# Equivalence principle

**strong equivalence principleequivalentPrinciple of Equivalenceweak equivalence principleEinstein equivalence principleequivalencephysically indistinguishableto an unprecedented level of accuracyunprecedented levels of accuracy**

In the theory of general relativity, the equivalence principle is the equivalence of gravitational and inertial mass, and Albert Einstein's observation that the gravitational "force" as experienced locally while standing on a massive body (such as the Earth) is the same as the pseudo-force experienced by an observer in a non-inertial (accelerated) frame of reference.wikipedia

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### Mass

**inertial massgravitational massweight**

In the theory of general relativity, the equivalence principle is the equivalence of gravitational and inertial mass, and Albert Einstein's observation that the gravitational "force" as experienced locally while standing on a massive body (such as the Earth) is the same as the pseudo-force experienced by an observer in a non-inertial (accelerated) frame of reference. Something like the equivalence principle emerged in the early 17th century, when Galileo expressed experimentally that the acceleration of a test mass due to gravitation is independent of the amount of mass being accelerated.

This is sometimes referred to as gravitational mass. Repeated experiments since the 17th century have demonstrated that inertial and gravitational mass are identical; since 1915, this observation has been entailed a priori in the equivalence principle of general relativity.

### General relativity

**general theory of relativityrelativitygeneral relativity theory**

In the theory of general relativity, the equivalence principle is the equivalence of gravitational and inertial mass, and Albert Einstein's observation that the gravitational "force" as experienced locally while standing on a massive body (such as the Earth) is the same as the pseudo-force experienced by an observer in a non-inertial (accelerated) frame of reference. 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.

According to Newton's law of gravity, and independently verified by experiments such as that of Eötvös and its successors (see Eötvös experiment), there is a universality of free fall (also known as the weak equivalence principle, or the universal equality of inertial and passive-gravitational mass): the trajectory of a test body in free fall depends only on its position and initial speed, but not on any of its material properties.

### Accelerometer

**accelerometersG-sensoracceleration sensor**

This is why an accelerometer in free-fall doesn't register any acceleration; there isn't any.

Put another way, at any point in spacetime the equivalence principle guarantees the existence of a local inertial frame, and an accelerometer measures the acceleration relative to that frame.

### Force

**forcesattractiveforce vector**

By contrast, in Newtonian mechanics, gravity is assumed to be a force.

Since there is no experiment that can distinguish whether it is the vehicle that is at rest or the outside world that is at rest, the two situations are considered to be physically indistinguishable.

### Spacetime

**space-timespace-time continuumspacelike**

Analogously, in a curved spacetime the world line of an inertial particle or pulse of light is as straight as possible (in space and time).

In addition, Einstein in 1905 superseded previous attempts of an electromagnetic mass-energy relation by introducing the general equivalence of mass and energy, which was instrumental for his subsequent formulation of the equivalence principle in 1907, which declares the equivalence of inertial and gravitational mass. By using the mass-energy equivalence, Einstein showed, in addition, that the gravitational mass of a body is proportional to its energy content, which was one of early results in developing general relativity.

### MICROSCOPE (satellite)

**MICROSCOPEMICROSCOPE (MICROSatellite à traînée Compensée pour l'Observation du Principe d'Équivalence)**

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

The Micro-Satellite à traînée Compensée pour l'Observation du Principe d'Equivalence (MICROSCOPE) is a 300 kg class minisatellite operated by CNES to test the universality of free fall (the equivalence principle) with a precision to the order of, 100 times more precise than can be achieved on Earth.

### Fictitious force

**inertial forcefictitious forcesinertial**

In the theory of general relativity, the equivalence principle is the equivalence of gravitational and inertial mass, and Albert Einstein's observation that the gravitational "force" as experienced locally while standing on a massive body (such as the Earth) is the same as the pseudo-force experienced by an observer in a non-inertial (accelerated) frame of reference.

He noted that a freefalling observer in a closed box would not be able to detect the force of gravity; hence, freefalling reference frames are equivalent to an inertial reference frame (the equivalence principle).

### Gravity

**gravitationgravitationalgravitational force**

By contrast, in Newtonian mechanics, gravity is assumed to be a force. Something like the equivalence principle emerged in the early 17th century, when Galileo expressed experimentally that the acceleration of a test mass due to gravitation is independent of the amount of mass being accelerated.

The equivalence principle, explored by a succession of researchers including Galileo, Loránd Eötvös, and Einstein, expresses the idea that all objects fall in the same way, and that the effects of gravity are indistinguishable from certain aspects of acceleration and deceleration.

### Free fall

**free-fallfreefallhighest fall without a parachute**

From this principle, Einstein deduced that free-fall is inertial motion.

The experimental observation that all objects in free fall accelerate at the same rate, as noted by Galileo and then embodied in Newton's theory as the equality of gravitational and inertial masses, and later confirmed to high accuracy by modern forms of the Eötvös experiment, is the basis of the equivalence principle, from which basis Einstein's theory of general relativity initially took off.

### Geodesics in general relativity

**geodesicgeodesicsnull geodesic**

Such a world line is called a geodesic and from the point of view of the inertial frame is a straight line.

Physicist Steven Weinberg has presented a derivation of the geodesic equation of motion directly from the equivalence principle.

### Frame-dragging

**frame draggingdragsrotating spacetime**

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.

Due to the equivalence principle, gravitational effects are locally indistinguishable from inertial effects, so this rotation rate, at which when she extends her arms nothing happens, is her local reference for non-rotation.

### Albert Einstein

**EinsteinA. EinsteinEinstein, Albert**

The equivalence principle was properly introduced by Albert Einstein in 1907, when he observed that the acceleration of bodies towards the center of the Earth at a rate of 1'g' (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 1g.

This argument is called the equivalence principle.

### Robert H. Dicke

**DickeRobert DickeBob Dicke**

This was developed by Robert Dicke as part of his program to test general relativity.

He spent the remainder of his career developing a program of precision tests of general relativity using the framework of the equivalence principle.

### Fifth force

**fifth fundamental forceunobserved fundamental forces**

Proposals that may lead to a quantum theory of gravity such as string theory and loop quantum gravity predict violations of the weak equivalence principle because they contain many light scalar fields with long Compton wavelengths, which should generate fifth forces and variation of the fundamental constants.

One way to search for a fifth force is with tests of the strong equivalence principle: this is one of the most powerful tests of Einstein's theory of gravity: general relativity.

### Gravitational redshift

**gravitational red shiftEinstein shiftgravitationally redshifted**

Other tests of the Einstein equivalence principle are gravitational redshift experiments, such as the Pound–Rebka experiment which test the position independence of experiments.

Einstein's equivalence principle ("all bodies fall with the same acceleration, independent of their composition") and was found by Einstein eight years before

### Acceleration

**decelerationacceleratem/s 2**

Something like the equivalence principle emerged in the early 17th century, when Galileo expressed experimentally that the acceleration of a test mass due to gravitation is independent of the amount of mass being accelerated.

Albert Einstein called this the equivalence principle, and said that only observers who feel no force at all—including the force of gravity—are justified in concluding that they are not accelerating.

### Brans–Dicke theory

**Brans–DickeBrans-Dicke theoryJordan/Brans/Dicke theory**

A number of alternative theories, such as Brans–Dicke theory, satisfy only the Einstein equivalence principle.

All metric theories satisfy the Einstein equivalence principle, which in modern geometric language states that in a very small region (too small to exhibit measurable curvature effects), all the laws of physics known in special relativity are valid in local Lorentz frames.

### Equivalence principle (geometric)

**geometric Equivalence Principle geometric equivalence principle**

Equivalence principle (geometric)

The equivalence principle is one of the corner-stones of gravitation theory.

### STEP (satellite)

**STEPSatellite Test of the Equivalence PrincipleSatellite Test of the Equivalence Principle (STEP)**

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

The Satellite Test of the Equivalence Principle (STEP) is a proposed space science experiment to test the equivalence principle of general relativity.

### Nordtvedt effect

**Self-gravitating system**

Other limits, looking for much longer-range forces, have been placed by searching for the Nordtvedt effect, a "polarization" of solar system orbits that would be caused by gravitational self-energy accelerating at a different rate from normal matter.

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 differently to its gravitational mass than to its inertial mass. If observed, the Nordtvedt effect would violate the strong equivalence principle, which indicates that an object's movement in a gravitational field does not depend on its mass or composition.

### Tests of general relativity

**confirmedanomalous precessionclassical tests of general relativity**

Einstein combined (postulated) the equivalence principle with special relativity 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.

Einstein predicted the gravitational redshift of light from the equivalence principle in 1907, and it was predicted that this effect might be measured in the spectral lines of a white dwarf star, which has a very high gravitational field.

### Einstein's thought experiments

**Einstein and the quantumEinstein's thought experimentthought experiment**

Einstein's thought experiments

This correspondence between gravitational mass and inertial mass is the equivalence principle.

### Entropic gravity

**entropy and gravity**

Verlinde's entropic gravity theory apparently leads naturally to the correct observed strength of dark energy; previous failures to explain its incredibly small magnitude have been called by such people as cosmologist Michael Turner (who is credited as having coined the term "dark energy") as "the greatest embarrassment in the history of theoretical physics".

In 1995, Jacobson demonstrated that the Einstein field equations describing relativistic gravitation can be derived by combining general thermodynamic considerations with the equivalence principle.

### Lunar Laser Ranging experiment

**lunar laser rangingLLRLunar Laser Ranging experiments**

This effect has been sensitively tested by the Lunar Laser Ranging Experiment.

The likelihood of any Nordtvedt effect (a differential acceleration of the Moon and Earth towards the Sun caused by their different degrees of compactness) has been ruled out to high precision, strongly supporting the validity of the strong equivalence principle.

### Fredkin finite nature hypothesis

The Fredkin Finite Nature Hypothesis is an even more radical challenge to the equivalence principle and has even fewer supporters.

According to Witten, "string theory leads in a remarkably simple way to a reasonable rough draft of particle physics unified with gravity"; if Fredkin is correct about inertia, then there is the highly controversial hypothesis that the foundations of physics might depend upon either string theory with the infinite nature hypothesis or some modified version of string theory with Fredkin's finite nature hypothesis, in which inertial mass-energy obeys Milgrom's modified Newtonian dynamics and not the equivalence principle.