Cambridge University Press, Cambridge (1993). This is the standard technical reference for tests of general relativity. C. M. Will, Was Einstein Right?: Putting General Relativity to the Test, Basic Books (1993). This is a popular account of tests of general relativity. C. M. Will, The Confrontation between General Relativity and Experiment, (http://www.livingreviews.org/lrr2006-3) Living Reviews in Relativity (2006). An online, technical review, covering much of the material in Theory and experiment in gravitational physics. The Einstein and strong variants of the equivalence principles are discussed in sections 2.1 (http://relativity.livingreviews.org/open?pubNo=lrr-2006-3&page=articlesu1.html) and 3.1 (http://relativity.livingreviews.org/open?pubNo=lrr-2006-3&page=articlesu4.html), respectively. Michael Friedman, Foundations of Space-Time Theories, Princeton University Press, Princeton (1983). Chapter V discusses the equivalence principle.
External links
Equivalence Principle (http://science.nasa.gov/headlines/y2007/18may_equivalenceprinciple.htm) at NASA, including tests Introducing The Einstein Principle of Equivalence (http://www.phy.syr.edu/courses/modules/LIGHTCONE/equivalence.html) from Syracuse University The Equivalence Principle (http://www.mathpages.com/rr/s5-06/5-06.htm) at MathPages The Einstein Equivalence Principle (http://emis.math.ecnu.edu.cn/journals/LRG/Articles/lrr-20014/node3.html) at Living Reviews on General Relativity http://cafe.daum.net/grelativitycosmology Retrieved from "http://en.wikipedia.org/w/index.php?title=Equivalence_principle&oldid=569047875" Categories: Concepts in physics General relativity Albert Einstein Principles This page was last modified on 18 August 2013 at 08:16. Text is available under the Creative Commons Attribution-ShareAlike License; additional terms may apply. By using this site, you agree to the Terms of Use and Privacy Policy. Wikipedia is a registered trademark of the Wikimedia Foundation, Inc., a non-profit organization.