Equivalence principleFrom Wikipedia, the free encyclopedia

In the physics of general relativity, the equivalence principle is any of several related concepts dealing with theequivalence of gravitational and inertial mass, and to Albert Einstein's observation that the gravitational "force" asexperienced locally while standing on a massive body (such as the Earth) is actually the same as the pseudo-forceexperienced by an observer in a non-inertial (accelerated) frame of reference.

Contents1 Einstein's statement of the equivalence principle2 Development of gravitation theory3 Modern usage

3.1 The weak equivalence principle3.1.1 Active, passive, and inertial masses3.1.2 Tests of the weak equivalence principle

3.2 The Einstein equivalence principle3.2.1 Tests of the Einstein equivalence principle

3.3 The strong equivalence principle3.3.1 Tests of the strong equivalence principle

4 Challenges to the equivalence principle5 Explanations of the equivalence principle6 Experiments7 See also8 Notes9 References10 External links

Einstein's statement of the equivalence principle

A little reflection will show that the law of the equality of the inertial and gravitational mass isequivalent to the assertion that the acceleration imparted to a body by a gravitational field isindependent of the nature of the body. For Newton's equation of motion in a gravitational field,written out in full, it is:

(Inertial mass) (Acceleration) (Intensity of the gravitational field) (Gravitational mass).

It is only when there is numerical equality between the inertial and gravitational mass that theacceleration is independent of the nature of the body.

— Albert Einstein, [1]

See momentum and velocity.

Development of gravitation theorySomething like the equivalence principle emerged in the late 16th and early 17th centuries, when Galileo expressedexperimentally that the acceleration of a test mass due to gravitation is independent of the amount of mass beingaccelerated. These findings led to gravitational theory, in which the inertial and gravitational masses are identical.

The equivalence principle was properly introduced by Albert Einstein in 1907, when he observed that theacceleration of bodies towards the center of the Earth at a rate of 1g (g = 9.81 m/s2 being a standard reference ofgravitational acceleration at the Earth's surface) is equivalent to the acceleration of an inertially moving body thatwould be observed on a rocket in free space being accelerated at a rate of 1g. Einstein stated it thus:

we [...] assume the complete physical equivalence of a gravitational field and a correspondingacceleration of the reference system.

—Einstein, 1907

That is, being at rest on the surface of the Earth is equivalent to being inside a spaceship (far from any sources ofgravity) that is being accelerated by its engines. From this principle, Einstein deduced that free-fall is actually inertialmotion. Objects in free-fall do not really accelerate. In an inertial frame of reference bodies (and light) obeyNewton's first law, moving at constant velocity in straight lines. Analogously, in a curved spacetime the worldline ofan inertial particle or pulse of light is as straight as possible (in space and time).[2] Such a worldline is called ageodesic. Viewed across time from the viewpoint of an observer "stationary" on the surface of a gravitating body,the geodesics appear to curve towards the body. This is why an accelerometer in free-fall doesn't register anyacceleration; there isn't any. By contrast, in Newtonian mechanics, gravity is assumed to be a force. This forcedraws objects having mass towards the center of any massive body. At the Earth's surface, the force of gravity iscounteracted by the mechanical (physical) resistance of the Earth's surface. So in Newtonian physics, a person atrest on the surface of a (non-rotating) massive object is in an inertial frame of reference. These considerationssuggest the following corollary to the equivalence principle, which Einstein formulated precisely in 1911:

Whenever an observer detects the local presence of a force that acts on all objects in directproportion to the inertial mass of each object, that observer is in an accelerated frame of reference.

Einstein also referred to two reference frames, K and K'. K is a uniform gravitational field, whereas K' has nogravitational field but is uniformly accelerated such that objects in the two frames experience identical forces:

We arrive at a very satisfactory interpretation of this law of experience, if we assume that the systemsK and K' are physically exactly equivalent, that is, if we assume that we may just as well regard thesystem K as being in a space free from gravitational fields, if we then regard K as uniformlyaccelerated. This assumption of exact physical equivalence makes it impossible for us to speak of theabsolute acceleration of the system of reference, just as the usual theory of relativity forbids us to talkof the absolute velocity of a system; and it makes the equal falling of all bodies in a gravitational fieldseem a matter of course.

—Einstein, 1911

This observation was the start of a process that culminated in general relativity. Einstein suggested that it should beelevated to the status of a general principle when constructing his theory of relativity:

As long as we restrict ourselves to purely mechanical processes in the realm where Newton'smechanics holds sway, we are certain of the equivalence of the systems K and K'. But this view ofours will not have any deeper significance unless the systems K and K' are equivalent with respect toall physical processes, that is, unless the laws of nature with respect to K are in entire agreement withthose 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 placerelatively to a system of reference with uniform acceleration, we obtain information as to the career ofprocesses in a homogeneous gravitational field.

—Einstein, 1911

Einstein combined (postulated) the equivalence principle with special relativity to predict that clocks run at differentrates in a gravitational potential, and light rays bend in a gravitational field, even before he developed the concept ofcurved spacetime.

So the original equivalence principle, as described by Einstein, concluded that free-fall and inertial motion werephysically equivalent. This form of the equivalence principle can be stated as follows. An observer in a windowlessroom cannot distinguish between being on the surface of the Earth, and being in a spaceship in deep spaceaccelerating at 1g. This is not strictly true, because massive bodies give rise to tidal effects (caused by variations inthe 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 ofrelativity but rather a simple consequence of the geometrical nature of the theory. In general relativity, objects infree-fall follow geodesics of spacetime, and what we perceive as the force of gravity is instead a result of our beingunable to follow those geodesics of spacetime, because the mechanical resistance of matter prevents us from doingso.

Since Einstein developed general relativity, there was a need to develop a framework to test the theory againstother possible theories of gravity compatible with special relativity. This was developed by Robert Dicke as part ofhis program to test general relativity. Two new principles were suggested, the so-called Einstein equivalenceprinciple and the strong equivalence principle, each of which assumes the weak equivalence principle as a startingpoint. They only differ in whether or not they apply to gravitational experiments.

Modern usageThree forms of the equivalence principle are in current use: weak (Galilean), Einsteinian, and strong.

The weak equivalence principle

The weak equivalence principle, also known as the universality of free fall or the Galilean equivalenceprinciple can be stated in many ways. The strong EP includes (astronomic) bodies with gravitational bindingenergy[3] (e.g., 1.74 solar-mass pulsar PSR J1903+0327, 15.3% of whose separated mass is absent asgravitational binding energy[4]). The weak EP assumes falling bodies are bound by non-gravitational forces only.Either way,

The trajectory of a point mass in a gravitational field depends only on its initial position and velocity, and isindependent of its composition and structure.

All test particles at the alike spacetime point in a given gravitational field will undergo the same acceleration,

independent of their properties, including their rest mass.[5]

All local centers of mass vacuum free fall along identical (parallel-displaced, same speed) minimum actiontrajectories 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 acceleratedobserver in flat space, without exception.

Mass (measured with a balance) and weight (measured with a scale) are locally in identical ratio for allbodies (the opening page to Newton's Philosophiæ 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'sconceptualization. The equivalence principle does not deny the existence of measurable effects caused by arotating gravitating mass (frame dragging), or bear on the measurements of light deflection and gravitational timedelay 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:

By definition of inertial mass:

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

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:

must be equal and opposite to

It follows that:

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

The dimensionless Eötvös-parameter is the difference of the ratios of gravitational and inertial massesdivided 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 Method Result

JohnPhiloponus

6thcentury

Described correctly the effect ofdropping balls of different masses no detectable difference

SimonStevin[6] ~1586 Dropped lead balls of different

masses off the Delft churchtowerno detectable difference

GalileoGalilei ~1610 Rolling balls down inclined planes no detectable difference

Isaac ~1680measure the period of pendulumsof different mass but identical no measurable difference

Newton~1680 of different mass but identical

lengthno measurable difference

FriedrichWilhelmBessel

1832measure the period of pendulumsof different mass but identicallength

no measurable difference

LorándEötvös 1908

measure the torsion on a wire,suspending a balance beam,between two nearly identicalmasses under the acceleration ofgravity and the rotation of theEarth

difference is less than 1 part in 109

Roll,Krotkov andDicke

1964Torsion balance experiment,dropping aluminum and gold testmasses

[7]

David Scott 1971Dropped a falcon feather and ahammer at the same time on theMoon

no detectable difference (not a rigorous experiment, butvery dramatic being the first lunar one[8])

Braginskyand Panov 1971

Torsion balance, aluminum andplatinum test masses, measuringacceleration towards the sun

difference is less than 1 part in 1012

Eöt-Washgroup 1987–

Torsion balance, measuringacceleration of different massestowards the earth, sun andgalactic center, using severaldifferent kinds of masses

[9][10]

See:[11]

Year Investigator Sensitivity Method

500? Philoponus [12] "small" Drop Tower

1585 Stevin [13] 5×10-2 Drop Tower

1590? Galileo [14] 2×10-2 Pendulum, DropTower

1686 Newton [15] 10-3 Pendulum

1832 Bessel [16] 2×10-5 Pendulum

1910 Southerns [17] 5×10-6 Pendulum

1918 Zeeman [18] 3×10-8 Torsion Balance

1922 Eötvös [19] 5×10-9 Torsion Balance

1923 Potter [20] 3×10-6 Pendulum

1935 Renner [21] 2×10-9 Torsion Balance

1964 Dicke,Roll,Krotkov [22] 3x10-11 Torsion Balance

1972 Braginsky,Panov [23] 10-12 Torsion Balance

1976 Shapiro, et al.[24] 10-12 Lunar LaserRanging

1981 Keiser,Faller [25] 4×10-11 Fluid Support

1987 Niebauer, et al.[26] 10-10 Drop Tower

1989 Heckel, et al.[27] 10-11 Torsion Balance

1990 Adelberger, et al.[28] 10-12 Torsion Balance

1999 Baessler, et al.[29] 5x10-14 Torsion Balance

cancelled? MiniSTEP (http://einstein.stanford.edu/STEP/) 10-17 Earth Orbit

2015? MICROSCOPE (http://smsc.cnes.fr/MICROSCOPE/index.htm) 10-16 Earth Orbit

2015?Reasenberg/SR-POEM(http://www.cfa.harvard.edu/pag/index_files/Page1098.htm)[30] 2×10-17 vacuum free fall

Experiments are still being performed at the University of Washington which have placed limits on the differentialacceleration of objects towards the Earth, the sun and towards dark matter in the galactic center. Future satelliteexperiments[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 iscompatible with observations. However, no quantum theory of gravity is known, and most suggestions violate oneof the equivalence principles at some level. String theory, supergravity and even quintessence, for example, seem toviolate the weak equivalence principle because they contain many light scalar fields with long Comptonwavelengths. These fields should generate fifth forces and variation of the fundamental constants. There are anumber of mechanisms that have been suggested by physicists to reduce these violations of the equivalenceprinciple to below observable levels.

The Einstein equivalence principle

The Einstein equivalence principle states that the weak equivalence principle holds, and that:[32]

The outcome of any local non-gravitational experiment in a freely falling laboratory is independent ofthe velocity of the laboratory and its location in spacetime.

Here "local" has a very special meaning: not only must the experiment not look outside the laboratory, but it mustalso be small compared to variations in the gravitational field, tidal forces, so that the entire laboratory is freelyfalling. It also implies the absence of interactions with "external" fields other than the gravitationalfield.[citation needed]

The principle of relativity implies that the outcome of local experiments must be independent of the velocity of theapparatus, so the most important consequence of this principle is the Copernican idea that dimensionless physical

values such as the fine-structure constant and electron-to-proton mass ratio must not depend on where in space ortime we measure them. Many physicists believe that any Lorentz invariant theory that satisfies the weak equivalenceprinciple 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. TheEinstein equivalence principle has been criticized as imprecise, because there is no universally accepted way todistinguish 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 bysearching for variation of dimensionless constants and mass ratios. The present best limits on the variation of thefundamental 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 undergroundapproximately two billion years ago. These reactions are extremely sensitive to the values of the fundamentalconstants.

Constant Year Method Limit on fractional change

fine structure constant 1976 Oklo 10−7

weak interaction constant 1976 Oklo 10−2

electron-proton mass ratio 2002 quasars 10−4

proton gyromagnetic factor 1976 astrophysical 10−1

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 thereported detection of variation (at the 10−5 level) of the fine-structure constant from measurements of distantquasars, see Webb et al.[35] Other researchers dispute these findings. Other tests of the Einstein equivalenceprinciple are gravitational redshift experiments, such as the Pound-Rebka experiment which test the positionindependence of experiments.

The strong equivalence principle

The strong equivalence principle suggests the laws of gravitation are independent of velocity and location. Inparticular,

The gravitational motion of a small test body depends only on its initial position in spacetime andvelocity, and not on its constitution.

and

The outcome of any local experiment (gravitational or not) in a freely falling laboratory isindependent of the velocity of the laboratory and its location in spacetime.

The first part is a version of the weak equivalence principle that applies to objects that exert a gravitational force on

themselves, such as stars, planets, black holes or Cavendish experiments. The second part is the Einsteinequivalence principle (with the same definition of "local"), restated to allow gravitational experiments and self-gravitating bodies. The freely-falling object or laboratory, however, must still be small, so that tidal forces may beneglected (hence "local experiment").

This is the only form of the equivalence principle that applies to self-gravitating objects (such as stars), which havesubstantial internal gravitational interactions. It requires that the gravitational constant be the same everywhere in theuniverse 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 alonedetermines the effect of gravity) and does not have any extra fields associated with it. If an observer measures apatch of space to be flat, then the strong equivalence principle suggests that it is absolutely equivalent to any otherpatch of flat space elsewhere in the universe. Einstein's theory of general relativity (including the cosmologicalconstant) is thought to be the only theory of gravity that satisfies the strong equivalence principle. A number ofalternative 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 Gover the life of the universe, or equivalently, variation in the masses of the fundamental particles. A number ofindependent constraints, from orbits in the solar system and studies of big bang nucleosynthesis have shown that Gcannot have varied by more than 10%.

Thus, the strong equivalence principle can be tested by searching for fifth forces (deviations from the gravitationalforce-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 mostaccurate tests over short distances have been performed by the Eöt-Wash group. A future satellite experiment,SEE (Satellite Energy Exchange), will search for fifth forces in space and should be able to further constrainviolations of the strong equivalence principle. Other limits, looking for much longer-range forces, have been placedby searching for the Nordtvedt effect, a "polarization" of solar system orbits that would be caused by gravitationalself-energy accelerating at a different rate from normal matter. This effect has been sensitively tested by the LunarLaser Ranging Experiment. Other tests include studying the deflection of radiation from distant radio sources by thesun, which can be accurately measured by very long baseline interferometry. Another sensitive test comes frommeasurements of the frequency shift of signals to and from the Cassini spacecraft. Together, these measurementshave put tight limits on Brans-Dicke theory and other alternative theories of gravity.

Challenges to the equivalence principleOne challenge to the equivalence principle is the Brans-Dicke theory. Self-creation cosmology is a modification ofthe Brans-Dicke theory. The Fredkin Finite Nature Hypothesis is an even more radical challenge to the equivalenceprinciple and has even fewer supporters.

In August 2010, researchers from the School of Physics, University of New South Wales, Australia; the Centre forAstrophysics and Supercomputing, Swinburne University of Technology, Australia; and the Institute of Astronomy,Cambridge, United Kingdom; published the paper "Evidence for spatial variation of the fine structure constant",whose tentative conclusion is that, "qualitatively, [the] results suggest a violation of the Einstein EquivalencePrinciple, and could infer a very large or infinite universe, within which our `local' Hubble volume represents a tinyfraction."[36]

fraction."

Explanations of the equivalence principleDutch physicist and string theorist Erik Verlinde has generated a self-contained, logical derivation of the equivalenceprinciple based on the starting assumption of a holographic universe. Given this situation, gravity would not be a truefundamental force as is currently thought but instead an "emergent property" related to entropy. Verlinde's approachto explaining gravity apparently leads naturally to the correct observed strength of dark energy; previous failures toexplain its incredibly small magnitude have been called by such people as cosmologist Michael Turner (who iscredited as having coined the term "dark energy") as "the greatest embarrassment in the history of theoreticalphysics".[37] However, it should be noted that these ideas are far from settled and still very controversial.

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 theequivalence principle at the level of atoms..."[44]

See also

General RelativityGeneral covarianceClassical MechanicsFrame of referenceInertial frame of referenceMach's principleEquivalence principle (geometric)

Brans-Dicke theoryGauge gravitation theorySelf-creation cosmologyFredkin Finite Nature HypothesisTests of general relativityUnsolved problems in astronomyUnsolved problems in physics

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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 equivalenceprinciple", 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/?

id=dSv8ksxHR0oC&printsec=frontcover&dq=intitle:Five+intitle:Dimensional+intitle:Physics). World Scientific.p. 82. ISBN 981-256-661-9.

6. ^ 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.

7. ^ P. G. Roll, R. Krotkov, R. H. Dicke, The equivalence of inertial and passive gravitational mass, Annals ofPhysics, Volume 26, Issue 3, 20 February 1964, Pages 442-517

8. ^ http://www.youtube.com/watch?v=MJyUDpm9Kvk9. ^ 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).

10. ^ Schlamminger; Choi; Wagner; Gundlach; Adelberger (2007). "Test of the Equivalence Principle Using a RotatingTorsion 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).

11. ^ Ciufolini & Wheeler, "Gravitation and Inertia" (Princeton University Press: Princeton, 1995) pp. 117-11912. ^ Philoponus, J. "Corollaries on Place and Void" David Furley trans. (Ithaca, NY: Cornell University Press, 1987)13. ^ Stevin, Simon. De Beghinselen der Weeghconst "Principles of the Art of Weighing" (Leyden, 1586); Dijksterhuis,

EJ. "The Principal Works of Simon Stevin" (Amsterdam 1955)14. ^ 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)

15. ^ Newton, Isaac. "Philosophiae Naturalis Principia Mathematica" (Mathematical Principles of Natural Philosophyand 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 andAnne Whitman, with the assistance of Julia Budenz (University of California Press: Berkeley, 1999)

16. ^ Ann. Physik und Chemie (Poggendorff) 25 401 (1832)17. ^ Proc. Roy. Soc. Lond. 84 325 (1910)18. ^ Proc. K. Akad. Amsterdam 20(4) 542 (1918)19. ^ Math. Naturw. Ber. aus. Ungarn 8 65 (1889); Ann. Physik (Leipzig) 68 11 (1922); Phys. Rev. D 61(2) 022001

(1999)20. ^ Proc. Roy. Soc. Lond. 104 588 (1923)21. ^ és Természettudományi Értesitö 53 569 (1935)22. ^ Ann. Phys. (NY) 26 442 (1964)23. ^ Zh. Eksp. Teor. Fiz. 61 873 (1971)24. ^ Phys. Rev. Lett. 36 555 (1976)25. ^ Bull. Am. Phys. Soc. 24 579 (1979)26. ^ Phys. Rev. Lett. 59 609 (1987)27. ^ Phys. Rev. Lett. 62 609 (1989)28. ^ Phys. Rev. D 42 3267 (1990)29. ^ Class. Quantum. Grav. 18(13) 2393 (2001); Phys.Rev. Lett 83(18) 3585 (1999)30. ^ http://arxiv.org/abs/1206.0028 , Class. Quantum Grav. 27, 095005 (2010); http://www.cfa.harvard.edu/PAG/6-

%2520Presentations/Reasenberg_Q2C3_web.pdf31. ^ Dittus, H; C. Lāmmerzahl. "Experimental Tests of the Equivalence Principle and Newton’s 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. AIPConference 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).

32. ^ Haugen, Mark P.; C. Lämmerzahl (2001). Principles of Equivalence: Their Role in Gravitation Physics andExperiments that Test Them. Springer. arXiv:gr-qc/0103067 (http://arxiv.org/abs/gr-qc/0103067). ISBN 978-3-

Experiments that Test Them. Springer. arXiv:gr-qc/0103067 (http://arxiv.org/abs/gr-qc/0103067). ISBN 978-3-540-41236-6.

33. ^ Hadley (1997). "The Logic of Quantum Mechanics Derived from Classical General Relativity". Found.Phys.Lett.10: 43–60. 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).

34. ^ http://stacks.iop.org/ob/4/S35135. ^ 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).

36. ^ Webb; King; Murphy; Flambaum; Carswell; Bainbridge (2010). "Evidence for spatial variation of the finestructure constant". arXiv:1008.3907 (http://arxiv.org/abs/1008.3907) [astro-ph.CO (http://arxiv.org/archive/astro-ph.CO)].

37. ^ Wright, Karen (March 01, 2001). "Very Dark Energy"(http://discovermagazine.com/2001/mar/featdark#.USwYk6XmjoI). Discover Magazine. Retrieved 26 February2013.

38. ^ Eöt-Wash group (http://www.npl.washington.edu/eotwash/)39. ^ http://funphysics.jpl.nasa.gov/technical/grp/lunar-laser.html40. ^ http://eotvos.dm.unipi.it/nobili/41. ^ http://einstein.stanford.edu/STEP/42. ^ http://smsc.cnes.fr/MICROSCOPE/index.htm43. ^ http://www.phys.utk.edu/see/44. ^ 16 November 2004, physicsweb: Equivalence principle passes atomic test

(http://physicsworld.com/cws/article/news/2004/nov/16/equivalence-principle-passes-atomic-test)

ReferencesR. H. Dicke, "New Research on Old Gravitation," Science 129, 3349 (1959). This paper is the first to make thedistinction between the strong and weak equivalence principles.R. H. Dicke, "Mach's Principle and Equivalence," in Evidence for gravitational theories: proceedings of course 20of the International School of Physics "Enrico Fermi", ed C. Møller (Academic Press, New York, 1962). Thisarticle outlines the approach to precisely testing general relativity advocated by Dicke and pursued from 1959onwards.Albert Einstein, "Über das Relativitätsprinzip und die aus demselben gezogene Folgerungen," Jahrbuch derRadioaktivitaet 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, 1900–1909 (Princeton UniversityPress, Princeton, NJ, 1989), Anna Beck translator. This is Einstein's first statement of the equivalence principle.Albert Einstein, "Über den Einfluß 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 AlbertEinstein. Vol. 3 : The Swiss years: writings, 1909–1911 (Princeton University Press, Princeton, NJ, 1994), AnnaBeck translator, and in The Principle of Relativity, (Dover, 1924), pp 99–108, W. Perrett and G. B. Jefferytranslators, ISBN 0-486-60081-5. The two Einstein papers are discussed online at The Genesis of GeneralRelativity (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 historyof attempts to construct gravity theories with a scalar field and the relation to the equivalence principle and Mach'sprinciple.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 0-393-96501-5 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 thestrong 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 thevariation of the fundamental constants.C. M. Will, Theory and experiment in gravitational physics, Cambridge University Press, Cambridge (1993). Thisis 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 popularaccount of tests of general relativity.C. M. Will, The Confrontation between General Relativity and Experiment, (http://www.livingreviews.org/lrr-2006-3) Living Reviews in Relativity (2006). An online, technical review, covering much of the material in Theoryand experiment in gravitational physics. The Einstein and strong variants of the equivalence principles arediscussed 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 Vdiscusses the equivalence principle.

External linksEquivalence Principle (http://science.nasa.gov/headlines/y2007/18may_equivalenceprinciple.htm) at NASA,including testsIntroducing The Einstein Principle of Equivalence(http://www.phy.syr.edu/courses/modules/LIGHTCONE/equivalence.html) from Syracuse UniversityThe Equivalence Principle (http://www.mathpages.com/rr/s5-06/5-06.htm) at MathPagesThe Einstein Equivalence Principle (http://emis.math.ecnu.edu.cn/journals/LRG/Articles/lrr-2001-4/node3.html) at Living Reviews on General Relativityhttp://cafe.daum.net/grelativitycosmology

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