The principle of relativity implies that the outcome of local experiments must be independent of the velocity of the apparatus, so the most important consequence
of this principle is the Copernican idea that dimensionless physical values such as the fine-structure constant and electron-to-proton mass ratio must not depend on where in space or time we measure them.
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
1g (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 assumption of exact physical equivalence makes it impossible for us to speak of the absolute acceleration of the system of reference, just as the usual theory of relativity
forbids us to talk of the absolute velocity of a system; and it makes the equal falling of all bodies in a gravitational field seem a matter of course.
 Development of gravitational theory 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 second part is the Einstein equivalence principle (with the same definition of “local”), restated to allow gravitational experiments and self-gravitating bodies.
 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.
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.
The strong equivalence principle suggests that gravity is entirely geometrical by nature (that is, the metric alone determines the effect of gravity) and does not have any
extra fields associated with it.
 The Einstein equivalence principle What is now called 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.
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.
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: We
arrive at a very satisfactory interpretation of this law of experience, if we assume that the systems K and K’ are physically exactly equivalent, that is, if we assume that we may just as well regard the system K as being in a space free from
gravitational fields, if we then regard K as uniformly accelerated.
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
These considerations suggest the following corollary to the equivalence principle, which Einstein formulated precisely in 1911: Whenever an observer detects the local presence
of a force that acts on all objects in direct proportion to the inertial mass of each object, that observer is in an accelerated frame of reference.
Einstein stated it thus: we … assume the complete physical equivalence of a gravitational field and a corresponding acceleration of the reference 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.
For by theoretical consideration of processes which take place relatively to a system of reference with uniform acceleration, we obtain information as to the career of processes
in a homogeneous gravitational field.
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.
— Einstein, 1911 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.
• 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
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.
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:
As long as we restrict ourselves to purely mechanical processes in the realm where Newton’s mechanics holds sway, we are certain of the equivalence of the systems K and K’.
Given this situation, gravity would not be a true fundamental force as is currently thought but instead an “emergent property” related to entropy.
The system provided them a chance to test the strong equivalence principle in a strong gravitational field with high accuracy.
Thus, the strong equivalence principle can be tested by searching for fifth forces (deviations from the gravitational force-law predicted by general relativity).
In general relativity, objects in free-fall follow geodesics 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 Earth’s matter or surface prevents us from doing so.
Noting the time to collision for each mass is the same gives Kepler’s statement that, without knowing the time to collision or how or if the acceleration force from gravity
is a function of distance.
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.
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.
Experiments are still being performed at the University of Washington which have placed limits on the differential acceleration of objects towards the Earth, the Sun and towards
dark matter in the Galactic Center.
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”, 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 represents a tiny fraction.
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.
So the original equivalence principle, as described by Einstein, concluded that free-fall and inertial motion were physically equivalent.
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.
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”.
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
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.
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
For Newton’s equation of motion in a gravitational field, written out in full, it is: The numerical equality between inertial mass and gravitational mass and acceleration
are independent of the properties of the body.
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.
With the first successful production of antimatter, in particular anti-hydrogen, a new approach to test the weak equivalence principle has been proposed.
If two stones were placed in any part of the world near each other, and beyond the sphere of influence of a third cognate body, these stones, like two magnetic needles, would
come together in the intermediate point, each approaching the other by a space proportional to the comparative mass of the other.
Future satellite experiments – STEP (Satellite Test of the Equivalence Principle), and Galileo Galilei – will test the weak equivalence principle in space, to much higher
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.
A number of independent constraints, from orbits in the Solar System and studies of Big Bang nucleosynthesis have shown that G cannot have varied by more than 10%.
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.
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…”
 • All local centers of mass free-fall (in vacuum) along identical (parallel-displaced, same speed) minimum action trajectories independent of all observable properties.
The present best limits on the variation of the fundamental constants have mainly been set by studying the naturally occurring Oklo natural nuclear fission reactor, where
nuclear reactions similar to ones we observe today have been shown to have occurred underground approximately two billion years ago.
Modern usage Three forms of the equivalence principle are in current use: weak (Galilean), Einsteinian, and strong.
This is the only form of the equivalence principle that applies to self-gravitating objects (such as stars), which have substantial internal gravitational interactions.
[‘• 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.
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, ISBN 0-486-60081-5. The two Einstein papers
are discussed online at The Genesis of General Relativity.
• Brans, Carl H.; “The roots of scalar-tensor theory: an approximate history”, arXiv:gr-qc/0506063. 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, ISBN 0-393-96501-5 Chapter 1 discusses the equivalence principle, but incorrectly, according to modern usage, states that the strong equivalence principle is wrong.
Jean-Philippe; “The fundamental constants and their variation: Observational status and theoretical motivations”, Reviews of Modern Physics 75, 403 (2003). arXiv:hep-ph/0205340 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 sections 2.1 Archived 16 April 2016 at the Wayback
Machine and 3.1, respectively.
• Friedman, Michael; Foundations of Space-Time Theories, Princeton, New Jersey: Princeton University Press, 1983. Chapter V discusses the equivalence principle.
• Ghins, Michel; Budden, Tim (2001), “The Principle
of Equivalence”, Stud. Hist. Phil. Mod. Phys., 32 (1): 33–51, Bibcode:2001SHPMP..32…33G, doi:10.1016/S1355-2198(00)00038-1
• Ohanian, Hans C. (1977), “What is the Principle of Equivalence?”, American Journal of Physics, 45 (10): 903–909, Bibcode:1977AmJPh..45..903O,
• Di Casola, E.; Liberati, S.; Sonego, S. (2015), “Nonequivalence of equivalence principles”, American Journal of Physics, 83 (1): 39, arXiv:1310.7426, Bibcode:2015AmJPh..83…39D, doi:10.1119/1.4895342, S2CID 119110646