Equivalence principle

# Equivalence principle

Overview
In the physics
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...

of general relativity
General relativity
General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...

, the equivalence principle is any of several related concepts dealing with the equivalence of gravitational and inertial mass, and to Albert Einstein's
Albert Einstein
Albert Einstein was a German-born theoretical physicist who developed the theory of general relativity, effecting a revolution in physics. For this achievement, Einstein is often regarded as the father of modern physics and one of the most prolific intellects in human history...

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
Fictitious force
A fictitious force, also called a pseudo force, d'Alembert force or inertial force, is an apparent force that acts on all masses in a non-inertial frame of reference, such as a rotating reference frame....

experienced by an observer in a non-inertial
Inertial frame of reference
In physics, an inertial frame of reference is a frame of reference that describes time homogeneously and space homogeneously, isotropically, and in a time-independent manner.All inertial frames are in a state of constant, rectilinear motion with respect to one another; they are not...

(accelerated) frame of reference.
Discussion

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Encyclopedia
In the physics
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...

of general relativity
General relativity
General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...

, the equivalence principle is any of several related concepts dealing with the equivalence of gravitational and inertial mass, and to Albert Einstein's
Albert Einstein
Albert Einstein was a German-born theoretical physicist who developed the theory of general relativity, effecting a revolution in physics. For this achievement, Einstein is often regarded as the father of modern physics and one of the most prolific intellects in human history...

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
Fictitious force
A fictitious force, also called a pseudo force, d'Alembert force or inertial force, is an apparent force that acts on all masses in a non-inertial frame of reference, such as a rotating reference frame....

experienced by an observer in a non-inertial
Inertial frame of reference
In physics, an inertial frame of reference is a frame of reference that describes time homogeneously and space homogeneously, isotropically, and in a time-independent manner.All inertial frames are in a state of constant, rectilinear motion with respect to one another; they are not...

(accelerated) frame of reference.

## Einstein's statement of the equivalence principle

See momentum
Momentum
In classical mechanics, linear momentum or translational momentum is the product of the mass and velocity of an object...

and velocity
Velocity
In physics, velocity is speed in a given direction. Speed describes only how fast an object is moving, whereas velocity gives both the speed and direction of the object's motion. To have a constant velocity, an object must have a constant speed and motion in a constant direction. Constant ...

.

## Development of gravitation theory

Something like the equivalence principle emerged in the late 16th and early 17th centuries, when Galileo
Galileo Galilei
Galileo Galilei , was an Italian physicist, mathematician, astronomer, and philosopher who played a major role in the Scientific Revolution. His achievements include improvements to the telescope and consequent astronomical observations and support for Copernicanism...

expressed experiment
Experiment
An experiment is a methodical procedure carried out with the goal of verifying, falsifying, or establishing the validity of a hypothesis. Experiments vary greatly in their goal and scale, but always rely on repeatable procedure and logical analysis of the results...

ally that the acceleration
Acceleration
In physics, acceleration is the rate of change of velocity with time. In one dimension, acceleration is the rate at which something speeds up or slows down. However, since velocity is a vector, acceleration describes the rate of change of both the magnitude and the direction of velocity. ...

of a test mass due to gravitation
Gravitation
Gravitation, or gravity, is a natural phenomenon by which physical bodies attract with a force proportional to their mass. Gravitation is most familiar as the agent that gives weight to objects with mass and causes them to fall to the ground when dropped...

is independent of the amount of mass
Mass
Mass can be defined as a quantitive measure of the resistance an object has to change in its velocity.In physics, mass commonly refers to any of the following three properties of matter, which have been shown experimentally to be equivalent:...

being accelerated. These findings led to gravitational theory
Newton's law of universal gravitation
Newton's law of universal gravitation states that every point mass in the universe attracts every other point mass with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them...

, in which the inertial and gravitational masses are identical.

The equivalence principle proper was introduced by Albert Einstein in 1907, when he observed that the acceleration of bodies towards the center of the Earth
Earth
Earth is the third planet from the Sun, and the densest and fifth-largest of the eight planets in the Solar System. It is also the largest of the Solar System's four terrestrial planets...

at a rate of 1g
G-force
The g-force associated with an object is its acceleration relative to free-fall. This acceleration experienced by an object is due to the vector sum of non-gravitational forces acting on an object free to move. The accelerations that are not produced by gravity are termed proper accelerations, and...

(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 1g. Einstein stated it thus:
That is, being at rest on the surface of the Earth is equivalent to being inside a spaceship (far from any sources of gravity) that is being accelerated by its engines. From this principle, Einstein deduced that free-fall
Free-fall
Free fall is any motion of a body where gravity is the only force acting upon it, at least initially. These conditions produce an inertial trajectory so long as gravity remains the only force. Since this definition does not specify velocity, it also applies to objects initially moving upward...

is actually inertial motion. Objects in free-fall really do not accelerate, but rather the closer they get to an object such as the Earth, the more the time scale becomes stretched due to spacetime distortion around the planetary object (this is gravity). An object in free-fall is in actuality inertial, but as it approaches the planetary object the time scale stretches at an accelerated rate, giving the appearance that it is accelerating towards the planetary object when, in fact, the falling body really isn't accelerating at all. This is why an accelerometer
Accelerometer
An accelerometer is a device that measures proper acceleration, also called the four-acceleration. This is not necessarily the same as the coordinate acceleration , but is rather the type of acceleration associated with the phenomenon of weight experienced by a test mass that resides in the frame...

in free-fall doesn't register any acceleration; there isn't any. By contrast, in Newtonian mechanics, gravity is assumed to be a force
Force
In physics, a force is any influence that causes an object to undergo a change in speed, a change in direction, or a change in shape. In other words, a force is that which can cause an object with mass to change its velocity , i.e., to accelerate, or which can cause a flexible object to deform...

. 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
General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...

. Einstein suggested that it should be elevated to the status of a general principle when constructing his theory of relativity:
Einstein combined the equivalence principle with special relativity
Special relativity
Special relativity is the physical theory of measurement in an inertial frame of reference proposed in 1905 by Albert Einstein in the paper "On the Electrodynamics of Moving Bodies".It generalizes Galileo's...

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
Tidal force
The tidal force is a secondary effect of the force of gravity and is responsible for the tides. It arises because the gravitational force per unit mass exerted on one body by a second body is not constant across its diameter, the side nearest to the second being more attracted by it than the side...

(caused by variations in the strength and direction of the gravitational field) which are absent from an accelerating spaceship in deep space.

Although the equivalence principle guided the development of general relativity
General relativity
General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It 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 geodesic
Geodesic (general relativity)
In general relativity, a geodesic generalizes the notion of a "straight line" to curved spacetime. Importantly, the world line of a particle free from all external, non-gravitational, force is a particular type of geodesic...

s of spacetime, and what we perceive as the force of gravity is instead a result of our being unable to follow those geodesics of spacetime, because the mechanical resistance of matter prevents us from doing so.

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
Special relativity
Special relativity is the physical theory of measurement in an inertial frame of reference proposed in 1905 by Albert Einstein in the paper "On the Electrodynamics of Moving Bodies".It generalizes Galileo's...

. This was developed by Robert Dicke
Robert H. Dicke
Robert Henry Dicke was an American physicist who made important contributions to the fields of astrophysics, atomic physics, cosmology and gravity.-Biography:...

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.

## 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 trajectory of a point mass in a gravitational field depends only on its initial position and velocity, and is independent of its composition.

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 vacuum free fall 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 space (gravitation) are indistinguishable from those of an accelerated observer in flat space, 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 "Principia").

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. Relativistic particles and photons do not fall like local masses. Photons in a gravitational field experience twice the local gravitational acceleration (tracing a null geodesic
Geodesic
In mathematics, a geodesic is a generalization of the notion of a "straight line" to "curved spaces". In the presence of a Riemannian metric, geodesics are defined to be the shortest path between points in the space...

) - an important test of general relativity versus Newton. Divergent trajectories arising from gravitomagnetism
Gravitomagnetism
Gravitomagnetism , refers to a set of formal analogies between Maxwell's field equations and an approximation, valid under certain conditions, to the Einstein field equations for general relativity. The most common version of GEM is valid only far from isolated sources, and for slowly moving test...

(frame dragging, Lense-Thirring effect), gravitoelectric effects, geodetic effect
Geodetic effect
The geodetic effect represents the effect of the curvature of spacetime, predicted by general relativity, on a vector carried along with an orbiting body...

, Shapiro delay
Shapiro delay
The Shapiro time delay effect, or gravitational time delay effect, is one of the four classic solar system tests of general relativity. Radar signals passing near a massive object take slightly longer to travel to a target and longer to return than it would if the mass of the object were not...

, etc., do not contradict the equivalence principle.

#### 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 mass2 due to the gravitational field of mass0 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:

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 two contrasted objects in hard vacuum, e.g., inside Fallturm Bremen
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 has a 123-metre-high drop tube , in which for 4.74 seconds , or for over 9 seconds weightlessness can be produced...

.
 Researcher Year Method Result John PhiloponusJohn PhiloponusJohn Philoponus , also known as John the Grammarian or John of Alexandria, was a Christian and Aristotelian commentator and the author of a considerable number of philosophical treatises and theological works... 6th century Described correctly the effect of dropping balls of different masses no detectable difference Simon StevinSimon StevinSimon Stevin was a Flemish mathematician and military engineer. He was active in a great many areas of science and engineering, both theoretical and practical... ~1586 Dropped lead balls of different masses off the Delft churchtowerNieuwe Kerk (Delft)Nieuwe Kerk is a landmark Protestant church in Delft, Netherlands. The building is located on Delft Market Square , opposite to the City Hall . In 1584, William the Silent was entombed here in a mausoleum designed by Hendrick and Pieter de Keyser. Since then members of the House of Orange-Nassau... no detectable difference Galileo GalileiGalileo GalileiGalileo Galilei , was an Italian physicist, mathematician, astronomer, and philosopher who played a major role in the Scientific Revolution. His achievements include improvements to the telescope and consequent astronomical observations and support for Copernicanism... ~1610 Rolling balls down inclined planes no detectable difference Isaac NewtonIsaac NewtonSir Isaac Newton PRS was an English physicist, mathematician, astronomer, natural philosopher, alchemist, and theologian, who has been "considered by many to be the greatest and most influential scientist who ever lived."... ~1680 measure the periodFrequencyFrequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency.The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency... of pendulums of different mass but identical length no measurable difference Friedrich Wilhelm Bessel 1832 measure the period of pendulums of different mass but identical length no measurable difference Loránd EötvösLoránd EötvösBaron Loránd Eötvös de Vásárosnamény , more commonly called Baron Roland von Eötvös in English literature, was a Hungarian physicist. He is remembered today largely for his work on gravitation and surface tension.-Life:... 1908 measure the torsionTorsion (mechanics)In solid mechanics, torsion is the twisting of an object due to an applied torque. In sections perpendicular to the torque axis, the resultant shear stress in this section is perpendicular to the radius.... on a wire, suspending a balance beam, between two nearly identical masses under the acceleration of gravity and the rotationRotationA rotation is a circular movement of an object around a center of rotation. A three-dimensional object rotates always around an imaginary line called a rotation axis. If the axis is within the body, and passes through its center of mass the body is said to rotate upon itself, or spin. A rotation... of the EarthEarthEarth is the third planet from the Sun, and the densest and fifth-largest of the eight planets in the Solar System. It is also the largest of the Solar System's four terrestrial planets... difference is less than 1 part in 109 Roll, Krotkov and DickeRobert H. DickeRobert Henry Dicke was an American physicist who made important contributions to the fields of astrophysics, atomic physics, cosmology and gravity.-Biography:... 1964 Torsion balance experiment, dropping aluminum and goldGoldGold is a chemical element with the symbol Au and an atomic number of 79. Gold is a dense, soft, shiny, malleable and ductile metal. Pure gold has a bright yellow color and luster traditionally considered attractive, which it maintains without oxidizing in air or water. Chemically, gold is a... test masses David ScottDavid ScottDavid Randolph Scott is an American engineer, test pilot, retired U.S. Air Force officer, and former NASA astronaut and engineer, who was one of the third group of astronauts selected by NASA in October 1963... 1971 Dropped a falcon feather and a hammer at the same time on the Moon no detectable difference (not a rigorous experiment, but very dramatic being the first lunar one) Braginsky and Panov 1971 Torsion balance, aluminum and platinumPlatinumPlatinum is a chemical element with the chemical symbol Pt and an atomic number of 78. Its name is derived from the Spanish term platina del Pinto, which is literally translated into "little silver of the Pinto River." It is a dense, malleable, ductile, precious, gray-white transition metal... test masses, measuring acceleration towards the sun difference is less than 1 part in 1012 Eöt-Wash group 1987– Torsion balance, measuring acceleration of different masses towards the earth, sun and galactic center, using several different kinds of masses

See:
 Year Investigator Sensitivity Method 500? Philoponus "small" Drop Tower 1585 Stevin 5x10-2 Drop Tower 1590? Galileo 2x10-2 Pendulum, Drop Tower 1686 Newton 10-3 Pendulum 1832 Bessel 2x10-5 Pendulum 1910 Southerns 5x10-6 Pendulum 1918 Zeeman 3x10-8 Torsion Balance 1922 Eötvös 5x10-9 Torsion Balance 1923 Potter 3x10-6 Pendulum 1935 Renner 2x10-9 Torsion Balance 1964 Dicke,Roll,Krotkov 3x10-11 Torsion Balance 1972 Braginsky,Panov 10-12 Torsion Balance 1976 Shapiro, et al. 10-12 Lunar Laser Ranging 1981 Keiser,Faller 4x10-11 Fluid Support 1987 Niebauer, et al. 10-10 Drop Tower 1989 Heckel, et al. 10-11 Torsion Balance 1990 Adelberger, et al. 10-12 Torsion Balance 1999 Baeßler, et al. 5x10-13 Torsion Balance cancelled? MiniSTEP 10-17 Earth Orbit 2015? MICROSCOPE 10-16 Earth Orbit

Experiments are still being performed at the University of Washington
University of Washington
University of Washington is a public research university, founded in 1861 in Seattle, Washington, United States. The UW is the largest university in the Northwest and the oldest public university on the West Coast. The university has three campuses, with its largest campus in the University...

which have placed limits on the differential acceleration of objects towards the Earth
Earth
Earth is the third planet from the Sun, and the densest and fifth-largest of the eight planets in the Solar System. It is also the largest of the Solar System's four terrestrial planets...

, the sun
Sun
The Sun is the star at the center of the Solar System. It is almost perfectly spherical and consists of hot plasma interwoven with magnetic fields...

and towards dark matter
Dark matter
In astronomy and cosmology, dark matter is matter that neither emits nor scatters light or other electromagnetic radiation, and so cannot be directly detected via optical or radio astronomy...

in the galactic center
Galactic Center
The Galactic Center is the rotational center of the Milky Way galaxy. It is located at a distance of 8.33±0.35 kpc from the Earth in the direction of the constellations Sagittarius, Ophiuchus, and Scorpius where the Milky Way appears brightest...

. Future satellite experiments – STEP (Satellite Test of the Equivalence Principle), Galileo Galilei, and MICROSCOPE (MICROSatellite pour l'Observation de Principe d'Equivalence) – will test the weak equivalence principle in space, to much higher accuracy.

The need to continue testing Einstein's theory of gravity may seem superfluous, as the theory is elegant and is compatible with almost all observations to date (except for instance the Pioneer anomaly
Pioneer anomaly
The Pioneer anomaly or Pioneer effect is the observed deviation from predicted accelerations of the Pioneer 10 and Pioneer 11 spacecraft after they passed about on their trajectories out of the Solar System....

). However, no quantum theory of gravity
Quantum gravity
Quantum gravity is the field of theoretical physics which attempts to develop scientific models that unify quantum mechanics with general relativity...

is known, and most suggestions violate one of the equivalence principles at some level. String theory
String theory
String theory is an active research framework in particle physics that attempts to reconcile quantum mechanics and general relativity. It is a contender for a theory of everything , a manner of describing the known fundamental forces and matter in a mathematically complete system...

, supergravity
Supergravity
In theoretical physics, supergravity is a field theory that combines the principles of supersymmetry and general relativity. Together, these imply that, in supergravity, the supersymmetry is a local symmetry...

and even quintessence
Quintessence (physics)
In physics, quintessence is a hypothetical form of dark energy postulated as an explanation of observations of an accelerating universe. It has been proposed by some physicists to be a fifth fundamental force...

, for example, seem to violate the weak equivalence principle because they contain many light scalar field
Scalar field
In mathematics and physics, a scalar field associates a scalar value to every point in a space. The scalar may either be a mathematical number, or a physical quantity. Scalar fields are required to be coordinate-independent, meaning that any two observers using the same units will agree on the...

s with long Compton wavelength
Compton wavelength
The Compton wavelength is a quantum mechanical property of a particle. It was introduced by Arthur Compton in his explanation of the scattering of photons by electrons...

s. These fields should generate fifth force
Fifth force
Occasionally, physicists have postulated the existence of a fifth force in addition to the four known fundamental forces. The force is generally believed to have roughly the strength of gravity Occasionally, physicists have postulated the existence of a fifth force in addition to the four known...

s 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.

#### Proposed geometric test of the weak equivalence principle

Teleparallel gravity theory allows equivalence principle violation in a geometric parity Eötvös experiment. Spacetime geometry (chiral spacetime torsion as a vacuum left foot) is interrogated with test mass geometry (metaphoric opposite shoes) emergent at atomic bond distances. A difference in fit appears as non-identical minimum action vacuum free fall trajectories (divergent in path and/or rate) - an equivalence principle violation.

There is no boson
Boson
In particle physics, bosons are subatomic particles that obey Bose–Einstein statistics. Several bosons can occupy the same quantum state. The word boson derives from the name of Satyendra Nath Bose....

photon vacuum refraction, dispersion (optics)
Dispersion (optics)
In optics, dispersion is the phenomenon in which the phase velocity of a wave depends on its frequency, or alternatively when the group velocity depends on the frequency.Media having such a property are termed dispersive media...

, dichroism
Dichroism
Dichroism has two related but distinct meanings in optics. A dichroic material is either one which causes visible light to be split up into distinct beams of different wavelengths , or one in which light rays having different polarizations are absorbed by different amounts.The original meaning of...

, or gyrotropy even for billion lightyear pathlengths. Nobody knows if the vacuum is measurably anisotropic toward resolved opposite chirality fermion
Fermion
In particle physics, a fermion is any particle which obeys the Fermi–Dirac statistics . Fermions contrast with bosons which obey Bose–Einstein statistics....

atomic mass distributions.

Laboratory equivalence principle tests contrast net residual divergences of chemical composition, spin (angular momentum
Angular momentum
In physics, angular momentum, moment of momentum, or rotational momentum is a conserved vector quantity that can be used to describe the overall state of a physical system...

: mechanical; quantum particle spin and quantum orbital ), nuclear binding energy
Nuclear binding energy
Nuclear binding energy is the energy required to split a nucleus of an atom into its component parts. The component parts are neutrons and protons, which are collectively called nucleons...

, etc. Eötvös experiment
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 the same accuracy. The earliest experiments were...

s detect no composition or field equivalence principle violations to 5x10-14 difference/average. Lunar laser ranging observes zero Nordtvedt effect
Nordtvedt effect
In theoretical astrophysics, the Nordtvedt effect refers to the relative motion between the Earth and the Moon which would be observed if the gravitational self-energy of a body contributed to its gravitational mass but not its inertial mass...

. Astronomic pulsar
Pulsar
A pulsar is a highly magnetized, rotating neutron star that emits a beam of electromagnetic radiation. The radiation can only be observed when the beam of emission is pointing towards the Earth. This is called the lighthouse effect and gives rise to the pulsed nature that gives pulsars their name...

binary star systems allow strong field extreme physical, compositional, relativistic, and quantum mechanical contrasts heroically beyond local measurements.

1.74 solar-mass 465.1 Hz pulsar PSR J1903+0327
PSR J1903+0327
PSR J1903+0327 is a millisecond pulsar in a highly eccentric binary orbit.The pulsar was discovered in an ongoing L-band survey with the 305 m diameter Arecibo radio telescope....

plus a 1.05 solar-mass star are a 95.17-day orbit binary system. 15.3% (AP4 model radius); vs. 0.0001% gravitational binding energy
Gravitational binding energy
The gravitational binding energy of an object consisting of loose material, held together by gravity alone, is the amount of energy required to pull all of the material apart, to infinity...

, 1.8x1011 vs. 30 surface gees, 2x108 gauss vs. 5 gauss magnetic field; compressed superfluid
Superfluid
Superfluidity is a state of matter in which the matter behaves like a fluid without viscosity and with extremely high thermal conductivity. The substance, which appears to be a normal liquid, will flow without friction past any surface, which allows it to continue to circulate over obstructions and...

neutrons and superconductive protons vs. proton-electron plasma
Plasma (physics)
In physics and chemistry, plasma is a state of matter similar to gas in which a certain portion of the particles are ionized. Heating a gas may ionize its molecules or atoms , thus turning it into a plasma, which contains charged particles: positive ions and negative electrons or ions...

, extreme isospin
Isospin
In physics, and specifically, particle physics, isospin is a quantum number related to the strong interaction. This term was derived from isotopic spin, but the term is confusing as two isotopes of a nucleus have different numbers of nucleons; in contrast, rotations of isospin maintain the number...

and lepton number
Lepton number
In particle physics, the lepton number is the number of leptons minus the number of antileptons.In equation form,so all leptons have assigned a value of +1, antileptons −1, and non-leptonic particles 0...

divergence; and pulsar 11% (AP4) of lightspeed equatorial spin velocity are differentially EP-inert for orbit, apsidal precession
Apsidal precession
In celestial mechanics, perihelion precession, apsidal precession or orbital precession is the precession of the orbit of a celestial body. More precisely it is the gradual rotation of the line joining the apsides of an orbit, which are the points of closest and farthest approach...

, and gravitational radiation orbital decay. 1.97 solar-mass 317.5 Hz PSR J1614-2230 and a 0.5 solar-mass He-C-O white dwarf
White dwarf
A white dwarf, also called a degenerate dwarf, is a small star composed mostly of electron-degenerate matter. They are very dense; a white dwarf's mass is comparable to that of the Sun and its volume is comparable to that of the Earth. Its faint luminosity comes from the emission of stored...

contrast the pulsar with Fermi-degenerate matter
Degenerate matter
Degenerate matter is matter that has such extraordinarily high density that the dominant contribution to its pressure is attributable to the Pauli exclusion principle. The pressure maintained by a body of degenerate matter is called the degeneracy pressure, and arises because the Pauli principle...

, 20% versus 0.01% gravitational binding energy, to no detected equivalence principle anomaly.

No measurable observable violates the equivalence principle in laboratory, local, and astronomic contrasts. Atomic mass distribution geometric parity (chirality
Chirality (physics)
A chiral phenomenon is one that is not identical to its mirror image . The spin of a particle may be used to define a handedness for that particle. A symmetry transformation between the two is called parity...

in all directions) can be observed and calculated but it cannot be measured. (Specific rotation
Specific rotation
In stereochemistry, the specific rotation of a chemical compound [α] is defined as the observed angle of optical rotation α when plane-polarized light is passed through a sample with a path length of 1 decimeter and a sample concentration of 1 gram per 1 millilitre. It is the main property used to...

of plane-polarized light is an electronic effect that does not measure atomic mass distribution chirality. It is unknown if (metaphoric) opposite shoes violate the equivalence principle.

Crystallography
Crystallography
Crystallography is the experimental science of the arrangement of atoms in solids. The word "crystallography" derives from the Greek words crystallon = cold drop / frozen drop, with its meaning extending to all solids with some degree of transparency, and grapho = write.Before the development of...

affords 230 unique ways to arrange points in three dimensions, the space group
Space group
In mathematics and geometry, a space group is a symmetry group, usually for three dimensions, that divides space into discrete repeatable domains.In three dimensions, there are 219 unique types, or counted as 230 if chiral copies are considered distinct...

s. 11 pairs of enantiomorphic space groups are mathematical geometric parity (physics)
Parity (physics)
In physics, a parity transformation is the flip in the sign of one spatial coordinate. In three dimensions, it is also commonly described by the simultaneous flip in the sign of all three spatial coordinates:...

pairs independent of composition. Delete individual space groups containing racemic
Racemic
In chemistry, a racemic mixture, or racemate , is one that has equal amounts of left- and right-handed enantiomers of a chiral molecule. The first known racemic mixture was "racemic acid", which Louis Pasteur found to be a mixture of the two enantiomeric isomers of tartaric acid.- Nomenclature :A...

or opposing sense screw axes. There remain enantiomorphic space groups P3121 | P3221 (e.g., alpha-quartz
Quartz
Quartz is the second-most-abundant mineral in the Earth's continental crust, after feldspar. It is made up of a continuous framework of SiO4 silicon–oxygen tetrahedra, with each oxygen being shared between two tetrahedra, giving an overall formula SiO2. There are many different varieties of quartz,...

) and P31 | P32 (e.g., gamma-glycine
Glycine
Glycine is an organic compound with the formula NH2CH2COOH. Having a hydrogen substituent as its 'side chain', glycine is the smallest of the 20 amino acids commonly found in proteins. Its codons are GGU, GGC, GGA, GGG cf. the genetic code.Glycine is a colourless, sweet-tasting crystalline solid...

). A geometric parity Eötvös experiment opposes chemically and macroscopically identical, left-handed versus right-handed atomic mass distributions as single crystal test masses - opposite shoes emergent at atomic bond lengths. The Eötvös apparatus and experimental protocol are otherwise unchanged.

Calorimetry detects geometric parity violation 40 times smaller than a torsion balance composition violation. Enthalpies of fusion of enantiomorphic space groups P3121 and P3221 benzil
Benzil
Benzil is the organic compound with the formula 2, generally abbreviated 2. This yellow solid is one of the most common diketones...

single crystals are simultaneously determined in paired differential scanning calorimeters to OEM 0.1% precision. That corresponds to 1.3x10−15 difference/average torsion balance sensitivity. Secondary standard 95°C calibration of calorimeters with powdered racemic benzil tolerates a 10−12 relative signal for resolved single crystals. Paired measurements on new crystals made each 30 minutes for 24 hours detect both vacuum insertion energy differences and inertial acceleration (Earth's spin) versus gravitational acceleration (Earth's orbit) varying chirality alignments - Lorentz invariance and equivalence principle violations.

### 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 freely falling laboratory is independent of the velocity of the laboratory and its location in spacetime.

Here "local" has a very special meaning: not only must the experiment not look outside the laboratory, but it must also be small compared to variations in the gravitational field, tidal forces, so that the entire laboratory is freely falling. It also implies the absence of interactions with "external" fields other than the gravitational field.

The principle of relativity
Principle of relativity
In physics, the principle of relativity is the requirement that the equations describing the laws of physics have the same form in all admissible frames of reference....

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
Fine-structure constant
In physics, the fine-structure constant is a fundamental physical constant, namely the coupling constant characterizing the strength of the electromagnetic interaction. Being a dimensionless quantity, it has constant numerical value in all systems of units...

and electron
Electron
The electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...

-to-proton
Proton
The proton is a subatomic particle with the symbol or and a positive electric charge of 1 elementary charge. One or more protons are present in the nucleus of each atom, along with neutrons. The number of protons in each atom is its atomic number....

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
Leonard I. Schiff
Leonard Isaac Schiff was born in Fall River, Massachusetts on March 29, 1915 and died on Jan 21, 1971.He was a physicist best known for his book Quantum Mechanics.-Education:...

's conjecture
suggests that the weak equivalence principle actually implies the Einstein equivalence principle, but it has not been proven. Nonetheless, the two principles are tested with very different kinds of experiments. The Einstein equivalence principle has been criticized as imprecise, because there is no universally accepted way to distinguish gravitational from non-gravitational experiments (see for instance Hadley 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
Oklo is a region near the town of Franceville, in the Haut-Ogooué province of the Central African state of Gabon. Several natural nuclear fission reactors were discovered in the uranium mines in the region in 1972.-History:...

natural nuclear fission reactor
Natural nuclear fission reactor
A natural nuclear fission reactor is a uranium deposit where analysis of isotope ratios has shown that self-sustaining nuclear chain reactions have occurred. The existence of this phenomenon was discovered in 1972 at Oklo in Gabon, Africa, by French physicist Francis Perrin. The conditions under...

, 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.
 Constant Year Method Limit on fractional change fine structure constant 1976 Oklo 10−7 weak interactionWeak interactionWeak interaction , is one of the four fundamental forces of nature, alongside the strong nuclear force, electromagnetism, and gravity. It is responsible for the radioactive decay of subatomic particles and initiates the process known as hydrogen fusion in stars... constant 1976 Oklo 10−2 electronElectronThe electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...-protonProtonThe proton is a subatomic particle with the symbol or and a positive electric charge of 1 elementary charge. One or more protons are present in the nucleus of each atom, along with neutrons. The number of protons in each atom is its atomic number.... mass ratio 2002 quasars 10−4 proton gyromagnetic factor 1976 astrophysical 10−1

There have been a number of controversial attempts to constrain the variation of the strong interaction
Strong interaction
In particle physics, the strong interaction is one of the four fundamental interactions of nature, the others being electromagnetism, the weak interaction and gravitation. As with the other fundamental interactions, it is a non-contact force...

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 quasar
Quasar
A quasi-stellar radio source is a very energetic and distant active galactic nucleus. Quasars are extremely luminous and were first identified as being high redshift sources of electromagnetic energy, including radio waves and visible light, that were point-like, similar to stars, rather than...

s, see Webb et al. Other researchers dispute these findings. Other tests of the Einstein equivalence principle are gravitational redshift
Gravitational redshift
In astrophysics, gravitational redshift or Einstein shift describes light or other forms of electromagnetic radiation of certain wavelengths that originate from a source that is in a region of a stronger gravitational field that appear to be of longer wavelength, or redshifted, when seen or...

experiments, such as the Pound-Rebka experiment
Pound-Rebka experiment
The Pound–Rebka experiment is a well known experiment to test Albert Einstein's theory of general relativity. It was proposed by Robert Pound and his graduate student Glen A. Rebka Jr. in 1959, and was the last of the classical tests of general relativity to be verified...

which test the position independence of experiments.

### The strong equivalence principle

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

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

The first part is a version of the weak equivalence principle that applies to objects that exert a gravitational force on themselves, such as stars, planets, black holes or Cavendish experiment
Cavendish experiment
The Cavendish experiment, performed in 1797–98 by British 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 constant. Because of the unit conventions then in use,...

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
Gravitational constant
The gravitational constant, denoted G, is an empirical physical constant involved in the calculation of the gravitational attraction between objects with mass. It appears in Newton's law of universal gravitation and in Einstein's theory of general relativity. It is also known as the universal...

be the same everywhere in the universe and is incompatible with a fifth force
Fifth force
Occasionally, physicists have postulated the existence of a fifth force in addition to the four known fundamental forces. The force is generally believed to have roughly the strength of gravity Occasionally, physicists have postulated the existence of a fifth force in addition to the four known...

. 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 tensor (general relativity)
In general relativity, the metric tensor is the fundamental object of study. It may loosely be thought of as a generalization of the gravitational field familiar from Newtonian gravitation...

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
Cosmological constant
In physical cosmology, the cosmological constant was proposed by Albert Einstein as a modification of his original theory of general relativity to achieve a stationary universe...

) 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
Brans-Dicke theory
In theoretical physics, the Brans–Dicke theory of gravitation is a theoretical framework to explain gravitation. It is a well-known competitor of Einstein's more popular theory of general relativity...

, 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
Big Bang nucleosynthesis
In physical cosmology, Big Bang nucleosynthesis refers to the production of nuclei other than those of H-1 during the early phases of the universe...

have shown that G cannot have varied by more than 10%.

Thus, the strong equivalence principle can be tested by searching for fifth force
Fifth force
Occasionally, physicists have postulated the existence of a fifth force in addition to the four known fundamental forces. The force is generally believed to have roughly the strength of gravity Occasionally, physicists have postulated the existence of a fifth force in addition to the four known...

s (deviations from the gravitational force-law predicted by general relativity). These experiments typically look for failures of the inverse-square law
Inverse-square law
In physics, an inverse-square law is any physical law stating that a specified physical quantity or strength is inversely proportional to the square of the distance from the source of that physical quantity....

(specifically Yukawa forces or failures of Birkhoff's theorem
Birkhoff's theorem (relativity)
In general relativity, Birkhoff's theorem states that any spherically symmetric solution of the vacuum field equations must be static and asymptotically flat. This means that the exterior solution must be given by the Schwarzschild metric....

) 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
Nordtvedt effect
In theoretical astrophysics, the Nordtvedt effect refers to the relative motion between the Earth and the Moon which would be observed if the gravitational self-energy of a body contributed to its gravitational mass but not its inertial mass...

, 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
Lunar laser ranging experiment
The ongoing Lunar Laser Ranging Experiment measures the distance between the Earth and the Moon using laser ranging. Lasers on Earth are aimed at retroreflectors planted on the moon during the Apollo program, and the time for the reflected light to return is determined...

. 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
Very Long Baseline Interferometry is a type of astronomical interferometry used in radio astronomy. It allows observations of an object that are made simultaneously by many telescopes to be combined, emulating a telescope with a size equal to the maximum separation between the telescopes.Data...

. Another sensitive test comes from measurements of the frequency shift of signals to and from the Cassini
Cassini-Huygens
Cassini–Huygens is a joint NASA/ESA/ASI spacecraft mission studying the planet Saturn and its many natural satellites since 2004. Launched in 1997 after nearly two decades of gestation, it includes a Saturn orbiter and an atmospheric probe/lander for the moon Titan, although it has also returned...

spacecraft. Together, these measurements have put tight limits on Brans-Dicke theory
Brans-Dicke theory
In theoretical physics, the Brans–Dicke theory of gravitation is a theoretical framework to explain gravitation. It is a well-known competitor of Einstein's more popular theory of general relativity...

and other alternative theories of gravity.

## Challenges to the equivalence principle

The best known challenge to the equivalence principle is the Brans-Dicke theory
Brans-Dicke theory
In theoretical physics, the Brans–Dicke theory of gravitation is a theoretical framework to explain gravitation. It is a well-known competitor of Einstein's more popular theory of general relativity...

; however, the theory represents the viewpoint of a tiny minority in the physics community. Self-creation cosmology
Self-creation cosmology
Self-creation cosmology theories are gravitational theories in which the mass of the universe is created out of its self-contained gravitational and scalar fields, as opposed to the theory of continuous creation cosmology or the steady state theory which depend on an extra 'creation'...

is a modification of the Brans-Dicke theory
Brans-Dicke theory
In theoretical physics, the Brans–Dicke theory of gravitation is a theoretical framework to explain gravitation. It is a well-known competitor of Einstein's more popular theory of general relativity...

. The Fredkin Finite Nature Hypothesis
Fredkin finite nature hypothesis
In digital physics, the Fredkin Finite Nature Hypothesis states that ultimately all quantities of physics, including space and time, are discrete and finite. All measurable physical quantities arise from some Planck scale substrate for multiverse information processing...

is an even more radical challenge to the equivalence principle and has even fewer supporters.

In August 2010, researchers from the School of Physics, University of New South Wales, Australia; the Centre for Astrophysics and Supercomputing, Swinburne University of Technology, Australia; and the Institute of Astronomy, Cambridge, United Kingdom; published the paper "Evidence for spatial variation of the fine structure constant", whose tentative conclusion is that, "qualitatively, [the] results suggest a violation of the Einstein Equivalence Principle, and could infer a very large or infinite universe, within which our `local' Hubble volume
Hubble volume
In cosmology, the Hubble volume, or Hubble sphere, is the region of the Universe surrounding an observer beyond which objects recede from the observer at a rate greater than the speed of light, due to the expansion of the Universe....

represents a tiny fraction."

## Explanations of the equivalence principle

Dutch physicist and string theorist
String theory
String theory is an active research framework in particle physics that attempts to reconcile quantum mechanics and general relativity. It is a contender for a theory of everything , a manner of describing the known fundamental forces and matter in a mathematically complete system...

Erik Verlinde
Erik Verlinde
Erik Peter Verlinde 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 topological field theory, is named after him. His research deals with string theory,...

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
Entropy is a thermodynamic property that can be used to determine the energy available for useful work in a thermodynamic process, such as in energy conversion devices, engines, or machines. Such devices can only be driven by convertible energy, and have a theoretical maximum efficiency when...

. Verlinde's approach to explaining gravity apparently leads naturally to the correct observed strength of dark energy
Dark energy
In physical cosmology, astronomy and celestial mechanics, dark energy is a hypothetical form of energy that permeates all of space and tends to accelerate the expansion of the universe. Dark energy is the most accepted theory to explain recent observations that the universe appears to be expanding...

; previous failures to explain its incredibly small magnitude have been called "the greatest embarassment in the history of theoretical physics". However, it should be noted that these ideas are far from settled and still very controversial.

The equivalence principle guarantees that a gravity field (a central force) cannot be distinguished from forces due to uniform acceleration. If two balls are dropped toward a gravitating mass the balls will converge as they fall towards the mass centroid. Under uniform acceleration, such as the ubiquitous accelerating elevator, the dropped balls will not converge, but fall in parallel paths.

## Experiments

• University of Washington
• Lunar Laser Ranging
• Galileo-Galilei satellite experiment
• Satellite Test of the Equivalence Principle (STEP)
STEP (satellite)
The Satellite Test of the Equivalence Principle is a proposed space science experiment to test the equivalence principle of general relativity...

• 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..."

• General Relativity
General relativity
General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...

• General covariance
General covariance
In theoretical physics, general covariance is the invariance of the form of physical laws under arbitrary differentiable coordinate transformations...

• Classical Mechanics
Classical mechanics
In physics, classical mechanics is one of the two major sub-fields of mechanics, which is concerned with the set of physical laws describing the motion of bodies under the action of a system of forces...

• Frame of reference
Frame of reference
A frame of reference in physics, may refer to a coordinate system or set of axes within which to measure the position, orientation, and other properties of objects in it, or it may refer to an observational reference frame tied to the state of motion of an observer.It may also refer to both an...

• Inertial frame of reference
• Mach's principle
Mach's principle
In theoretical physics, particularly in discussions of gravitation theories, Mach's principle is the name given by Einstein to an imprecise hypothesis often credited to the physicist and philosopher Ernst Mach....

• Brans-Dicke theory
Brans-Dicke theory
In theoretical physics, the Brans–Dicke theory of gravitation is a theoretical framework to explain gravitation. It is a well-known competitor of Einstein's more popular theory of general relativity...

• Gauge gravitation theory
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.The first gauge model of gravity was...

• Self-creation cosmology
Self-creation cosmology
Self-creation cosmology theories are gravitational theories in which the mass of the universe is created out of its self-contained gravitational and scalar fields, as opposed to the theory of continuous creation cosmology or the steady state theory which depend on an extra 'creation'...

• Fredkin Finite Nature Hypothesis
Fredkin finite nature hypothesis
In digital physics, the Fredkin Finite Nature Hypothesis states that ultimately all quantities of physics, including space and time, are discrete and finite. All measurable physical quantities arise from some Planck scale substrate for multiverse information processing...

• Tests of general relativity
Tests of general relativity
At its introduction in 1915, the general theory of relativity did not have a solid empirical foundation. It was known that it correctly accounted for the "anomalous" precession of the perihelion of Mercury and on philosophical grounds it was considered satisfying that it was able to unify Newton's...

• Unsolved problems in astronomy
• Unsolved problems in physics
Unsolved problems in physics
This is a list of some of the major unsolved problems in physics. Some of these problems are theoretical, meaning that existing theories seem incapable of explaining a certain observed phenomenon or experimental result...