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| | == Abercrombie & Fitch en Megaupload wat fouten gemaakt == |
| PLEASE read the whole article before deciding to make changes: Your concern may be covered already.
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| -->{{General relativity|cTopic=Fundamental concepts}}
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| In the [[physics]] of [[general relativity]], the '''equivalence principle''' is any of several related concepts dealing with the equivalence of [[Gravitational mass|gravitational]] and [[inertial mass]], and to [[Albert Einstein|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 ''[[fictitious force|pseudo-force]]'' experienced by an observer in a non-[[inertial frame of reference|inertial]] (accelerated) frame of reference.
| | De inhoud van de NFTS schijf kan op afstand worden benaderd vanuit een andere computer of smartphone met behulp van apps voor iOS en Android. Voortbordurend op dit thema, Sir Martin Sorrell van reclamebureau gigantische WPP dramatisch weggeredeneerd zijn bedrijf zijn vooruitzichten voor 2012 nog maar eens te verlagen, de schuld te geven van vier "Grijze Zwanen" (The Guardian). <br><br>Ha Hebben we een hekel aan elkaar vanwege onze polaire visies over een onderwerp zo dicht bij ons hart? Nee, natuurlijk niet. Zoals ik stapte de Terra Bus, ze waren er met een glimlach en een beroemde groene notitieboekje bij McMurdo wel het groene hersenen. <br><br>Ze draagt hakken naar die verdomde APPARTEMENT! Als je het dragen van hakken je niet rond in een bovenwoning lopen. Opmerking: De NYT gaf de url voor Awlaki s site, maar toen ik probeerde om te gaan. Dow mensen over de hele wereld te ontwikkelen oplossingen voor de maatschappij op basis van inherente kracht van Dow in wetenschap en technologie. <br><br>Het is waar dat elke file sharing website anders wordt uitgevoerd, en Megaupload wat fouten gemaakt, maar de FBI probeert duidelijk te zeggen: "Als wij kunnen afsluiten Megaupload, niemand is veilig." De Feds hebben effectief afgesneden van de kop van het beest en wat weet je, hebben een heleboel websites vrijwillig hun deuren gesloten sinds.. <br><br>Open de video sectie van uw site up voor user generated video's, maar zijn kieskeurig. Steve Massam ging te vermelden dat Chris Biondo zal worden in het land in een paar weken tijd en Steve zei dat hij hoopt van harte dat Chris hem zal vergezellen op "The Sunday Show" voor een praatje over Eva's muziek. <br><br>Met ingang van 2012 heeft het gilde een minder inspannende benadering van het spel genomen, en momenteel staan 10 man tevreden met een 3 nachten schema (met een nacht potentieel toegevoegd tijdens progressie). Deze eer, de McAuley Medal, is de [http://www.chromect.com/custpics/events/domit.asp Abercrombie & Fitch] hoogste [http://www.chromect.com/custpics/events/domit.asp Abercrombie London] onderscheiding die kan worden verleend door het college. <br><br>Pluto is dichter bij de zon dan Neptunus toen hij op de top van zijn ovale baan zo is Orcus wanneer hij op de top van zijn. Simon Helmore, project engineer bij General Compression, bracht een aantal jaren [http://www.chromect.com/custpics/events/domit.asp Abercrombie Suomi] ervaring met behulp van Autodesk Inventor software om General Compression meer recent, toen zijn interesse in duurzame energie lokte hem uit de buurt van een vorige baan ontwerpen handheld medische hulpmiddelen: "Een van mijn grootste zorgen bij de start was het verschil in omvang van wat ik gewend was, "zegt hij. <br><br>Zielig!. 2, terwijl ik de sprongen in reden kom je met kan zien, ik ben niet per se overtuigd van hoe je lijkt te uw ideeën dat de werkelijke conclusie produceren verenigen.. Het ongelooflijk. Ik heb de hybride schijven geprobeerd in het verleden, en ik heb bezat vele SSD's, mijn laatste favoriet is de Crucial M500 960GB, dat is ongeveer $ [http://www.chromect.com/custpics/events/domit.asp Abercrombie Suomeen] 600 in de VS.<ul> |
| | | |
| == Einstein's statement of the equivalence principle ==
| | <li>[http://www.histoirepassion.eu/spip.php?article7/ http://www.histoirepassion.eu/spip.php?article7/]</li> |
| {{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:
| | <li>[http://www.epsworldlink.com/index.php?option=com_kunena&func=view&catid=2&id=172478&Itemid=861&lang=en#172478 http://www.epsworldlink.com/index.php?option=com_kunena&func=view&catid=2&id=172478&Itemid=861&lang=en#172478]</li> |
| :(Inertial mass) <math>\cdot</math> (Acceleration) <math> = </math> (Intensity of the gravitational field) <math>\cdot</math> (Gravitational mass).
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| 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 |<ref>Einstein, Albert; “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 a talk in Japan on 14 December 1922.</ref> }}
| | <li>[http://blhsalumni.com/forum/read.php?1,13154 http://blhsalumni.com/forum/read.php?1,13154]</li> |
| | | |
| See [[momentum]] and [[velocity]].
| | <li>[http://verdamilio.net/tonio/spip.php?article303/ http://verdamilio.net/tonio/spip.php?article303/]</li> |
| | | |
| == Development of gravitation theory ==
| | <li>[http://audeladeleau.free.fr/spip.php?article3/ http://audeladeleau.free.fr/spip.php?article3/]</li> |
| Something like the equivalence principle emerged in the late 16th and early 17th centuries, when [[Galileo Galilei|Galileo]] expressed [[experiment]]ally that the [[acceleration]] of a [[test mass]] due to [[gravitation]] is independent of the amount of [[mass]] being accelerated. These findings led to [[Newton's law of universal gravitation|gravitational theory]], in which the inertial and gravitational masses are identical.
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| | | </ul> |
| 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-force|''g'']]'' (''g'' = 9.81 m/s<sup>2</sup> 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:
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| {{quote|we [...] assume the complete physical equivalence of a gravitational field and a corresponding [[accelerated reference frame|acceleration of the reference system]].|Einstein, 1907}}
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| That is, being at rest 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. From this principle, Einstein deduced that [[free-fall]] is actually [[inertial frame|inertial motion]]. Objects in free-fall do not really accelerate. In an [[inertial frame of reference]] bodies (and light) obey [[Newton's laws of motion#Newton's first law|Newton's first law]], moving at constant velocity in straight lines. Analogously, in a curved [[spacetime]] the worldline of an inertial particle or pulse of light is ''as straight as possible'' (in space ''and'' time).<ref>{{cite web |url=http://faculty.luther.edu/~macdonal/EGR.pdf |page=32 |title=General Relativity in a Nutshell |first=Alan |last=Macdonald |date=September 15, 2012 |accessdate=February 8, 2013 |publisher=[[Luther College (Iowa)|Luther College]] }}</ref> Such a worldline is called a [[Geodesics in general relativity|geodesic]]. 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 any acceleration; there isn't any. 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:
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| {{quote|Whenever an observer detects the local presence of a force that acts on all objects in direct proportion to the inertial mass of each object, that observer is in an accelerated frame of reference.}}
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| Einstein also referred to two reference frames, K and K'. K is a uniform gravitational field, whereas K' has no gravitational field but is [[uniform acceleration|uniformly accelerated]] such that objects in the two frames experience identical forces:
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| | |
| {{quote|We arrive at a very satisfactory interpretation of this law of experience, if we assume that the systems K and K' are physically exactly equivalent, that is, if we assume that we may just as well regard the system K as being in a space free from gravitational fields, if we then regard K as uniformly accelerated. This assumption of exact physical equivalence makes it impossible for us to speak of the absolute acceleration of the system of reference, just as the usual theory of relativity forbids us to talk of the absolute velocity of a system; and it makes the equal falling of all bodies in a gravitational field seem a matter of course.|Einstein, 1911}}
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| 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 when constructing his theory of relativity:
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| {{quote|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}}
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| Einstein combined ([[postulate]]d) the equivalence principle with [[special relativity]] to predict that clocks run at different rates in a [[gravitational potential]], and light rays [[bending of starlight|bend]] in a gravitational field, even before he developed the concept of curved spacetime.
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| 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 force|tidal effects]] (caused by variations in the strength and direction of the gravitational field) which are absent from an accelerating spaceship in deep space.
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| 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 [[Geodesic (general relativity)|geodesic]]s 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.
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| Since Einstein developed general relativity, there was a need to develop a framework to test the theory against other possible theories of gravity compatible with [[special relativity]]. This was developed by [[Robert H. Dicke|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.
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| ==Modern usage==
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| Three forms of the equivalence principle are in current use: weak (Galilean), Einsteinian, and strong.
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| ===The weak equivalence principle===
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| <!-- Universality of free fall and weak equivalence principle redirect to this subsection. Please do not change its title without making sure the redirects work properly. -->
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| {{Cleanup|section|date=January 2010}}
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| The '''weak equivalence principle''', also known as the '''universality of free fall''' or the '''Galilean equivalence principle''' can be stated in many ways. The strong EP includes (astronomic) bodies with gravitational binding energy<ref>Wagner, Todd A.; Schlamminger, Stephan; Gundlach, Jens H.; Adelberger, Eric G.; "Torsion-balance tests of the weak equivalence principle", ''Classical Quantum Gravity'' 29, 184002 (2012); http://arXiv.org/abs/1207.2442</ref> (e.g., 1.74 solar-mass pulsar PSR J1903+0327, 15.3% of whose separated mass is absent as gravitational binding energy<ref>Champion, David J.; Ransom, Scott M.; Lazarus, Patrick; Camilo, Fernando; et al.; ''Science'' 320(5881), 1309 (2008), http://arXiv.org/abs/0805.2396</ref>). The weak EP assumes falling bodies are bound by non-gravitational forces only. Either way:
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| :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''.
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| :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.<ref name="Wesson">{{cite book |title=Five-dimensional Physics |first=Paul S. |last=Wesson |page=82 |url=http://books.google.com/?id=dSv8ksxHR0oC&printsec=frontcover&dq=intitle:Five+intitle:Dimensional+intitle:Physics |isbn=981-256-661-9 |publisher=World Scientific |year=2006 }}</ref>
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| :All local centers of mass vacuum free fall along identical (parallel-displaced, same speed) minimum action trajectories independent of all observable properties.
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| :The vacuum world line of a body immersed in a gravitational field is independent of all observable properties.
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| :The local effects of motion in a curved space (gravitation) are indistinguishable from those of an accelerated observer in flat space, without exception.
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| :Mass (measured with a balance) and weight (measured with a scale) are locally in identical ratio for all bodies (the opening page to Newton's ''[[Philosophiæ Naturalis Principia Mathematica]]'', 1687).
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| '''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 [[General relativity#Light deflection and gravitational time delay|light deflection and gravitational time delay]] made by non-local observers.
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| ==== Active, passive, and inertial masses ====
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| By definition of active and passive gravitational mass, the force on <math>M_1</math> due to the gravitational field of <math>M_0</math> is:
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| ::<math>F_1 = \frac{M_0^\mathrm{act} M_1^\mathrm{pass}}{r^2}</math>
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| Likewise the force on a second object of arbitrary mass<sub>2</sub> due to the gravitational field of mass<sub>0</sub> is:
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| ::<math>F_2 = \frac{M_0^\mathrm{act} M_2^\mathrm{pass}}{r^2}</math>
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| By definition of inertial mass:
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| ::<math>F = m^\mathrm{inert} a</math>
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| If <math>m_1</math> and <math>m_2</math> are the same distance <math>r</math> from <math>m_0</math> then, by the weak equivalence principle, they fall at the same rate (i.e. their accelerations are the same)
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| ::<math>a_1 = \frac{F_1}{m_1^\mathrm{inert}} = a_2 = \frac{F_2}{m_2^\mathrm{inert}}</math>
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| Hence:
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| ::<math>\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}}</math>
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| Therefore:
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| ::<math>\frac{M_1^\mathrm{pass}}{m_1^\mathrm{inert}} = \frac{M_2^\mathrm{pass}}{m_2^\mathrm{inert}}</math>
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| In other words, passive gravitational mass must be proportional to inertial mass for all objects.
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| Furthermore by [[Newton's third law of motion]]:
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| ::<math>F_1 = \frac{M_0^\mathrm{act} M_1^\mathrm{pass}}{r^2}</math>
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| must be equal and opposite to
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| ::<math>F_0 = \frac{M_1^\mathrm{act} M_0^\mathrm{pass}}{r^2}</math>
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| It follows that:
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| ::<math>\frac{M_0^\mathrm{act}}{M_0^\mathrm{pass}} = \frac{M_1^\mathrm{act}}{M_1^\mathrm{pass}}</math>
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| In other words, passive gravitational mass must be proportional to active gravitational mass for all objects.
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| The dimensionless Eötvös-parameter <math>\eta(A,B)</math> is the difference of the ratios of gravitational and inertial masses divided by their average for the two sets of test masses "A" and "B."
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| :<math>\eta(A,B)=2\frac{ \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}</math>
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| <!-- I have created [[User talk:Lemmiwinks2#Redundant edits (active, passive, and inertial masses)|a list of known places where the above material appears]]. -->
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| ====Tests of the weak equivalence principle====
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| Tests of the weak equivalence principle are those that verify the equivalence of gravitational mass and inertial mass. An obvious test is dropping two contrasted objects in hard vacuum, e.g., inside [[Fallturm Bremen]].
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| | |
| {| class="wikitable"
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| |-
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| ||'''Researcher'''
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| ||'''Year'''
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| ||'''Method'''
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| ||'''Result'''
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| |-
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| ||[[John Philoponus]]{{Clarify|date=August 2009}}
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| ||6th century
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| ||Described correctly the effect of dropping balls of different masses
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| ||no detectable difference
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| |-
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| ||[[Simon Stevin]]<ref>{{cite book |last1=Devreese |first1=Jozef T. |authorlink1=Jozef T. Devreese |last2=Vanden Berghe |first2=Guido |year=2008 |title='Magic Is No Magic': The Wonderful World of Simon Stevin |url=http://books.google.co.kr/books?isbn=1845643917 |page=154 |isbn=9781845643911 }}</ref>
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| ||~1586
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| ||Dropped lead balls of different masses off the [[Nieuwe Kerk (Delft)|Delft churchtower]]
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| ||no detectable difference
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| |-
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| ||[[Galileo Galilei]]{{Clarify|date=August 2009}}
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| ||~1610
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| ||Rolling balls down inclined planes
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| ||no detectable difference
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| |-
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| ||[[Isaac Newton]]
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| ||~1680
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| ||measure the [[Frequency|period]] of pendulums of different mass but identical length
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| ||no measurable difference
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| |-
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| ||[[Friedrich Wilhelm Bessel]]
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| ||1832
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| ||measure the period of pendulums of different mass but identical length
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| ||no measurable difference
| |
| |-
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| ||[[Loránd Eötvös]]
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| ||1908
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| ||measure the [[torsion (mechanics)|torsion]] on a wire, suspending a balance beam, between two nearly identical masses under the acceleration of [[gravity]] and the [[rotation]] of the [[Earth]]
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| ||difference is less than 1 part in 10<sup>9</sup>
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| |-
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| ||[[P. G. Roll|Roll]], [[Robert Krotkov|Krotkov]] and [[Robert H. Dicke|Dicke]]
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| ||1964
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| ||Torsion balance experiment, dropping [[aluminum]] and [[gold]] test masses
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| ||<math>|\eta(\mathrm{Al},\mathrm{Au})|=(1.3\pm1.0)\times10^{-11}</math><ref name="RollKrotkovDicke">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. 442-517</ref>
| |
| |-
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| ||[[David Scott]]
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| ||1971
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| ||Dropped a falcon feather and a hammer at the same time on the Moon
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| ||no detectable difference (not a rigorous experiment, but very dramatic being the first lunar one<ref>http://www.youtube.com/watch?v=MJyUDpm9Kvk</ref>)
| |
| |-
| |
| ||[[Vladimir Borisovich Braginski|Braginsky]] and [[Vladimir Ivanovich Panov|Panov]]
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| ||1971
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| ||Torsion balance, aluminum and [[platinum]] test masses, measuring acceleration towards the sun
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| ||difference is less than 1 part in 10<sup>12</sup>
| |
| |-
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| ||Eöt-Wash group
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| ||1987–
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| ||Torsion balance, measuring acceleration of different masses towards the earth, sun and galactic center, using several different kinds of masses
| |
| ||<math>\eta(\text{Earth},\text{Be-Ti})=(0.3 \pm 1.8)\times 10^{-13}</math><ref>{{cite journal |last1=Schlamminger |first1=Stephan |last2=Choi |first2=Ki-Young |last3=Wagner |first3=Todd A. |last4=Gundlach |first4=Jens H. |last5=Adelberger |first5=Eric G. |title=Test of the Equivalence Principle Using a Rotating Torsion Balance |journal=Physical Review Letters |volume=100 |issue=4 |year=2008 |doi=10.1103/PhysRevLett.100.041101 |bibcode=2008PhRvL.100d1101S |arxiv=0712.0607 }}</ref>
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| |}
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| | |
| See:<ref>Ciufolini, Ignazio; Wheeler, John A.; "Gravitation and Inertia", Princeton, NJ: Princeton University Press, 1995, pp. 117-119</ref>
| |
| | |
| {| class="wikitable"
| |
| |-
| |
| ||'''Year'''
| |
| ||'''Investigator'''
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| ||'''Sensitivity'''
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| ||'''Method'''
| |
| |-
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| ||500?
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| ||Philoponus <ref>Philoponus, John; "Corollaries on Place and Void", translated by David Furley, Ithaca, NY: Cornell University Press, 1987</ref>
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| ||"small"
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| ||Drop Tower
| |
| |-
| |
| ||1585
| |
| ||Stevin <ref>Stevin, Simon; ''De Beghinselen der Weeghconst ["Principles of the Art of Weighing"]'', Leyden, 1586; Dijksterhuis, Eduard J.; "The Principal Works of Simon Stevin", Amsterdam, 1955</ref>
| |
| ||5×10<SUP>-2</SUP>
| |
| ||Drop Tower
| |
| |-
| |
| ||1590?
| |
| ||Galileo <ref>Galilei, Galileo; "Discorsi e Dimostrazioni Matematiche Intorno a Due Nuove Scienze", Leida: Appresso gli Elsevirii, 1638; "Discourses and Mathematical Demonstrations Concerning Two New Sciences," Leiden: Elsevier Press, 1638</ref>
| |
| ||2×10<SUP>-2</SUP>
| |
| ||Pendulum, Drop Tower
| |
| |-
| |
| ||1686
| |
| ||Newton <ref>Newton, 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, CA: 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, CA: University of California Press, 1999</ref>
| |
| ||10<SUP>-3</SUP>
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| ||Pendulum
| |
| |-
| |
| ||1832
| |
| ||Bessel <ref>Bessel, Friedrich W.; "Versuche Uber die Kraft, mit welcher die Erde Körper von verschiedner Beschaffenhelt anzieht", ''Annalen der Physik und Chemie'', Berlin: J. Ch. Poggendorff, 25 401–408 (1832)</ref>
| |
| ||2×10<SUP>-5</SUP>
| |
| ||Pendulum
| |
| |-
| |
| ||1910
| |
| ||Southerns <ref>Southerns, Leonard; "A Determination of the Ratio of Mass to Weight for a Radioactive Substance", ''Proceedings of the Royal Society of London'', 84 325–344 (1910), doi:10.1098/rspa.1910.0078</ref>
| |
| ||5×10<SUP>-6</SUP>
| |
| ||Pendulum
| |
| |-
| |
| ||1918
| |
| ||Zeeman <ref>Zeeman, Pieter; "Some experiments on gravitation: The ratio of mass to weight for crystals and radioactive
| |
| substances", ''Proceedings of the Koninklijke Nederlandse Akademie van Wetenschappen'', Amsterdam 20(4) 542–553 (1918)</ref>
| |
| ||3×10<SUP>-8</SUP>
| |
| ||Torsion Balance
| |
| |-
| |
| ||1922
| |
| ||Eötvös <ref>Eötvös, Loránd; ''Mathematische and naturnissenschaftliche Berichte aus Ungarn'' 8 65 (1889); ''Annalen der Physik'' (Leipzig) 68 11 (1922); ''Physical Review D'' 61(2) 022001 (1999)</ref>
| |
| ||5×10<SUP>-9</SUP>
| |
| ||Torsion Balance
| |
| |-
| |
| ||1923
| |
| ||Potter <ref>Potter, Harold H.; "Some Experiments on the Proportionality of Mass and Weight", ''Proceedings of the Royal Society of London'' 104 588–610 (1923), doi:10.1098/rspa.1923.0130</ref>
| |
| ||3×10<SUP>-6</SUP>
| |
| ||Pendulum
| |
| |-
| |
| ||1935
| |
| ||Renner <ref>Renner, János; "Kísérleti vizsgálatok a tömegvonzás és tehetetlenség arányosságáról", ''Mathematikai és Természettudományi Értesítő'' 53 569 (1935), Budapest</ref>
| |
| ||2×10<SUP>-9</SUP>
| |
| ||Torsion Balance
| |
| |-
| |
| ||1964
| |
| ||Dicke, Roll, Krotkov <ref name="RollKrotkovDicke" />
| |
| ||3x10<SUP>-11</SUP>
| |
| ||Torsion Balance
| |
| |-
| |
| ||1972
| |
| ||Braginsky, Panov <ref>Braginski, Vladimir Borisovich; Panov, Vladimir Ivanovich; Журнал Экспериментальной и Теоретической Физики ''(Zhurnal Éksperimental’noĭ i Teoreticheskoĭ Fiziki, Journal of Experimental and Theoretical Physics)'' 61 873 (1971)</ref>
| |
| ||10<SUP>-12</SUP>
| |
| ||Torsion Balance
| |
| |-
| |
| ||1976
| |
| ||Shapiro, et al.<ref>Shapiro, Irwin I.; Counselman III, Charles C.; King, Robert W.; [http://prl.aps.org/pdf/PRL/v36/i11/p555_1 "Verification of the principle of equivalence for massive bodies"], ''Physical Review Letters'' 36 555–558 (1976)</ref>
| |
| ||10<SUP>-12</SUP>
| |
| ||Lunar Laser Ranging
| |
| |-
| |
| ||1981
| |
| ||Keiser, Faller <ref>Keiser, George M.; Faller, James E.; ''Bulletin of the American Physical Society'' 24 579 (1979)</ref>
| |
| ||4×10<SUP>-11</SUP>
| |
| ||Fluid Support
| |
| |-
| |
| ||1987
| |
| ||Niebauer, et al.<ref>Niebauer, Timothy M.; McHugh, Martin P.; Faller, James E.; "Galilean test for the fifth force", ''Physical Review Letters'' 59 609–612 (1987)</ref>
| |
| ||10<SUP>-10</SUP>
| |
| ||Drop Tower
| |
| |-
| |
| ||1989
| |
| ||Stubbs, et al.<ref>Stubbs, Christopher W.; Adelberger, Eric G.; Heckel, Blayne R.; Rogers, Warren F.; Swanson, H. Erik; Watanabe, R.; Gundlach, Jens H.; Raab, Frederick J.; "Limits on Composition-Dependent Interactions Using a Laboratory Source: Is There a ″Fifth Force″ Coupled to Isospin?", ''Physical Review Letters'' 62 609 (1989)</ref>
| |
| | |
| ||10<SUP>-11</SUP>
| |
| ||Torsion Balance
| |
| |-
| |
| ||1990
| |
| ||Adelberger, Eric G.; et al.<ref>Adelberger, Eric G.; Stubbs, Christopher W.; Heckel, Blayne R.; Su, Y.; Swanson, H. Erik; Smith, G. L.; Gundlach, Jens H.; Rogers, Warren F.; "Testing the equivalence principle in the field of the Earth: Particle physics at masses below 1 μeV?", ''Physical Review D'' 42 3267–3292 (1990)</ref>
| |
| ||10<SUP>-12</SUP>
| |
| ||Torsion Balance
| |
| |-
| |
| ||1999
| |
| ||Baessler, et al.<ref>Baeßler, Stefan; et al.; ''Classical Quantum Gravity'' 18(13) 2393 (2001); Baeßler, 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)</ref>
| |
| ||5x10<SUP>-14</SUP>
| |
| ||Torsion Balance
| |
| |-
| |
| ||cancelled?
| |
| ||[http://einstein.stanford.edu/STEP/ MiniSTEP]
| |
| ||10<SUP>-17</SUP>
| |
| ||Earth Orbit
| |
| |-
| |
| ||2015?
| |
| ||[http://smsc.cnes.fr/MICROSCOPE/index.htm MICROSCOPE]
| |
| ||10<SUP>-16</SUP>
| |
| ||Earth Orbit
| |
| |-
| |
| ||2015?
| |
| ||[http://www.cfa.harvard.edu/pag/index_files/Page1098.htm Reasenberg/SR-POEM]<ref>Reasenberg, Robert D.; Patla, Biju R.; Phillips, James D.; Thapa, Rajesh; [http://arxiv.org/abs/1206.0028 "Design and characteristics of a WEP test in a sounding-rocket payload"], ''Classical Quantum Gravity'' 27, 095005 (2010); http://www.cfa.harvard.edu/PAG/6-%2520Presentations/Reasenberg_Q2C3_web.pdf
| |
| </ref>
| |
| ||2×10<SUP>-17</SUP>
| |
| ||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<ref name="Dittus">{{cite journal |last=Dittus |first=Hansjörg |first2=Claus |last2=Lāmmerzahl |title=Experimental Tests of the Equivalence Principle and Newton’s Law in Space |page=95 |volume=758 | doi=10.1063/1.1900510 |journal=Gravitation and Cosmology: 2nd Mexican Meeting on Mathematical and Experimental Physics, AIP Conference Proceedings |url=http://www.zarm.uni-bremen.de/2forschung/gravi/publications/papers/2005DittusLaemmerzahl.pdf |bibcode=2005AIPC..758...95D |format=PDF }}</ref> – [[STEP (Satellite Test of the Equivalence Principle)]], Galileo Galilei, and [[MICROSCOPE (satellite)|MICROSCOPE (MICROSatellite pour l'Observation de Principe d'Equivalence)]] – will test the weak equivalence principle in space, to much higher accuracy.
| |
| | |
| Proposals that may lead to a [[quantum gravity|quantum theory of gravity]] such as [[string theory]] and [[loop quantum gravity]] predict violations of the weak equivalence principle because they contain many light [[scalar field]]s with long [[Compton wavelength]]s, which should generate [[fifth force]]s and variation of the fundamental constants. Heuristic arguments suggest that the magnitude of these equivalence principle violations could be in the 10<sup>−13</sup> to 10<sup>−18</sup> range.<ref name="Overduin2009" /> Currently envisioned tests of the weak equivalence principle are approaching a degree of sensitivity such that ''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.<ref name="Overduin2009">{{cite doi|10.1016/j.asr.2009.02.012|noedit}}</ref>
| |
| | |
| ===The Einstein equivalence principle===<!-- This section is linked from [[Gravitational field]] --> | |
| The Einstein equivalence principle states that the weak equivalence principle holds, and that:<ref name="Lāmmerzahl">{{cite book |last=Haugen |first=Mark P. |first2=Claus |last2=Lämmerzahl |title=Principles of Equivalence: Their Role in Gravitation Physics and Experiments that Test Them |year=2001 |publisher=Springer |isbn=978-3-540-41236-6 |arxiv=gr-qc/0103067}}</ref>
| |
| : ''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.''
| |
| Here "local" has a very special meaning: not only must the experiment not look outside the laboratory, but it must also be small compared to variations in the gravitational field, [[tidal forces]], so that the entire laboratory is freely falling. It also implies the absence of interactions with "external" fields ''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 invariance|Lorentz invariant]] theory that satisfies the weak equivalence principle also satisfies the Einstein equivalence principle.
| |
| | |
| ''[[Leonard I. Schiff|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<ref>{{cite journal |first=Mark J. |last=Hadley |doi=10.1007/BF02764119 |journal=Foundations of Physics Letters |volume=10 |title=The Logic of Quantum Mechanics Derived from Classical General Relativity |pages=43–60 |year=1997 |arxiv=quant-ph/9706018|bibcode = 1997FoPhL..10...43H }}</ref> and Durand<ref>Durand, Stéphane; [http://stacks.iop.org/ob/4/S351 "An amusing analogy: modelling quantum-type behaviours with wormhole-based time travel"], ''Journal of Optics B: Quantum and Semiclassical Optics'', vol. 4, no. 4, doi:10.1088/1464-4266/4/4/319</ref>).
| |
| | |
| ====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]] [[fundamental physical constants|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'''
| |
| |-
| |
| ||[[fine structure constant]]
| |
| ||1976
| |
| ||Oklo
| |
| ||10<sup>−7</sup>
| |
| |-
| |
| ||[[weak interaction]] constant
| |
| ||1976
| |
| ||Oklo
| |
| ||10<sup>−2</sup>
| |
| |-
| |
| ||[[electron]]-[[proton]] mass ratio
| |
| ||2002
| |
| ||quasars
| |
| ||10<sup>−4</sup>
| |
| |-
| |
| ||proton [[gyromagnetic ratio|gyromagnetic factor]]
| |
| ||1976
| |
| ||astrophysical
| |
| ||10<sup>−1</sup>
| |
| |}
| |
| | |
| 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 10<sup>−5</sup> level) of the fine-structure constant from measurements of distant [[quasar]]s, see Webb et al.<ref>{{cite journal |first1=John K. |last1=Webb |first2=Michael T. |last2=Murphy |first3=Victor V. |last3=Flambaum |first4=Vladimir A. |last4=Dzuba |first5=John D. |last5=Barrow |first6=Chris W. |last6=Churchill |first7=Jason X. |last7=Prochaska |first8=Arthur M. |last8=Wolfe |doi=10.1103/PhysRevLett.87.091301 |journal=Physical Review Letters |title=Further Evidence for Cosmological Evolution of the Fine Structure Constant |volume=87 |issue=9 |year=2000 |arxiv=astro-ph/0012539 |pmid=11531558 |bibcode=2001PhRvL..87i1301W }}</ref> 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.
| |
| | |
| ===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.''
| |
| and
| |
| : ''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.''
| |
| 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 experiment]]s. The second part is the Einstein equivalence 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 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 tensor (general relativity)|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 force]]s (deviations from the gravitational force-law predicted by general relativity). These experiments typically look for failures of the [[inverse-square law]] (specifically [[Yukawa potential|Yukawa forces]] or failures of [[Birkhoff's theorem (relativity)|Birkhoff's theorem]]) behavior of gravity in the laboratory. The most accurate 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 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 [[astronomical radio source|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-Huygens|Cassini]] spacecraft. Together, these measurements have put tight limits on [[Brans-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 dwarf]]s orbiting it. The system will provide them a chance to test strong equivalence prinple in a strong gravitational field.<ref>{{cite journal |url=http://www.nature.com/nature/journal/vaop/ncurrent/full/nature12917.html#ref7 |title=A millisecond pulsar in a stellar triple system |first1=Scott M. |last1=Ransom |author2=et al. |journal=Nature |year=2014 |accessdate=8 January 2014 }}</ref>
| |
| | |
| ==Challenges to the equivalence principle==
| |
| One challenge to the equivalence principle is the [[Brans-Dicke theory]]. [[Self-creation cosmology]] is a modification of the [[Brans-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 School of Physics, University of New South Wales, Australia; the Centre for Astrophysics 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 Equivalence Principle, and could infer a very large or infinite universe, within which our `local' [[Hubble volume]] represents a tiny fraction."<ref>{{cite arxiv |eprint=1008.3907 |first1=John K. |last1=Webb |first2=Julian A. |last2=King |first3=Michael T. |last3=Murphy |first4=Victor V. |last4=Flambaum |first5=Robert F. |last5=Carswell |first6=Matthew B. |last6=Bainbridge |title=Evidence for spatial variation of the fine structure constant |class=astro-ph.CO |year=2010 }}</ref>
| |
| | |
| ==Explanations of the equivalence principle==
| |
| | |
| Dutch physicist and [[string theory|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 approach to explaining gravity 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 (cosmologist)|Michael Turner]] (who is credited as having coined the term "dark energy") as "the greatest embarrassment in the history of theoretical physics".<ref name=Wright2001>{{cite web |last=Wright |first=Karen |title=Very Dark Energy |url=http://discovermagazine.com/2001/mar/featdark#.USwYk6XmjoI |publisher=Discover Magazine |accessdate=26 February 2013 |date=01 March 2001 }}</ref> However, it should be noted that these ideas are far from settled and still very controversial.
| |
| | |
| ==Experiments==
| |
| *University of Washington<ref>[http://www.npl.washington.edu/eotwash/ Eöt-Wash group]</ref>
| |
| *Lunar Laser Ranging<ref>http://funphysics.jpl.nasa.gov/technical/grp/lunar-laser.html</ref>
| |
| *Galileo-Galilei satellite experiment<ref>http://eotvos.dm.unipi.it/nobili/</ref>
| |
| *[[STEP (satellite)|Satellite Test of the Equivalence Principle (STEP)]]<ref>http://einstein.stanford.edu/STEP/</ref>
| |
| *MICROSCOPE<ref>http://smsc.cnes.fr/MICROSCOPE/index.htm</ref>
| |
| *Satellite Energy Exchange (SEE)<ref>http://www.phys.utk.edu/see/</ref>
| |
| *"...Physicists in Germany have used an atomic interferometer to perform the most accurate ever test of the equivalence principle at the level of atoms..."<ref>[http://physicsworld.com/cws/article/news/2004/nov/16/equivalence-principle-passes-atomic-test 16 November 2004, physicsweb: Equivalence principle passes atomic test]</ref>
| |
| | |
| ==See also==
| |
| {{top}}
| |
| *[[General Relativity]]
| |
| *[[General covariance]]
| |
| *[[Classical Mechanics]]
| |
| *[[Frame of reference]]
| |
| *[[Inertial frame|Inertial frame of reference]]
| |
| *[[Mach's principle]]
| |
| *[[Equivalence principle (geometric)]]
| |
| {{mid}}
| |
| *[[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]]
| |
| {{bottom}}
| |
| | |
| ==Notes==
| |
| {{Reflist}}
| |
| | |
| ==References==
| |
| {{reflist|colwidth=30em}}
| |
| {{Refbegin}}
| |
| * 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. Møller (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; "Über das Relativitätsprinzip 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, NJ, 1989), Anna Beck translator. This is Einstein's first statement of the equivalence principle.
| |
| * Einstein, Albert; "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 Albert Einstein. Vol. 3 : The Swiss years: writings, 1909–1911'' (Princeton University Press, Princeton, NJ, 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 [http://www1.kcn.ne.jp/~h-uchii/gen.GR.html 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, NY: W. H. Freeman and Company, 1973, Chapter 16 discusses the equivalence principle.
| |
| * Ohanian, Hans; and Ruffini, Remo; ''Gravitation and Spacetime 2nd edition'', New York, NY: 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.; [http://www.livingreviews.org/lrr-2006-3 ''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 [http://relativity.livingreviews.org/open?pubNo=lrr-2006-3&page=articlesu1.html 2.1] and [http://relativity.livingreviews.org/open?pubNo=lrr-2006-3&page=articlesu4.html 3.1], respectively.
| |
| * Friedman, Michael; ''Foundations of Space-Time Theories'', Princeton, NJ: Princeton University Press, 1983. Chapter V discusses the equivalence principle.
| |
| {{Refend}}
| |
| | |
| ==External links==
| |
| * [http://science.nasa.gov/headlines/y2007/18may_equivalenceprinciple.htm Equivalence Principle] at NASA, including tests
| |
| * [http://www.phy.syr.edu/courses/modules/LIGHTCONE/equivalence.html Introducing The Einstein Principle of Equivalence] from Syracuse University
| |
| * [http://www.mathpages.com/rr/s5-06/5-06.htm The Equivalence Principle] at MathPages
| |
| * [http://emis.math.ecnu.edu.cn/journals/LRG/Articles/lrr-2001-4/node3.html The Einstein Equivalence Principle] at Living Reviews on General Relativity
| |
| | |
| {{Einstein}}
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| {{Relativity}}
| |
| {{Use dmy dates|date=August 2011}}
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| | |
| {{DEFAULTSORT:Equivalence Principle}}
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| [[Category:Concepts in physics]]
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| [[Category:General relativity]]
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| [[Category:Albert Einstein]]
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| [[Category:Principles]]
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| [[Category:Philosophy of astronomy]]
| |