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In the
theory A theory is a rational type of abstract thinking about a phenomenon, or the results of such thinking. The process of contemplative and rational thinking is often associated with such processes as observational study or research. Theories may ...
of
general relativity General relativity, also known as the general theory of relativity and Einstein's theory of gravity, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics ...
, the equivalence principle is the equivalence of
gravitational In physics, gravity () is a fundamental interaction which causes mutual attraction between all things with mass or energy. Gravity is, by far, the weakest of the four fundamental interactions, approximately 1038 times weaker than the str ...
and inertial mass, and
Albert Einstein Albert Einstein ( ; ; 14 March 1879 – 18 April 1955) was a German-born theoretical physicist, widely acknowledged to be one of the greatest and most influential physicists of all time. Einstein is best known for developing the theor ...
'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 In physics and astronomy, a frame of reference (or reference frame) is an abstract coordinate system whose origin, orientation, and scale are specified by a set of reference points― geometric points whose position is identified both math ...
.


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


Development of gravitational theory

Something like the equivalence principle emerged in the early 17th century, when Galileo expressed
experiment An experiment is a procedure carried out to support or refute a hypothesis, or determine the efficacy or likelihood of something previously untried. Experiments provide insight into cause-and-effect by demonstrating what outcome occurs whe ...
ally that the
acceleration In mechanics, acceleration is the rate of change of the velocity of an object with respect to time. Accelerations are vector quantities (in that they have magnitude and direction). The orientation of an object's acceleration is given by ...
of a test mass due to
gravitation In physics, gravity () is a fundamental interaction which causes mutual attraction between all things with mass or energy. Gravity is, by far, the weakest of the four fundamental interactions, approximately 1038 times weaker than the stron ...
is independent of the amount of
mass Mass is an intrinsic property of a body. It was traditionally believed to be related to the quantity of matter in a physical body, until the discovery of the atom and particle physics. It was found that different atoms and different ele ...
being accelerated. Johannes 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 Johannes Kepler (; ; 27 December 1571 – 15 November 1630) was a German astronomer, mathematician, astrologer, natural philosopher and writer on music. He is a key figure in the 17th-century Scientific Revolution, best known for his laws o ...
's estimate of the Moon–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 Albert Einstein ( ; ; 14 March 1879 – 18 April 1955) was a German-born theoretical physicist, widely acknowledged to be one of the greatest and most influential physicists of all time. Einstein is best known for developing the theor ...
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 In physics, spacetime is a mathematical model that combines the three dimensions of space and one dimension of time into a single four-dimensional manifold. Spacetime diagrams can be used to visualize relativistic effects, such as why differ ...
the world line of an inertial particle or pulse of light is ''as straight as possible'' (in space ''and'' time). 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 An accelerometer is a tool that measures proper acceleration. Proper acceleration is the acceleration (the rate of change of velocity) of a body in its own instantaneous rest frame; this is different from coordinate acceleration, which is acce ...
in free-fall doesn't register any acceleration; there isn't any between the internal test mass and the accelerometer's body. 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 In physics, gravity () is a fundamental interaction which causes mutual attraction between all things with mass or energy. Gravity is, by far, the weakest of the four fundamental interactions, approximately 1038 times weaker than the stro ...
is assumed to be a
force In physics, a force is an influence that can change the motion of an object. A force can cause an object with mass to change its velocity (e.g. moving from a state of rest), i.e., to accelerate. Force can also be described intuitively as a ...
. 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 General relativity, also known as the general theory of relativity and Einstein's theory of gravity, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics ...
. 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 In physics, the special theory of relativity, or special relativity for short, is a scientific theory regarding the relationship between space and time. In Albert Einstein's original treatment, the theory is based on two postulates: # The law ...
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 General relativity, also known as the general theory of relativity and Einstein's theory of gravity, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics ...
, 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 In physics, gravity () is a fundamental interaction which causes mutual attraction between all things with mass or energy. Gravity is, by far, the weakest of the four fundamental interactions, approximately 1038 times weaker than the stro ...
is instead a result of our being unable to follow those geodesics of spacetime, because the mechanical resistance of Earth's matter or surface 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 In physics, the special theory of relativity, or special relativity for short, is a scientific theory regarding the relationship between space and time. In Albert Einstein's original treatment, the theory is based on two postulates: # The law ...
. 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, a generalization of the weak EP, includes astronomic bodies with gravitational self-binding energy (e.g., 1.74 solar-mass pulsar PSR J1903+0327, 15.3% of whose separated mass is absent as gravitational binding energy) Instead, the weak EP assumes falling bodies are self-bound by non-gravitational forces only (e.g. a stone). 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. *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 '' Philosophiæ Naturalis Principia Mathematica'', 1687). Locality eliminates measurable tidal forces originating from a radial divergent gravitational field (e.g., the Earth) upon finite sized physical bodies. The "falling" equivalence principle embraces Galileo's, Newton's, and Einstein's conceptualization. The equivalence principle does not deny the existence of measurable effects caused by a ''rotating'' gravitating mass (
frame dragging Frame-dragging is an effect on spacetime, predicted by Albert Einstein's general theory of relativity, that is due to non-static stationary distributions of mass–energy. A stationary field is one that is in a steady state, but the masses cau ...
), 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 Likewise the force on a second object of arbitrary mass2 due to the gravitational field of mass0 is: F_2 = \frac By definition of inertial mass: F = m^\mathrm a If m_1 and m_2 are the same distance r from m_0 then, by the weak equivalence principle, they fall at the same rate (i.e. their accelerations are the same) a_1 = \frac = a_2 = \frac Hence: \frac = \frac Therefore: \frac = \frac In other words, passive gravitational mass must be proportional to inertial mass for all objects. Furthermore, by Newton's third law of motion: F_1 = \frac must be equal and opposite to F_0 = \frac It follows that: \frac = \frac In other words, passive gravitational mass must be proportional to active gravitational mass for all objects. The dimensionless Eötvös-parameter \eta(A,B) 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". \eta(A,B)=2\frac


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. See: Experiments are still being performed at the
University of Washington The University of Washington (UW, simply Washington, or informally U-Dub) is a public research university in Seattle, Washington. Founded in 1861, Washington is one of the oldest universities on the West Coast; it was established in Seatt ...
which have placed limits on the differential acceleration of objects towards the Earth, the Sun and towards
dark matter Dark matter is a hypothetical form of matter thought to account for approximately 85% of the matter in the universe. Dark matter is called "dark" because it does not appear to interact with the electromagnetic field, which means it does not ...
in the Galactic Center. Future satellite experimentsSTEP (Satellite Test of the Equivalence Principle), and Galileo Galilei – will test the weak equivalence principle in space, to much higher accuracy. With the first successful production of antimatter, in particular anti-hydrogen, a new approach to test the weak equivalence principle has been proposed. Experiments to compare the gravitational behavior of matter and antimatter are currently being developed. Proposals that may lead to a 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 fields with long Compton wavelengths, which should generate
fifth force In physics, there are four observed fundamental interactions (also known as fundamental forces) that form the basis of all known interactions in nature: gravitational, electromagnetic, strong nuclear, and weak nuclear forces. Some speculative ...
s and variation of the fundamental constants. Heuristic arguments suggest that the magnitude of these equivalence principle violations could be in the 10−13 to 10−18 range. 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.


The Einstein equivalence principle

What is now called the "Einstein equivalence principle" states that the weak equivalence principle holds, and that: 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''. 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 The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family, and are generally thought to be elementary particles because they have n ...
-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 Hadley and Durand).


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 Oklo is a region near the town of Franceville, in the Haut-Ogooué province of the Central African country of Gabon. Several natural nuclear fission reactors were discovered in the uranium mines in the region in 1972. History Gabon was a Frenc ...
natural nuclear fission reactor A natural nuclear fission reactor is a uranium deposit where self-sustaining nuclear chain reactions occur. The conditions under which a natural nuclear reactor could exist had been predicted in 1956 by Japanese American chemist Paul Kuroda. ...
, 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. There have been a number of controversial attempts to constrain the variation of the
strong interaction The strong interaction or strong force is a fundamental interaction that confines quarks into proton, neutron, and other hadron particles. The strong interaction also binds neutrons and protons to create atomic nuclei, where it is called th ...
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, see Webb et al. Other researchers dispute these findings. Other tests of the Einstein equivalence principle are gravitational redshift experiments, such as the
Pound–Rebka experiment The Pound–Rebka experiment was an experiment in which gamma rays were emitted from the top of a tower and measured by a receiver at the bottom of the tower. The purpose of the experiment was to test Albert Einstein's theory of general relativit ...
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, and The first part is a version of the weak equivalence principle that applies to objects that exert a gravitational force on themselves, such as stars, planets, black holes or Cavendish experiments. The second part is the 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 In physics, there are four observed fundamental interactions (also known as fundamental forces) that form the basis of all known interactions in nature: gravitational, electromagnetic, strong nuclear, and weak nuclear forces. Some speculative ...
. 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 Metric or metrical may refer to: * Metric system, an internationally adopted decimal system of measurement * An adjective indicating relation to measurement in general, or a noun describing a specific type of measurement Mathematics In mathe ...
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 In physics, there are four observed fundamental interactions (also known as fundamental forces) that form the basis of all known interactions in nature: gravitational, electromagnetic, strong nuclear, and weak nuclear forces. Some speculative ...
s (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 (Satellite Energy Exchange), will search for fifth forces in space and should be able to further constrain violations of the strong equivalence principle. Other limits, looking for much longer-range forces, have been placed by searching for the Nordtvedt effect, a "polarization" of solar system orbits that would be caused by gravitational self-energy accelerating at a different rate from normal matter. This effect has been sensitively tested by the Lunar Laser Ranging Experiment. Other tests include studying the deflection of radiation from distant radio sources by the sun, which can be accurately measured by very long baseline interferometry. Another sensitive test comes from measurements of the frequency shift of signals to and from the Cassini spacecraft. Together, these measurements have put tight limits on Brans–Dicke theory and other alternative theories of gravity. In 2014, astronomers discovered a stellar triple system containing 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. In 2020 a group of astronomers analyzed data from the Spitzer Photometry and Accurate Rotation Curves (SPARC) sample, together with estimates of the large-scale external gravitational field from an all-sky galaxy catalog. They concluded that there was highly statistically significant evidence of violations of the strong equivalence principle in weak gravitational fields in the vicinity of rotationally supported galaxies. They observed an effect consistent with the external field effect of
Modified Newtonian dynamics Modified Newtonian dynamics (MOND) is a hypothesis that proposes a modification of Newton's law of universal gravitation to account for observed properties of galaxies. It is an alternative to the hypothesis of dark matter in terms of explaini ...
(MOND), a hypothesis that proposes a modified gravity theory beyond
general relativity General relativity, also known as the general theory of relativity and Einstein's theory of gravity, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics ...
, and inconsistent with tidal effects in the
Lambda-CDM model The ΛCDM (Lambda cold dark matter) or Lambda-CDM model is a parameterization of the Big Bang cosmological model in which the universe contains three major components: first, a cosmological constant denoted by Lambda ( Greek Λ) associated ...
paradigm, commonly known as the Standard Model of Cosmology.


Challenges

One challenge to the equivalence principle is the Brans–Dicke theory. Self-creation cosmology is a modification of the Brans–Dicke theory. 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 In physics, the fine-structure constant, also known as the Sommerfeld constant, commonly denoted by (the Greek letter ''alpha''), is a fundamental physical constant which quantifies the strength of the electromagnetic interaction between ele ...
", whose tentative conclusion is that, "qualitatively, heresults 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."


Explanations

Dutch physicist and string theorist
Erik Verlinde Erik Peter Verlinde (; born 21 January 1962) is a Dutch theoretical physicist and string theorist. He is the identical twin brother of physicist Herman Verlinde. The Verlinde formula, which is important in conformal field theory and topolog ...
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 Entropy is a scientific concept, as well as a measurable physical property, that is most commonly associated with a state of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodyna ...
. Verlinde's
entropic gravity Entropic gravity, also known as emergent gravity, is a theory in modern physics that describes gravity as an ''entropic force''—a force with macro-scale homogeneity but which is subject to quantum-level disorder—and not a fundamental inte ...
theory apparently leads naturally to the correct observed strength of
dark energy In physical cosmology and astronomy, dark energy is an unknown form of energy that affects the universe on the largest scales. The first observational evidence for its existence came from measurements of supernovas, which showed that the univ ...
; 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". These ideas are far from settled and still very controversial.


Experiments

*University of Washington *Lunar Laser Ranging *Galileo-Galilei satellite experiment * Satellite Test of the Equivalence Principle (STEP) *MICROSCOPE *Satellite Energy Exchange (SEE) *"...Physicists in Germany have used an atomic interferometer to perform the most accurate ever test of the equivalence principle at the level of atoms..."


See also

*
Classical mechanics Classical mechanics is a physical theory describing the motion of macroscopic objects, from projectiles to parts of machinery, and astronomical objects, such as spacecraft, planets, stars, and galaxies. For objects governed by classi ...
*
Eötvös experiment The Eötvös experiment was a famous physics experiment that measured the correlation between inertial mass and gravitational mass, demonstrating that the two were one and the same, something that had long been suspected but never demonstrated with ...
* Einstein's thought experiments *
Equivalence principle (geometric) The equivalence principle is one of the corner-stones of gravitation theory. Different formulations of the equivalence principle are labeled ''weakest'', ''weak'', ''middle-strong'' and ''strong.'' All of these formulations are based on the emp ...
*
Gauge gravitation theory In quantum field theory, gauge gravitation theory is the effort to extend Yang–Mills theory, which provides a universal description of the fundamental interactions, to describe gravity. ''Gauge gravitation theory'' should not be confused with th ...
*
General covariance In theoretical physics, general covariance, also known as diffeomorphism covariance or general invariance, consists of the invariance of the ''form'' of physical laws under arbitrary differentiable coordinate transformations. The essential idea ...
* Mach's principle * Tests of general relativity * Unsolved problems in astronomy * Unsolved problems in physics


Notes


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. 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, New Jersey, 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, New Jersey, 1994), Anna Beck translator, and in ''The Principle of Relativity'', (Dover, 1924), pp 99–108, W. Perrett and G. B. Jeffery translators, . The two Einstein papers are discussed online a

* Brans, Carl H.; "The roots of scalar-tensor theory: an approximate history", . 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, 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). 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 section

an

respectively. * Friedman, Michael; ''Foundations of Space-Time Theories'', Princeton, New Jersey: Princeton University Press, 1983. Chapter V discusses the equivalence principle. * * *


External links



at NASA, including tests

from Syracuse University

at MathPages

at Living Reviews on General Relativity {{DEFAULTSORT:Equivalence Principle General relativity Fictitious forces Albert Einstein Principles Acceleration Philosophy of astronomy Articles containing video clips