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Equivalence principle

The equivalence principle is the hypothesis that the observed equivalence of gravitational and inertial mass is a consequence of nature. The weak form, known for centuries, relates to masses of any composition in free fall taking the same trajectories and landing at identical times. The extended form by Albert Einstein requires special relativity to also hold in free fall and requires the weak equivalence to be valid everywhere. This form was a critical input for the development of the theory of general relativity. The strong form requires Einstein's form to work for stellar objects. Highly precise experimental tests of the principle limit possible deviations from equivalence to be very small.

This article is about the principle in gravitation. For the principle in electromagnetism, see surface equivalence principle.

"All uncharged, freely falling test particles follow the same trajectories, once an initial position and velocity have been prescribed".: 6 

[8]

"... in a uniform gravitational field all objects, regardless of their composition, fall with precisely the same acceleration." "The weak equivalence principle implicitly assumes that the falling objects are bound by non-gravitational forces."

[11]

"... in a gravitational field the acceleration of a test particle is independent of its properties, including its rest mass."

[12]

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 , 1687).

Philosophiæ Naturalis Principia Mathematica

Experimental tests[edit]

Tests of the weak equivalence principle[edit]

Tests of the weak equivalence principle are those that verify the equivalence of gravitational mass and inertial mass. An obvious test is dropping different objects and verifying that they land at the same time. Historically this was the first approach, though probably not by Galileo's Leaning Tower of Pisa experiment[18]: 19–21  but earlier by Simon Stevin[19] who dropped lead balls of different masses off the Delft churchtower and listened for the sound they made on a wooden plank.


Isaac Newton measured the period of pendulums made with different materials as an alternative test giving the first precision measurements.[2] Loránd Eötvös's approach in 1908 used a very sensitive torsion balance to give precision approaching 1 in a billion. Modern experiments have improved this by another factor of a million.


A popular exposition of this measurement was done on the Moon by David Scott in 1971. He dropped a falcon feather and a hammer at the same time, showing on video[20] that they landed at the same time.

Gravity and the principle of equivalence – The Feynman Lectures on Physics

from Syracuse University

Introducing The Einstein Principle of Equivalence

at MathPages

The Equivalence Principle

at Living Reviews on General Relativity

The Einstein Equivalence Principle

"...Physicists in Germany have used an atomic interferometer to perform the most accurate ever test of the equivalence principle at the level of atoms..."