![Elevator gravity](https://upload.wikimedia.org/wikipedia/commons/b/b7/Elevator_gravity.png)
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 be ...
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 stron ...
and
inertial 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 elementa ...
, 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 theory ...
'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
A fictitious force is a force that appears to act on a mass whose motion is described using a non-inertial frame of reference, such as a linearly accelerating or rotating reference frame.
It is related to Newton's second law of motion, which trea ...
'' experienced by an observer in a non-
inertial
In classical physics and special relativity, an inertial frame of reference (also called inertial reference frame, inertial frame, inertial space, or Galilean reference frame) is a frame of reference that is not undergoing any acceleration. ...
(accelerated)
frame of reference.
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 Causality, cause-and-effect by demonstrating what outcome oc ...
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 t ...
of a
test mass In physical theories, a test particle, or test charge, is an idealized model of an object whose physical properties (usually mass, charge, or size) are assumed to be negligible except for the property being studied, which is considered to be insu ...
due to
gravitation 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 eleme ...
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
. 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 D
moon/D
Earth=M
Earth/M
moon, without knowing the time to collision or how or if the acceleration force from gravity is a function of distance.
Newton's
gravitational theory
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 strong ...
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 theory ...
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/s
2 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
In Newtonian physics, free fall is any motion of a body where gravity is the only force acting upon it. In the context of general relativity, where gravitation is reduced to a space-time curvature, a body in free fall has no force acting on i ...
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
In classical physics and special relativity, an inertial frame of reference (also called inertial reference frame, inertial frame, inertial space, or Galilean reference frame) is a frame of reference that is not undergoing any acceleration. ...
bodies (and photons, or light) obey
Newton's first law
Newton's laws of motion are three basic laws of classical mechanics that describe the relationship between the motion of an object and the forces acting on it. These laws can be paraphrased as follows:
# A body remains at rest, or in motion ...
, 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
The world line (or worldline) of an object is the path that an object traces in 4-dimensional spacetime. It is an important concept in modern physics, and particularly theoretical physics.
The concept of a "world line" is distinguished from c ...
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 acc ...
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. 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 (
postulate
An axiom, postulate, or assumption is a statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments. The word comes from the Ancient Greek word (), meaning 'that which is thought worthy or f ...
d) 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 laws ...
to predict that clocks run at different rates in a
gravitational potential
In classical mechanics, the gravitational potential at a location is equal to the work (energy transferred) per unit mass that would be needed to move an object to that location from a fixed reference location. It is analogous to the electric ...
, 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 laws ...
. This was developed by
Robert Dicke
Robert Henry Dicke (; May 6, 1916 – March 4, 1997) was an American astronomer and physicist who made important contributions to the fields of astrophysics, atomic physics, cosmology and gravity. He was the Albert Einstein Professor in Scienc ...
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), 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
due to the gravitational field of
is:
Likewise the force on a second object of arbitrary mass
2 due to the gravitational field of mass
0 is:
By definition of inertial mass:
If
and
are the same distance
from
then, by the weak equivalence principle, they fall at the same rate (i.e. their accelerations are the same)
Hence:
Therefore:
In other words, passive gravitational mass must be proportional to inertial mass for all objects.
Furthermore, by
Newton's third law of motion
Newton's laws of motion are three basic laws of classical mechanics that describe the relationship between the motion of an object and the forces acting on it. These laws can be paraphrased as follows:
# A body remains at rest, or in motio ...
:
must be equal and opposite to
It follows that:
In other words, passive gravitational mass must be proportional to active gravitational mass for all objects.
The dimensionless Eötvös-parameter
is the difference of the ratios of gravitational and inertial masses divided by their average for the two sets of test masses "A" and "B".
Tests of the weak equivalence principle
Tests of the weak equivalence principle are those that verify the equivalence of gravitational mass and inertial mass. An obvious test is dropping different objects, ideally in a vacuum environment, e.g., inside the
Fallturm Bremen
Fallturm Bremen is a drop tower at the Center of Applied Space Technology and Microgravity at the University of Bremen in Bremen. It was built between 1988 and 1990, and includes a 122-metre-high drop tube (actual drop distance is 110 m), in whic ...
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 Seattl ...
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 a ...
in the
Galactic Center
The Galactic Center or Galactic Centre is the rotational center, the barycenter, of the Milky Way galaxy. Its central massive object is a supermassive black hole of about 4 million solar masses, which is called Sagittarius A*, a compact ra ...
. Future satellite experiments
–
STEP (Satellite Test of the Equivalence Principle) The Satellite Test of the Equivalence Principle (STEP) is a proposed () space science experiment to test the equivalence principle of general relativity. The experiment is thought to be sensitive enough to test Einstein's theory of gravity and other ...
, 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
Quantum gravity (QG) is a field of theoretical physics that seeks to describe gravity according to the principles of quantum mechanics; it deals with environments in which neither gravitational nor quantum effects can be ignored, such as in the vi ...
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 wavelength
The Compton wavelength is a quantum mechanical property of a particle. The Compton wavelength of a particle is equal to the wavelength of a photon whose energy is the same as the rest energy of that particle (see mass–energy equivalence). It was ...
s, which should generate
fifth forces 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
The tidal force is a gravitational effect that stretches a body along the line towards the center of mass of another body due to a gradient (difference in strength) in gravitational field from the other body; it is responsible for diverse phenomen ...
, 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
A dimensionless quantity (also known as a bare quantity, pure quantity, or scalar quantity as well as quantity of dimension one) is a quantity to which no physical dimension is assigned, with a corresponding SI unit of measurement of one (or 1) ...
physical values such as 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 el ...
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 no ...
-to-
proton mass ratio must not depend on where in space or time we measure them. Many physicists believe that any
Lorentz invariant
In a relativistic theory of physics, a Lorentz scalar is an expression, formed from items of the theory, which evaluates to a scalar, invariant under any Lorentz transformation. A Lorentz scalar may be generated from e.g., the scalar product of ...
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
A dimensionless quantity (also known as a bare quantity, pure quantity, or scalar quantity as well as quantity of dimension one) is a quantity to which no physical dimension is assigned, with a corresponding SI unit of measurement of one (or 1) ...
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 Fren ...
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 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
In physics and general relativity, gravitational redshift (known as Einstein shift in older literature) is the phenomenon that electromagnetic waves or photons travelling out of a gravitational well (seem to) lose energy. This loss of energy ...
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,
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 experiment
The Cavendish experiment, performed in 1797–1798 by English scientist Henry Cavendish, was the first experiment to measure the force of gravity between masses in the laboratory and the first to yield accurate values for the gravitational con ...
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
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 mathem ...
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
In cosmology, the cosmological constant (usually denoted by the Greek capital letter lambda: ), alternatively called Einstein's cosmological constant,
is the constant coefficient of a term that Albert Einstein temporarily added to his field eq ...
) 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
In physical cosmology, Big Bang nucleosynthesis (abbreviated BBN, also known as primordial nucleosynthesis) is the production of nuclei other than those of the lightest isotope of hydrogen ( hydrogen-1, 1H, having a single proton as a nucleu ...
have shown that ''G'' cannot have varied by more than 10%.
Thus, the strong equivalence principle can be tested by searching for
fifth forces (deviations from the gravitational force-law predicted by general relativity). These experiments typically look for failures of the
inverse-square law (specifically
Yukawa forces or failures of
Birkhoff's theorem) behavior of gravity in the laboratory. The most accurate tests over short distances have been performed by the 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
In theoretical astrophysics, the Nordtvedt effect refers to the relative motion between the Earth and the Moon that would be observed if the gravitational self-energy of a body contributed differently to its gravitational mass than to its inerti ...
, 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
Very-long-baseline interferometry (VLBI) is a type of astronomical interferometry used in radio astronomy. In VLBI a signal from an astronomical radio source, such as a quasar, is collected at multiple radio telescopes on Earth or in space. T ...
. 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 dwarf
A white dwarf is a stellar core remnant composed mostly of electron-degenerate matter. A white dwarf is very dense: its mass is comparable to the Sun's, while its volume is comparable to the Earth's. A white dwarf's faint luminosity comes ...
s 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 explaining ...
(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 with ...
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
In physics, string theory is a theoretical framework in which the point-like particles of particle physics are replaced by one-dimensional objects called strings. String theory describes how these strings propagate through space and intera ...
Erik Verlinde has generated a self-contained, logical derivation of the equivalence principle based on the starting assumption of a
holographic universe
The holographic principle is an axiom in string theories and a supposed property of quantum gravity that states that the description of a volume of space can be thought of as encoded on a lower-dimensional boundary to the region — such as a l ...
. Given this situation, gravity would not be a true
fundamental force
In physics, the fundamental interactions, also known as fundamental forces, are the interactions that do not appear to be reducible to more basic interactions. There are four fundamental interactions known to exist: the gravitational and electro ...
as is currently thought but instead an "
emergent property
In philosophy, systems theory, science, and art, emergence occurs when an entity is observed to have properties its parts do not have on their own, properties or behaviors that emerge only when the parts interact in a wider whole.
Emergence ...
" 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 thermodynam ...
. Verlinde's
entropic gravity 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 wit ...
*
Einstein's thought experiments
A hallmark of Albert Einstein's career was his use of visualized thought experiments (german: Gedankenexperiment) as a fundamental tool for understanding physical issues and for elucidating his concepts to others. Einstein's thought experiments too ...
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Equivalence principle (geometric)
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Gauge gravitation theory
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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 is ...
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Mach's principle
In theoretical physics, particularly in discussions of gravitation theories, Mach's principle (or Mach's conjecture) is the name given by Einstein to an imprecise hypothesis often credited to the physicist and philosopher Ernst Mach. The hypothe ...
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Tests of general relativity
Tests of general relativity serve to establish observational evidence for the theory of general relativity. The first three tests, proposed by Albert Einstein in 1915, concerned the "anomalous" precession of the perihelion of Mercury, the ben ...
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Unsolved problems in astronomy
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Unsolved problems in physics
The following is a list of notable unsolved problems grouped into broad areas of physics.
Some of the major unsolved problems in physics are theoretical, meaning that existing theories seem incapable of explaining a certain observed phenomenon ...
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.
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External links
at NASA, including tests
from Syracuse University
at MathPages
at Living Reviews on General Relativity
{{DEFAULTSORT:Equivalence Principle
General relativity
Fictitious forces
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