In relativity the equivalence principle is applied to several related concepts dealing with the uniformity of physical measurements in different frames of reference. They are related to the Copernican idea that the laws of physics should be the same everywhere in the universe, but also to Albert Einstein's assertion that the gravitational "force" as experienced locally while standing on a massive body (such as the Earth) is actually the same as the pseudo-force experienced by an observer in a non-inertial (accelerated) frame of reference. This principle is: In physics, the term relativity is used in several related contexts: Galileo first developed the principle of relativity, which was the postulate that claimed that the laws of physics be the same for all observers, and advocated a classical view that time was a universal constant. ... A frame of reference in physics is a set of axes which enable an observer to measure the aspect, position and motion of all points in a system relative to the reference frame. ... The Copernican Principle is the philosophical statement that no special observers should be proposed. ... Portrait of Albert Einstein taken by Yousuf Karsh on February 11, 1948 Albert Einstein (March 14, 1879 – April 18, 1955) was a theoretical physicist who is widely regarded as the greatest scientist of the 20th century. ... In physics, an inertial frame of reference, or inertial frame for short (also descibed as absolute frame of reference), is a frame of reference in which the observers move without the influence of any accelerating or decelerating force. ...

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

This (known as the weak equivalence principle) is a rule for determining if one is in an accelerated frame of reference. It played a crucial role in the development of general relativity. Two-dimensional visualisation of space-time distortion. ...

History

The origins of the equivalence principle begin with Galileo demonstrating in the late 16th century that all objects are accelerated towards the center of the Earth at the same rate. This was codified by Newton with his gravitational theory in which it was postulated that inertial and gravitational masses are one and the same. Galileo can refer to: Galileo Galilei, astronomer, philosopher, and physicist (1564 - 1642) the Galileo spacecraft, a NASA space probe that visited Jupiter and its moons the Galileo positioning system Life of Galileo, a play by Bertolt Brecht Galileo (1975) - screen adaptation of the play Life of Galileo by Bertolt Brecht...

In Newtonian mechanics, gravity is assumed to be a force. This force draws objects towards the center of a massive body. At the Earth's surface, the force of gravity is counter-balanced by the mechanical resistance of the Earth's surface. So a person at rest on the surface of a (non-rotating) massive object is in an inertial frame of reference. The force of gravity is counter-balanced by the upward force of the surface on that person, and the net force is zero. While this picture works very well for most calculations, it remains a mystery why the inertial mass in Newton's second law, F = ma, is equal to the gravitational mass in Newton's law of universal gravitation. Classical mechanics is a model of the physics of forces acting upon bodies. ... This article covers the physics of gravitation. ... In physics, a net force acting on a body causes that body to accelerate; that is, to change its velocity. ... Newtons laws of motion are the three scientific laws which Isaac Newton discovered concerning the behaviour of moving bodies. ... The law of universal gravitation states that gravitational force between masses decreases with the distance between them, according to an inverse-square law. ...

The equivalence principle proper was introduced by Albert Einstein in 1907. An that time, he made the observation that the acceleration of bodies towards the center of the Earth with acceleration 1g (g=9.81 m/s² is the acceleration of gravity at the Earth's surface) is equivalent to the acceleration of inertially moving bodies that one would observe if one was on a rocket in free space being accelerated at a rate of 1g. Einstein stated it thus: 1907 was a common year starting on Tuesday (see link for calendar). ... Acceleration is the time rate of change of velocity, and at any point on a v_t graph, it is given by the gradient of the tangent to that point In physics, acceleration (symbol: a) is defined as the rate of change (or time derivative) of velocity. ... Earth, also known as the Earth or Terra, is the third planet outward from the Sun. ...

we [...] assume the complete physical equivalence of a gravitational field and a corresponding acceleration of the reference system. (Einstein, 1907)

That is, remaining at rest in a uniform gravitational field is physically equivalent to experiencing an acceleration (e.g. being at rest with respect to the Earth, while under the influence of its gravitational field, is an accelerated state of motion). From this principle, Einstein deduced that free-fall is actually inertial motion. The idea was precisely formulated by Einstein in 1911, referring to two frames of reference K and K'. The frame K is in a uniform gravitational field, whereas K' has no gravitational field but is uniformly accelerated such that objects in two frames experience identical forces: Freefall or free fall in the strict sense is the condition of acceleration which is due only to gravity. ... In physics, an inertial frame of reference, or inertial frame for short (also descibed as absolute frame of reference), is a frame of reference in which the observers move without the influence of any accelerating or decelerating force. ...

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)

This observation was the start of a process that led to the development of general relativity. Einstein suggested that it should be elevated to the status of a general principle, when constructing his theory of relativity:

As long as we restrict ourselves to purely mechanical processes in the realm where Newton'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 heurisitic 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)

He used this principle, together with special relativity, to predict that clocks run at different rates in a gravitational potential and the bending of light-rays in a gravitational field, even before he developed the concept of curved-space time. In physics, gravitational potential is the measure of potential energy an object possesses due to its position in a gravitational field. ... The three principal experimental tests of general relativity are the perihelion shift of the planet Mercurys orbit, the bending of starlight by a massive object and the existence of gravitational waves. ...

Thus, in general relativity the situation is quite different than in Newtonian mechanics. Since inertial mass is the same as gravitational mass in the gravitational fields of massive bodies, the equivalence principle indicates that free-fall is actually inertial motion. In that case, there is only one force acting on a person standing on the surface of a massive object, and that is the upward force of the surface on that person. Although the equivalence principle helped to guide the development of general relativity, the equivalence principle, rather than being a founding principle, is a simple consequence of the geometrical nature of the theory. There is no place in the theory to set the inertial and gravitational masses equal, because there is no force law for gravity. The inertial reference frames are defined as those which are freely falling. This observation is now known as the weak equivalence principle. Inertial mass is a measure of the resistance of an entity to a change in its velocity relative to an inertial frame. ... Two-dimensional visualisation of space-time distortion. ...

Interest in the modern extensions of the equivalence principle was catalyzed in 1937 when Paul Dirac formulated his large numbers hypothesis which asserts that large, dimensionless numbers should not arise as fundamental quantities in physics: there should only be one fundamental energy scale in physics. He supported this by pointing out a coincidence: the dimensionless ratio of electric to gravitational forces in a hydrogen atom is about the same as the age of the universe, measured by the time it takes light to cross the hydrogen atom. Both are about 10⁴⁰. To explain this surprising coincidence, Dirac postulated that Newton's constant varied as the inverse of the age of the universe, and the feebleness of gravity was due to the great age of the universe. While he turned out to be wrong, he led people to consider that the laws of physics may be different at different points in space and time, and the values of the physical constants, rather than being fundamental, may be set dynamically. Paul Adrien Maurice Dirac, (August 8, 1902 - October 20, 1984) was a British theoretical physicist and a founder of the field of quantum physics. ... The Dirac large numbers hypothesis refers to an observation made by Paul Dirac in 1937 relating ratios of size scales in the universe to that of force scales. ... In physics, energy scale is a particular value of energy determined with the precision of one order (or a few orders) of magnitude. ... General Name, Symbol, Number Hydrogen, H, 1 Chemical series nonmetals Group, Period, Block 1 (IA), 1 , s Density, Hardness 0. ... In physics, dynamics is the branch of mechanics that is concerned with the effects of forces on the motion of objects. ...

Modern Usage

A number of different forms of the equivalence principle are used today. The weak equivalence principle, also known as the universality of free fall, is closest to Einstein's original statement:

The trajectory of a falling test body depends only on its initial position and velocity, and is independent of its composition.

The principle does not apply to large bodies, which might experience tidal forces, or heavy bodies, whose presence will substantially change the gravitational field around them.

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. 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 differ only in whether they apply to gravitational experiments or not. Special relativity (SR) or the special theory of relativity is the physical theory published in 1905 by Albert Einstein. ...

The Einstein equivalence principle states that the result of a local non-gravitational experiment in an inertial frame of reference is independent of the velocity or location in the universe of the experiment. This is an extension of the postulates of special relativity which require that dimensionless physical values such as the fine-structure constant and electron-to-proton mass ratio be constant. Many workers believe that any Lorentz invariant theory that satisfies the weak equivalence principle also satisfies the Einstein equivalence principle. In general, the principle of relativity is the requirement that the laws of physics be the same for all observers. ... In the physical sciences, a dimensionless number (or more precisely, a number with the dimensions of 1) is a quantity which describes a certain physical system and which is a pure number without any physical units; it does not change if one alters ones system of units of measurement... The fine-structure constant or Sommerfeld fine-structure constant, usually denoted , is the fundamental physical constant characterizing the strength of the electromagnetic interaction. ... Properties The electron (also called negatron, commonly represented as e−) is a subatomic particle. ... For alternative meanings see proton (disambiguation). ... Lorentz covariance is a term in physics for the property of space time, that in two different frames of reference, located at the same event in spacetime but moving relative to each other, all non-gravitational laws must make the same predictions for identical experiments. ...

The strong equivalence principle states that the results of any local experiment, gravitational or not, in an inertial frame of reference are independent of where and when in the universe it is conducted. 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. General relativity is the only known theory of gravity compatible with this form of the equivalence principle. According to the law of universal gravitation, the attractive force between two bodies is proportional to the product of their masses and inversely proportional to the square of the distance between them. ... Occasionally, physicists have hypothesized the existence of a fifth force in addition to the four (technically, three) known fundamental forces. ... Two-dimensional visualisation of space-time distortion. ...

Tests of the weak equivalence principle

Tests of the weak equivalence principle are those that verify the equivalence of gravitational mass and inertial mass. These experiments demonstrate that all objects fall at the same rate when the effect of air resistance is either eliminated or negligible. The simplest way to test the weak equivalence principle is to drop two objects of different masses or compositions in a vacuum, and see if they hit the ground at the same time. More sophisticated tests use a torsion balance of a type invented by Roland Eötvös.

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 – STEP (Satellite Test of the Equivalence Principle), Galileo Galilei, and MICROSCOPE (MICROSattelite pour l'Observation de Principe d'Equivalence) – will test the weak equivalence principle in space, to much higher accuracy. Galileo Galilei (Pisa, February 15, 1564 – Arcetri, January 8, 1642), was a Tuscan astronomer, philosopher, and physicist who is closely associated with the scientific revolution. ... Leaning tower of Pisa The Leaning Tower of Pisa (Italian: Torre di Pisa) is the campanile, or bell tower, for the Italian city of Pisas cathedral, located in the Campo dei Miracoli. ... Sir Isaac Newton in Knellers 1689 portrait Sir Isaac Newton (25 December 1642 – 20 March 1727 by the Julian calendar in use in England at the time; or 4 January 1643 – 31 March 1727 by the Gregorian calendar) was an English physicist, mathematician, astronomer, philosopher, and alchemist who wrote... A period is an arbitrary interval of time. ... Friedrich Wilhelm Bessel (July 22, 1784 – March 17, 1846) was a German mathematician, astronomer, and systematizer of the Bessel functions (which, despite their name, were discovered by Daniel Bernoulli). ... A period is an arbitrary interval of time. ... In mathematics, the term torsion has several meanings, mostly unrelated to each other. ... This article covers the physics of gravitation. ... This article is about rotation as a movement of a physical body. ... Earth, also known as the Earth or Terra, is the third planet outward from the Sun. ... The word billion, and its equivalents in other languages, refer to one of two different numbers. ... General Name, Symbol, Number aluminium, Al, 13 Chemical series poor metals Group, Period, Block 13 (IIIA), 3, p Density, Hardness 2700 kg/m3, 2. ... General Name, Symbol, Number Gold, Au, 79 Chemical series transition metals Group, Period, Block 11 (IB), 6, d Density, Hardness 19300 kg/m3, 2. ... David R. Scott (born June 6, 1932) a former NASA Astronaut, was one of the third group of astronauts named by NASA in October 1963 and is one of only twelve men who have walked on the moon. ... General Name, Symbol, Number aluminium, Al, 13 Chemical series poor metals Group, Period, Block 13 (IIIA), 3, p Density, Hardness 2700 kg/m3, 2. ... Platinum is also a certification by the RIAA and other world recording industries, see: RIAA certification General Name, Symbol, Number Platinum, Pt, 78 Chemical series transition metals Group, Period, Block 10 , 6, d Density, Hardness 21. ... The numeral trillion refers to one of two number values, depending on the context of where and how it is being used. ... The University of Washington, founded in 1861, is a major public research university in the Seattle metropolitan area. ... Earth, also known as the Earth or Terra, is the third planet outward from the Sun. ... The Sun (occasionally referred to as Sol) is the star at the centre of our solar system. ... In cosmology, dark matter consists of elementary particles that cannot be detected by their emitted radiation but whose presence can be inferred from gravitational effects on visible matter such as stars and galaxies. ... The Galactic Center is the rotational center of the Milky Way galaxy. ...

The need to continue testing Einstein's theory of gravity may seem superfluous, as it is by far the most elegant theory of gravity known, and is perfectly compatible with all observations to date. However, no quantum theory of gravity is known, and most suggestions violate one of the equivalence principles at some level. String theory, supergravity and even quintessence, for example, seem to violate the weak equivalence principle because they contain many light scalar fields with long Compton wavelengths. These fields should generate fifth forces and variation of the fundamental constants. There are a number of mechanisms that have been suggested by physicists to reduce these violations of the equivalence principle to below observable levels. Elegance is the attribute of being tastefully designed or decorated, with focus on basic features. ... Quantum gravity is the field of theoretical physics attempting to unify the theory of quantum mechanics, which describes three of the fundamental forces of nature, with general relativity, the theory of the fourth fundamental force: gravity. ... A string theory is a physical model whose fundamental building blocks are one-dimensional extended objects (strings) rather than the zero-dimensional points (particles) that were the basis of most earlier physics. ... A supergravity theory is a field theory combining supersymmetry and general relativity. ... The word Quintessence is used in different fields: In physics, Quintessence is a hypothetical form of energy postulated to exist as a possible explanation of observations of an accelerating universe. ... In mathematics and physics, a scalar field associates a single number (or scalar) to every point in space. ... The Compton wavelength of a particle is given by , where is the Planck constant, is the particles mass and is the speed of light. ... Occasionally, physicists have hypothesized the existence of a fifth force in addition to the four (technically, three) known fundamental forces. ...

The Einstein equivalence principle

The Einstein equivalence principle states that the weak equivalence principle holds, and that

The outcome of any local non-gravitational experiment in a laboratory moving in an inertial frame of reference is independent of the velocity of the laboratory, or 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 moving inertially. The tidal force is a secondary effect of the force of gravity and is responsible for the tides. ...

The most important consequence of this principle is that any of the fundamental physical parameters, other than masses and Newton's gravitational constant, must not depend on where in space or time we measure them. In practice, we measure dimensionless numbers, such as the ratio of two masses, or coupling constants such as the fine-structure constant.

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.

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 occuring Oklo fission reactor, where nuclear reactions similar to ones we observe today have been shown to have occured underground approximately two billion years ago. These reactions are extremely sensitive to the values of the fundamental constants. In the physical sciences, a dimensionless number (or more precisely, a number with the dimensions of 1) is a quantity which describes a certain physical system and which is a pure number without any physical units; it does not change if one alters ones system of units of measurement... Oklo is a place in the West African state of Gabon. ...

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^-5 level) of the fine-structure constant from measurements of distant quasars. Other researchers dispute these findings. Other tests of the Einstein equivalence principle are gravitational redshift experiments, which test the position independence of experiments. The fine-structure constant or Sommerfeld fine-structure constant, usually denoted , is the fundamental physical constant characterizing the strength of the electromagnetic interaction. ... The weak nuclear force or weak interaction is one of the four fundamental forces of nature. ... Properties The electron (also called negatron, commonly represented as e−) is a subatomic particle. ... For alternative meanings see proton (disambiguation). ... Gyromagnetic ratio is the ratio of magnetic dipole moment to the angular momentum of a system. ... The strong nuclear force or strong interaction (also called color force or colour force) is a fundamental force of nature which affects only quarks and antiquarks, and is mediated by gluons in a similar fashion to how the electromagnetic force is mediated by photons. ... This view, taken with infrared light, is a false-color image of a quasar-starburst tandem with the most luminous starburst ever seen in such a combination. ...

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, whether gravitational or not, in a laboratory moving in an inertial frame of reference is independent of velocity of the laboratory, or its location in spacetime.

The first part is a version of the weak equivalence principle that it applies to objects that exert a gravitational force on themselves, such as stars, planets, black holes or Cavendish experiments. The second part is the Einstein equivalence principle, 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. This idealized requirement has been misunderstood. This form of the equivalence principle does not imply that the effects of a gravitational field cannot be measured by observers in free-fall. For example, an observer in free-fall into a black hole will experience strong tidal forces: he will notice a more powerful force on his feet than his head. In physics, the purpose of the torsion bar experiment is to estimate the gravitational constant. ... This article is about an object in astrophysics. ...

The strong equivalence suggests that gravity is an entirely geometrical by nature (that is metric alone determines the effect of gravity) and does not have an 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. In mathematics, in Riemannian geometry, the metric tensor is a tensor of rank 2 that is used to measure distance and angle in a space. ... The cosmological constant (usually denoted by the Greek capital letter lambda: Λ) occurs in Einsteins theory of general relativity. ... Brans-Dicke theory is an extension to Einsteins theory of general relativity. ...

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%. In cosmology, Big Bang nucleosynthesis refers to the process of element production during the early phases of the universe, shortly after the Big Bang. ...

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 Eöt-Wash group. A future satellite experiment, SEE (Sattelite 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, using very long baseline interferometry, in particular the Lunar Laser Ranging Experiment. These measurments have put tight limits on Brans-Dicke theory. Occasionally, physicists have hypothesized the existence of a fifth force in addition to the four (technically, three) known fundamental forces. ... In physics, an inverse-square law is any physical law stating that some quantity is inversely proportional to the square of the distance from a point. ... A Yukawa potential (also called a screened Coulomb potential) is a potential of the form Hideki Yukawa showed in the 1930s that such a potential arises from the exchange of a massless scalar field such as the field of the pion whose mass is . ... This article needs cleanup. ... Categories: Physics stubs | Measuring instruments | Astronomy | General relativity | Apollo program ...

See also

• Mach's principle
• Principle of relativity
• Cosmological principle
• Copernican principle

In general, the principle of relativity is the requirement that the laws of physics be the same for all observers. ... The Cosmological Principle is a principle invoked in cosmology that severely restricts the large variety of possible cosmological theories: On large scales, the Universe is homogeneous and isotropic. ... The Copernican Principle is the philosophical statement that no special observers should be proposed. ...

References

• Albert Einstein, "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.
• Albert Einstein, "Über den Einfluß der Schwerkraft auf die Ausbreitung des Lichtes," Annalen der Physik 35 (1911); translated "On the Influence of Gravitation on the Propagation of Light" in The collected papers of 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 The Genesis of General Relativity (http://www1.kcn.ne.jp/~h-uchii/gen.GR.html).
• C. W. Misner, K. S. Thorne and J. A. Wheeler, Gravitation, W. H. Freeman and Company, New York (1973), Chapter 16 discusses the equivalence principle.
• Hans Ohanian and Remo Ruffini Gravitation and Spacetime 2nd edition, Norton, New York (1994). ISBN 0-393-96501-5 Chapter 1 discusses the equivalence principle, but incorrectly, according to modern usage, states that the strong equivalence principle is wrong.
• J. P. Uzan, "The fundamental constants and their variation: Observational status and theoretical motivations," Rev. Mod. Phys. 75, 403 (2003). [1] (http://www.arxiv.org/abs/hep-ph/0205340) This technical article reviews the best constraints on the variation of the fundamental constants.
• C. M. Will, Theory and experiment in gravitational physics, Cambridge University Press, Cambridge (1993). This is the standard technical reference for tests of general relativity.
• C. M. Will, Was Einstein Right?: Putting General Relativity to the Test, Basic Books (1993). This is a popular account of tests of general relativity.
• C. M. Will, The Confrontation between General Relativity and Experiment, (http://relativity.livingreviews.org/Articles/lrr-2001-4/index.html) Living Reviews in Relativity (2001). An online, technical review, covering much of the material in Theory and experiment in gravitational physics. The Einstein and strong variants of the equivalence principles are discussed in sections 2.1 (http://relativity.livingreviews.org/Articles/lrr-2001-4/node3.html) and 3.1 (http://relativity.livingreviews.org/Articles/lrr-2001-4/node7.html), respectively.

External links

• University of Washington Eöt-Wash group (http://www.npl.washington.edu/eotwash/)
• 16 November 2004, physicsweb: Equivalence principle passes atomic test (http://physicsweb.org/articles/news/8/11/8/1) Quote: "...Physicists in Germany have used an atomic interferometer to perform the most accurate ever test of the equivalence principle at the level of atoms..."
• Webarchive backup (without pictures ((incl. formulas)): Lecture 6: The Principle of Equivalence (1): In Which We See Gravity Doing Things To Time (http://web.archive.org/web/20040223110146/www.pa.uky.edu/~cvj/as500_lec6/as500_lec6.html), original broken address (http://www.pa.uky.edu/~cvj/as500_lec6/as500_lec6.html)

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