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equivalence principle

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**equivalence principle**is the equivalence of gravitational and inertial mass, and Albert Einstein's observation that the gravitational "force" as experienced locally while standing on a massive body (such as the Earth) is the same as the

*pseudo-force*experienced by an observer in a non-inertial (accelerated) frame of reference.

## Einstein's statement of the equality of inertial and gravitational mass

{{Quotation|A little reflection will show that the law of the equality of the inertial and gravitational mass is equivalent to the assertion that the acceleration imparted to a body by a gravitational field is independent of the nature of the body. For Newton's equation of motion in a gravitational field, written out in full, it is:
(Inertial mass) cdot (Acceleration) = (Intensity of the gravitational field) cdot (Gravitational mass).

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.Einstein, Albert, weblink" title="web.archive.org/web/20151222085312weblink">*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. 17â€“19, April 2005. Einstein recalls events of 1907 in a talk in Japan on 14 December 1922.BOOK, Einstein, Albert, The Meaning of Relativity, 2003, Routledge, 9781134449798, 59, }}

## Development of gravitational theory

File:Apollo 15 feather and hammer drop.ogv|thumb|During the Apollo 15 mission in 1971, astronaut (David Scott]] 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.)Something like the equivalence principle emerged in the early 17th century, when Galileo expressed experimentally that the acceleration of a test mass due to gravitation is independent of the amount of mass being accelerated.Kepler, using Galileo's discoveries, showed knowledge of the equivalence principle by accurately describing what would occur if the moon were stopped in its orbit and dropped towards Earth. This can be deduced without knowing if or in what manner gravity decreases with distance, but requires assuming the equivalency between gravity and inertia.The 1/54 ratio is Kepler's estimate of the Moonâ€“Earth mass ratio, based on their diameters. The accuracy of his statement can be deduced by using Newton's inertia law F=ma and Galileo's gravitational observation that distance D = (1/2)at^2. Setting these accelerations equal for a mass is the equivalence principle. Noting the time to collision for each mass is the same gives Kepler's statement that Dmoon/DEarth=MEarth/Mmoon, without knowing the time to collision or how or if the acceleration force from gravity is a function of distance.Newton's gravitational theory simplified and formalized Galileo's and Kepler's ideas by recognizing Kepler's "animal force or some other equivalent" beyond gravity and inertia were not needed, deducing from Kepler's planetary laws how gravity reduces with distance.The equivalence principle was properly introduced by Albert Einstein in 1907, when he observed that the acceleration of bodies towards the center of the Earth at a rate of 1*g (*

*g*= 9.81 m/s2 being a standard reference of gravitational acceleration at the Earth's surface) is equivalent to the acceleration of an inertially moving body that would be observed on a rocket in free space being accelerated at a rate of 1

*g*. Einstein stated it thus:That is, being on the surface of the Earth is equivalent to being inside a spaceship (far from any sources of gravity) that is being accelerated by its engines. The direction or vector of acceleration equivalence on the surface of the earth is "up" or directly opposite the center of the planet while the vector of acceleration in a spaceship is directly opposite from the mass ejected by its thrusters. From this principle, Einstein deduced that free-fall is inertial motion. Objects in free-fall do not experience being accelerated downward (e.g. toward the earth or other massive body) but rather weightlessness and no acceleration. In an inertial frame of reference bodies (and photons, or light) obey Newton's first law, moving at constant velocity in straight lines. Analogously, in a curved spacetime the world line of an inertial particle or pulse of light is

*as straight as possible*(in space

*and*time).WEB,weblink 32, General Relativity in a Nutshell, Alan, Macdonald, September 15, 2012, February 8, 2013, Luther College (Iowa), Luther College, Such a world line is called a geodesic and from the point of view of the inertial frame is a straight line. This is why an accelerometer in free-fall doesn't register any acceleration; there isn't any.As an example: an inertial body moving along a geodesic through space can be trapped into an orbit around a large gravitational mass without ever experiencing acceleration. This is possible because spacetime is radically curved in close vicinity to a large gravitational mass. In such a situation the geodesic lines bend inward around the center of the mass and a free-floating (weightless) inertial body will simply follow those curved geodesics into an elliptical orbit. An accelerometer on-board would never record any acceleration.By contrast, in Newtonian mechanics, gravity is assumed to be a force. This force draws objects having mass towards the center of any massive body. At the Earth's surface, the force of gravity is counteracted by the mechanical (physical) resistance of the Earth's surface. So in Newtonian physics, a person at rest on the surface of a (non-rotating) massive object is in an inertial frame of reference. These considerations suggest the following corollary to the equivalence principle, which Einstein formulated precisely in 1911:Einstein also referred to two reference frames, K and K'. K is a uniform gravitational field, whereas K' has no gravitational field but is uniformly accelerated such that objects in the two frames experience identical forces:This observation was the start of a process that culminated in general relativity. Einstein suggested that it should be elevated to the status of a general principle, which he called the "principle of equivalence" when constructing his theory of relativity: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. The room, therefore, should be small enough that tidal effects can be neglected.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.Another clarification needed is that the equivalence principle assumes a constant acceleration of 1g without considering the mechanics of generating 1g. If we do consider the mechanics of it, then we must assume the aforementioned windowless room has a fixed mass. Accelerating it at 1g means there is a constant force being applied, which = m*g where m is the mass of the windowless room along with its contents (including the observer). Now, if the observer jumps inside the room, an object lying freely on the floor will decrease in weight momentarily because the acceleration is going to decrease momentarily due to the observer pushing back against the floor in order to jump. The object will then gain weight while the observer is in the air and the resulting decreased mass of the windowless room allows greater acceleration; it will lose weight again when the observer lands and pushes once more against the floor; and it will finally return to its initial weight afterwards. To make all these effects equal those we would measure on a planet producing 1g, the windowless room must be assumed to have the same mass as that planet. Additionally, the windowless room must not cause its own gravity, otherwise the scenario changes even further. These are technicalities, clearly, but practical ones if we wish the experiment to demonstrate more or less precisely the equivalence of 1g gravity and 1g acceleration.

## Modern usage

Three 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 equivalence principle**can be stated in many ways. The strong EP includes (astronomic) bodies with gravitational binding energyWagner, Todd A.; Schlamminger, Stephan; Gundlach, Jens H.; Adelberger, Eric G.; "Torsion-balance tests of the weak equivalence principle",

*Classical and Quantum Gravity*29, 184002 (2012);weblink (e.g., 1.74 solar-mass pulsar PSR J1903+0327, 15.3% of whose separated mass is absent as gravitational binding energyChampion, David J.; Ransom, Scott M.; Lazarus, Patrick; Camilo, Fernando; et al.;

*Science*320(5881), 1309 (2008),weblink{{failed verification|date=June 2018}}). 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 is independent 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.BOOK, Five-dimensional Physics, Paul S., Wesson, 82,weblink 978-981-256-661-4, World Scientific, 2006,

All local centers of mass free-fall (in vacuum) 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 spacetime (gravitation) are indistinguishable from those of an accelerated observer in flat spacetime, 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

*PhilosophiÃ¦ 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 M_1 due to the gravitational field of M_0 is:
F_1 = frac{M_0^mathrm{act} M_1^mathrm{pass}}{r^2}

F_2 = frac{M_0^mathrm{act} M_2^mathrm{pass}}{r^2}

F = m^mathrm{inert} a

a_1 = frac{F_1}{m_1^mathrm{inert}} = a_2 = frac{F_2}{m_2^mathrm{inert}}

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}}

frac{M_1^mathrm{pass}}{m_1^mathrm{inert}} = frac{M_2^mathrm{pass}}{m_2^mathrm{inert}}

F_1 = frac{M_0^mathrm{act} M_1^mathrm{pass}}{r^2}

F_0 = frac{M_1^mathrm{act} M_0^mathrm{pass}}{r^2}

frac{M_0^mathrm{act}}{M_0^mathrm{pass}} = frac{M_1^mathrm{act}}{M_1^mathrm{pass}}

eta(A,B)=2frac{ left(frac{m_g}{m_i}right)_A-left(frac{m_g}{m_i}right)_B }{left(frac{m_g}{m_i}right)_A+left(frac{m_g}{m_i}right)_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 different objects, ideally in a vacuum environment, e.g., inside the Fallturm Bremen drop tower.{| class="wikitable"Researcher | Year | Method | Result |

John Philoponus | 6th century | Said that by observation, two balls of very different weights will fall at nearly the same speed | no detectable difference |

Simon StevinDEVREESE >FIRST1=JOZEF T. | LAST2=VANDEN BERGHE | YEAR=2008 | URL=HTTPS://BOOKS.GOOGLE.COM/BOOKS?ISBN=1845643917 | ISBN=9781845643911, | ~1586 | Dropped lead balls of different masses off the Delft churchtower | no detectable difference |

Galileo Galilei | ~1610 | Rolling balls of varying weight down inclined planes to slow the speed so that it was measurable | no detectable difference |

Isaac Newton | ~1680 | Measure the period of pendulums of different mass but identical length | difference is less than 1 part in 103 |

Friedrich Wilhelm Bessel | 1832 | Measure the period of pendulums of different mass but identical length | no measurable difference |

LorÃ¡nd EÃ¶tvÃ¶s | 1908 | 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 | difference is 10Â±2 part in 109 (H2O/Cu)EÃ¶tvÃ¶s, LorÃ¡nd; Annalen der Physik (Leipzig) 68 11 (1922) |

P. G. Roll | , Robert Krotkov>Krotkov and Dicke | 1964 | Torsion balance experiment, dropping aluminum and gold test masses | =(1.3pm1.0)times10^{-11}Roll, Peter G.; Krotkov, Robert; Dicke, Robert H.; The equivalence of inertial and passive gravitational mass, Annals of Physics, Volume 26, Issue 3, 20 February 1964, pp. 442â€“517 |

David Scott | 1971 | Dropped a falcon feather and a hammer at the same time on the Moon | no detectable difference (not a rigorous experiment, but very dramatic being the first lunar oneHTTPS://WWW.YOUTUBE.COM/WATCH?V=MJYUDPM9KVK > TITLE=WEAK EQUIVALENCE PRINCIPLE TEST ON THE MOON, ) |

Vladimir Borisovich Braginski | and Vladimir Ivanovich Panov>Panov | 1971 | Torsion balance, aluminum and platinum test masses, measuring acceleration towards the Sun | difference is less than 1 part in 1012 |

EÃ¶t-Wash group | 1987– | Torsion balance, measuring acceleration of different masses towards the Earth, Sun and galactic center, using several different kinds of masses | eta(text{Earth},text{Be-Ti})=(0.3 pm 1.8)times 10^{-13}SCHLAMMINGER >FIRST1=STEPHAN | FIRST2=KI-YOUNG | FIRST3=TODD A. | FIRST4=JENS H. | FIRST5=ERIC G. | JOURNAL=PHYSICAL REVIEW LETTERS | ISSUE=4 | DOI=10.1103/PHYSREVLETT.100.041101 | ARXIV=0712.0607 | PAGE=041101, |

Year | Investigator | Sensitivity | Method |

500? | PhiloponusPhiloponus, John; "Corollaries on Place and Void", translated by David Furley, Ithaca, New York: Cornell University Press, 1987 | "small" | Drop tower |

1585 | StevinStevin, Simon; De Beghinselen der Weeghconst ["Principles of the Art of Weighing"], Leyden, 1586; Dijksterhuis, Eduard J.; "The Principal Works of Simon Stevin", Amsterdam, 1955 | 5Ã—10âˆ’2 | Drop tower |

1590? | GalileoGalilei, 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, 1638 | 2Ã—10âˆ’2 | Pendulum, drop tower |

1686 | NewtonNewton, Isaac; "Philosophiae Naturalis Principia Mathematica" [Mathematical Principles of Natural Philosophy and his System of the World], 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 Whitman, with the assistance of Julia Budenz, Berkeley, California: University of California Press, 1999 | 10âˆ’3 | Pendulum |

1832 | BesselBessel, Friedrich W.; "Versuche Uber die Kraft, mit welcher die Erde KÃ¶rper von verschiedner Beschaffenhelt anzieht", Annalen der Physik und Chemie, Berlin: J. Ch. Poggendorff, 25 401â€“408 (1832) | 2Ã—10âˆ’5 | Pendulum |

1908 (1922) | EÃ¶tvÃ¶sEÃ¶tvÃ¶s, LorÃ¡nd; Mathematische and naturnissenschaftliche Berichte aus Ungarn 8 65 (1889); Annalen der Physik (Leipzig) 68 11 (1922); Physical Review D 61(2) 022001 (1999) | 2Ã—10âˆ’9 | Torsion balance |

1910 | SouthernsSoutherns, Leonard; "A Determination of the Ratio of Mass to Weight for a Radioactive Substance", Proceedings of the Royal Society of London, 84 325â€“344 (1910), {{DOI|10.1098/rspa.1910.0078}} | 5Ã—10âˆ’6 | Pendulum |

1918 | ZeemanZeeman, Pieter; "Some experiments on gravitation: The ratio of mass to weight for crystals and radioactivesubstances", Proceedings of the Koninklijke Nederlandse Akademie van Wetenschappen, Amsterdam 20(4) 542â€“553 (1918) | 3Ã—10âˆ’8 | Torsion balance |

1923 | PotterPOTTER > FIRST1 = HAROLD H. | TITLE = SOME EXPERIMENTS ON THE PROPORTIONALITY OF MASS AND WEIGHT | JOURNAL = PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON | ISSUE = 728 | DOI = 10.1098/RSPA.1923.0130, 1923RSPSA.104..588P, | 3Ã—10âˆ’6 | Pendulum |

1935 | RennerRenner, JÃ¡nos; "KÃsÃ©rleti vizsgÃ¡latok a tÃ¶megvonzÃ¡s Ã©s tehetetlensÃ©g arÃ¡nyossÃ¡gÃ¡rÃ³l", Mathematikai Ã©s TermÃ©szettudomÃ¡nyi Ã‰rtesÃtÅ‘ 53 569 (1935), Budapest | 2Ã—10âˆ’9 | Torsion balance |

1964 | Dicke, Roll, Krotkov | 3x10âˆ’11 | Torsion balance |

1972 | Braginsky, PanovBraginski, Vladimir Borisovich; Panov, Vladimir Ivanovich; Ð–ÑƒÑ€Ð½Ð°Ð» ÐÐºÑÐ¿ÐµÑ€Ð¸Ð¼ÐµÐ½Ñ‚Ð°Ð»ÑŒÐ½Ð¾Ð¹ Ð¸ Ð¢ÐµÐ¾Ñ€ÐµÑ‚Ð¸Ñ‡ÐµÑÐºÐ¾Ð¹ Ð¤Ð¸Ð·Ð¸ÐºÐ¸ (Zhurnal Ã‰ksperimentalâ€™noÄ i TeoreticheskoÄ Fiziki, Journal of Experimental and Theoretical Physics) 61 873 (1971) | 10âˆ’12 | Torsion balance |

1976 | Shapiro, et al.SHAPIRO >FIRST1=IRWIN I. | FIRST2=III | FIRST3=C. | FIRST4=ROBERT W. | TITLE=VERIFICATION OF THE PRINCIPLE OF EQUIVALENCE FOR MASSIVE BODIES | ARCHIVE-URL=HTTPS://ARCHIVE.IS/20140122182435/HTTP://PRL.APS.ORG/PDF/PRL/V36/I11/P555_1 | ARCHIVE-DATE=2014-01-22 | VOLUME=36 | PAGES=555â€“558 | BIBCODE=1976PHRVL..36..555S, | 10âˆ’12 | Lunar laser ranging |

1981 | Keiser, FallerKeiser, George M.; Faller, James E.; Bulletin of the American Physical Society 24 579 (1979) | 4Ã—10âˆ’11 | Fluid support |

1987 | Niebauer, et al.NIEBAUER > FIRST1 = TIMOTHY M. | FIRST2 = MARTIN P. | FIRST3 = JAMES E. | TITLE = GALILEAN TEST FOR THE FIFTH FORCE | JOURNAL = PHYSICAL REVIEW LETTERS | ISSUE = 6 | DOI=10.1103/PHYSREVLETT.59.609 | PMID=10035824, Submitted manuscript, | 10âˆ’10 | Drop tower |

1989 | Stubbs, et al.STUBBS > FIRST1 = CHRISTOPHER W. | FIRST2 = ERIC G. | FIRST3 = BLAYNE R. | FIRST4 = WARREN F. | FIRST5 = H. ERIK | FIRST6 = R. | FIRST7 = JENS H. | FIRST8 = FREDERICK J. | TITLE = LIMITS ON COMPOSITION-DEPENDENT INTERACTIONS USING A LABORATORY SOURCE: IS THERE A "FIFTH FORCE" COUPLED TO ISOSPIN? | JOURNAL = PHYSICAL REVIEW LETTERS | ISSUE = 6 | DOI=10.1103/PHYSREVLETT.62.609 | PMID=10040283, | 10âˆ’11 | Torsion balance |

1990 | Adelberger, Eric G.; et al.ADELBERGER > FIRST1 = ERIC G. | FIRST2 = CHRISTOPHER W. | FIRST3 = BLAYNE R. | FIRST4 = Y. | FIRST5 = H. ERIK | FIRST6 = G. L. | FIRST7 = JENS H. | FIRST8 = WARREN F. | TITLE = TESTING THE EQUIVALENCE PRINCIPLE IN THE FIELD OF THE EARTH: PARTICLE PHYSICS AT MASSES BELOW 1 Î¼EV? | JOURNAL = PHYSICAL REVIEW D | ISSUE = 10 | DOI=10.1103/PHYSREVD.42.3267, 1990PhRvD..42.3267A, | 10âˆ’12 | Torsion balance |

1999 | Baessler, et al.BaeÃŸler, Stefan; et al.; Classical and Quantum Gravity 18(13) 2393 (2001); BaeÃŸler, Stefan; Heckel, Blayne R.; Adelberger, Eric G.; Gundlach, Jens H.; Schmidt, Ulrich; Swanson, H. Erik; "Improved Test of the Equivalence Principle for Gravitational Self-Energy", Physical Review Letters 83(18) 3585 (1999) | 5x10âˆ’14 | Torsion balance |

2017 | MICROSCOPE (satellite) | 2017PHRVL.119W1101T, MICROSCOPE Mission: First Results of a Space Test of the Equivalence Principle, Touboul, Pierre, MÃ©tris, Gilles, Rodrigues, Manuel, AndrÃ©, Yves, Baghi, Quentin, BergÃ©, JoÃ«l, Boulanger, Damien, Bremer, Stefanie, Carle, Patrice, Chhun, Ratana, Christophe, Bruno, Cipolla, Valerio, Damour, Thibault, Danto, Pascale, Dittus, Hansjoerg, Fayet, Pierre, Foulon, Bernard, Gageant, Claude, Guidotti, Pierre-Yves, Hagedorn, Daniel, Hardy, Emilie, Huynh, Phuong-Anh, Inchauspe, Henri, Kayser, Patrick, Lala, StÃ©phanie, LÃ¤mmerzahl, Claus, Lebat, Vincent, Leseur, Pierre, Liorzou, FranÃ§oise, List, Meike, 29, Physical Review Letters, 119, 23, 2017, 231101, 1712.01176, 10.1103/PhysRevLett.119.231101, | 10âˆ’15 | Earth orbit |

*non-discovery*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 other forces of nature. A positive detection, on the other hand, would provide a major guidepost towards unification.JOURNAL, Overduin, James, Everitt, Francis, Mester, John, Worden, Paul, The Science Case for STEP, 10.1016/j.asr.2009.02.012, Advances in Space Research, 43, 10, 1532â€“1537, 2009, 0902.2247, 2009AdSpR..43.1532O,

### The Einstein equivalence principle

What is now called the "Einstein equivalence principle" states that the weak equivalence principle holds, and that:BOOK, Haugen, Mark P., Claus, LÃ¤mmerzahl, Principles of Equivalence: Their Role in Gravitation Physics and Experiments that Test Them, Gyros, 562, 195â€“212, 2001, 978-3-540-41236-6, gr-qc/0103067, 2001LNP...562..195H, 10.1007/3-540-40988-2_10,*The outcome of any local non-gravitational experiment in a freely falling laboratory is independent of the velocity of the laboratory and its location in spacetime.*

*other than the gravitational field*.{{Citation needed|reason = Definition of "local" in this context. In particular its relation to external fields as stated is dubious. If there are external fields than the equivalence principle doesn't trigger due to the "in a freely falling"-part in the statement. If *no external fields* would be part of the definition of "local", then "free falling" would be redundant.|date=August 2011}}The principle of relativity implies that the outcome of local experiments must be independent of the velocity of the apparatus, 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 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 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 HadleyJOURNAL, Mark J., Hadley, 10.1007/BF02764119, Foundations of Physics Letters, 10, 1, The Logic of Quantum Mechanics Derived from Classical General Relativity, 43â€“60, 1997, quant-ph/9706018, 1997FoPhL..10...43H, 10.1.1.252.6335, and DurandJOURNAL, Durand, StÃ©phane, 2002, An amusing analogy: modelling quantum-type behaviours with wormhole-based time travel,weblink Journal of Optics B: Quantum and Semiclassical Optics, 4, 4, S351â€“S357, 10.1088/1464-4266/4/4/319, 2002JOptB...4S.351D, ).

#### 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.{| class="wikitable"Constant | Year | Method | Limit on fractional change |

proton gyromagnetic factor | 1976 | astrophysical | 10âˆ’1 |

weak interaction constant | 1976 | Oklo | 10âˆ’2 |

fine structure constant | 1976 | Oklo | 10âˆ’7 |

electron–proton mass ratio | 2002 | quasars | 10âˆ’4 |

### The strong equivalence principle

The strong equivalence principle suggests the laws of gravitation are independent of velocity and location. In particular,*The gravitational motion of a small test body depends only on its initial position in spacetime and velocity, and not on its constitution.*

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

#### 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 EÃ¶tâ€“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 Bransâ€“Dicke theory and other alternative theories of gravity.In 2014, astronomers discovered a stellar triple system including a millisecond pulsar PSR J0337+1715 and two white dwarfs orbiting it. The system provided them a chance to test the strong equivalence principle in a strong gravitational field with high accuracy.JOURNAL,weblink A millisecond pulsar in a stellar triple system, Scott M., Ransom, etal, Nature, 2014, 8 January 2014, 10.1038/nature12917, 1401.0535, 2014Natur.505..520R, 505, 7484, 520â€“524, 24390352, JOURNAL, Universality of free fall from the orbital motion of a pulsar in a stellar triple system, Anne M. Archibald, etal, Nature, 559, 7712, 73â€“76, 4 July 2018, 10.1038/s41586-018-0265-1, 29973733, 1807.02059, 2018Natur.559...73A, NEWS, Even Phenomenally Dense Neutron Stars Fall like a Feather â€“ Einstein Gets It Right Again,weblink NRAO, 4 July 2018, 28 July 2018, Charles Blue, Paul Vosteen,

## Challenges

One challenge to the equivalence principle is the Bransâ€“Dicke theory. Self-creation cosmology is a modification of the Bransâ€“Dicke theory. The Fredkin Finite Nature Hypothesis is an even more radical challenge to the equivalence principle and has even fewer supporters.In August 2010, researchers from the University of New South Wales, Swinburne University of Technology, and Cambridge University published a paper titled "Evidence for spatial variation of the fine structure constant", whose tentative conclusion is that, "qualitatively, [the] results suggest a violation of the Einstein Equivalence Principle, and could infer a very large or infinite universe, within which our 'local' Hubble volume represents a tiny fraction."JOURNAL, 1008.3907, John K., Webb, Julian A., King, Michael T., Murphy, Victor V., Flambaum, Robert F., Carswell, Matthew B., Bainbridge, Evidence for spatial variation of the fine structure constant, 2010, 10.1103/PhysRevLett.107.191101, 22181590, 107, 19, 191101, Physical Review Letters, 2011PhRvL.107s1101W,## Explanations

Dutch physicist and string theorist Erik Verlinde has generated a self-contained, logical derivation of the equivalence principle based on the starting assumption of a holographic universe. Given this situation, gravity would not be a true fundamental force as is currently thought but instead an "emergent property" related to entropy. Verlinde's entropic gravity theory apparently leads naturally to the correct observed strength of dark energy; previous failures to explain its incredibly small magnitude have been called by such people as cosmologist Michael Turner (who is credited as having coined the term "dark energy") as "the greatest embarrassment in the history of theoretical physics".WEB, Wright, Karen, Very Dark Energy,weblink Discover Magazine, 26 February 2013, 1 March 2001, These ideas are far from settled and still very controversial.## Experiments

- University of WashingtonEÃ¶tâ€“Wash group
- Lunar Laser RangingWEB,weblink Fundamental Physics of Space - Technical Details, JOURNAL, Viswanathan, V, Fienga, A, Minazzoli, O, Bernus, L, Laskar, J, Gastineau, M, The new lunar ephemeris INPOP17a and its application to fundamental physics, Monthly Notices of the Royal Astronomical Society, May 2018, 476, 2, 1877â€“1888, 10.1093/mnras/sty096, 1710.09167,
- Galileo-Galilei satellite experimentWEB,weblink "GALILEO GALILEI" GG Small Mission Project,
- Satellite Test of the Equivalence Principle (STEP)WEB,weblink S T e P,
- MICROSCOPweblink
- Satellite Energy Exchange (SEE)WEB,weblink Archived copy, 2005-05-07, dead,weblink" title="web.archive.org/web/20050507195406weblink">weblink 7 May 2005, dmy-all,
- "...Physicists in Germany have used an atomic interferometer to perform the most accurate ever test of the equivalence principle at the level of atoms..."16 November 2004, physicsweb: Equivalence principle passes atomic test

## See also

{{div col|colwidth=27em}}- Classical mechanics
- Einstein's thought experiments
- Equivalence principle (geometric)
- Gauge gravitation theory
- General covariance
- Mach's principle
- Tests of general relativity
- Unsolved problems in astronomy
- Unsolved problems in physics

## Notes

{{Reflist|30em}}## References

- Dicke, Robert H.; "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. - Dicke, Robert H.; "Mach's Principle and Equivalence", in
*Evidence for gravitational theories: proceedings of course 20 of the International School of Physics "Enrico Fermi"*, ed. C. MÃ¸ller (Academic Press, New York, 1962). This article outlines the approach to precisely testing general relativity advocated by Dicke and pursued from 1959 onwards. - Einstein, Albert; "Ãœber das RelativitÃ¤tsprinzip 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, 1900–1909*(Princeton University Press, Princeton, New Jersey, 1989), Anna Beck translator. This is Einstein's first statement of the equivalence principle. - Einstein, Albert; "Ãœber den EinfluÃŸ 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, 1909–1911*(Princeton University Press, Princeton, New Jersey, 1994), Anna Beck translator, and in*The Principle of Relativity*, (Dover, 1924), pp 99–108, 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. - Brans, Carl H.; "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.
- Misner, Charles W.; Thorne, Kip S.; and Wheeler, John A.;
*Gravitation*, New York: W. H. Freeman and Company, 1973, Chapter 16 discusses the equivalence principle. - Ohanian, Hans; and Ruffini, Remo;
*Gravitation and Spacetime 2nd edition*, New York: Norton, 1994, {{ISBN|0-393-96501-5}} Chapter 1 discusses the equivalence principle, but incorrectly, according to modern usage, states that the strong equivalence principle is wrong. - Uzan, Jean-Philippe; "The fundamental constants and their variation: Observational status and theoretical motivations",
*Reviews of Modern Physics***75**, 403 (2003). {{arxiv|hep-ph/0205340}} This technical article reviews the best constraints on the variation of the fundamental constants. - Will, Clifford M.;
*Theory and experiment in gravitational physics*, Cambridge, UK: Cambridge University Press, 1993. This is the standard technical reference for tests of general relativity. - Will, Clifford M.;
*Was Einstein Right?: Putting General Relativity to the Test*, Basic Books (1993). This is a popular account of tests of general relativity. - Will, Clifford M.;
*The Confrontation between General Relativity and Experiment,*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 and weblink" title="web.archive.org/web/20140201221349weblink">3.1, respectively. - Friedman, Michael;
*Foundations of Space-Time Theories*, Princeton, New Jersey: Princeton University Press, 1983. Chapter V discusses the equivalence principle. - {{citation | first = Michel | last = Ghins| first2 = Tim |last2 = Budden |title= The Principle of Equivalence| journal = Stud. Hist. Phil. Mod. Phys.| volume = 32 | year = 2001 |issue = 1| pages = 33â€“51 | doi=10.1016/S1355-2198(00)00038-1}}
- {{citation|first = Hans C.|last = Ohanian|title= What is the Principle of Equivalence?|journal = American Journal of Physics| volume = 45 |year =1977|issue=10|pages=903â€“909|doi=10.1119/1.10744|bibcode=1977AmJPh..45..903O}}
- {{citation|first = E.|last = Di Casola|first2=S.|last2=Liberati|first3=S.|last3=Sonego|title= Nonequivalence of equivalence principles|journal = American Journal of Physics| volume =83 |year=2015|issue=1|pages=39|doi=10.1119/1.4895342|arxiv=1310.7426|bibcode=2015AmJPh..83...39D}}

## External links

- weblink" title="web.archive.org/web/20091004092116weblink">Equivalence Principle at NASA, including tests
- weblink" title="web.archive.org/web/20080515172036weblink">Introducing The Einstein Principle of Equivalence from Syracuse University
- The Equivalence Principle at MathPages
- weblink" title="web.archive.org/web/20090329031728weblink">The Einstein Equivalence Principle at Living Reviews on General Relativity

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