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Equivalence PrincipleThe equivalence principle may be summarized by the following statement: - Whenever an observer detects the local presence of a force that acts on all objects in direct proportion to the inertial mass of the object, that observer is in an accelerated frame of reference.
The equivalence principle is therefore a rule for determining if one is in an accelerated frame of reference. History The equivalence principle was introduced by Albert Einstein in 1907. An that time, he made the observation that the acceleration of bodies towards the center of the Earth at 1g is equivalent to the acceleration of inertially moving bodies that one would observe if one was on a rocket in free space being accelerated at a rate of 1g. (It is from this equivalence that the equivalence principle was named.) From this principle, Einstein deduced that freefall is actually inertial motion, while being at rest with respect to the Earth (while under the influence of its gravitational field) is really an accelerated state of motion. This observation was the start of a process that eventually led to the development of general relativity. Although the equivalence principle helped to guide the development of general relativity, it actually is in that theory a consequence instead of being a foundation principle. Once Einstein was able to explain why inertial motion is really freefall instead of being at rest with respect to the Earth, it was no longer necessary to demonstrate that this must be the case. However, the equivalence principle continues to be cited to this day because it is an excellent pedagogical tool, helping people to bridge the conceptual gap between Newtonian mechanics and the geometrical world of general relativity. Comparison with Newtonian mechanics In Newtonian mechanics, gravity is assumed to be a force drawing objects towards the center of a massive body (such as the Earth). At its surface, this force is counter-balanced by the mechanical resistance of the surface to being penetrated. So a person on the surface of a non-rotating massive object is at rest in an inertial frame of reference due to the force of gravity being counter-balanced by the upward force of the surface on that person. In general relativity and according to the equivalence principle, the situation is quite different. Since inertial mass is the same as gravitational mass in the gravitational fields of massive bodies, the equivalence principle indicates that free-fall is actually inertial motion. In that case, there is only one force acting on a person standing on the surface of a massive object, and that is the upward force of the surface on that person. Weak versus strong equivalence principles There are two flavors of the equivalence principle: weak and strong. The weak equivalence principle is what was stated above. The strong equivalence principle is often stated as: - The (local) effects of a gravitational field are identical in all respects to the effect of uniform acceleration.
The strong equivalence principle is not true. The gravitational fields for massive bodies such as the Earth are not uniform nor do such fields behave as if they were uniform. The strong equivalence principle indicates that no experiment can distinguish between being on the surface of the Earth and being accelerated by a rocket in free space. In fact, there are variations in both strength and direction between neighboring positions in the gravitational fields for massive objects. These variations create measurable tidal effects. On an accelerating rocket far from any gravitating object, the gravitational field is uniform, and no tidal effects will be observed. So the tides of the oceans are actually observational repudiations of the strong equivalence principle. Although only the weak equivalence principle is valid, it should be noted that being in an accelerated frame of reference is enough to explain the downward acceleration of massive objects and the bending of light due to gravitation, as well as gravitational time dilation. It should also be noted that the non-uniformity of the gravitational fields around massive objects is what forced Einstein to formulate general relativity. (This non-uniformity implies that spacetime is curved. General relativity relates that curvature to the presence of mass, energy, and momentum.) Validation Tests of the validity of the equivalence principle are those that verify the equivalence of gravitational mass and inertial mass. This is evidenced by all objects falling at the same rate when the effect of air resistance is either eliminated or negligible. Notable test are: | b>Researcher | |Year | |Method | |Result | | Galileo Galilei | |~1610 | |Dropping metal balls of different mass from the Tower of Pisa | |no detectable difference | | Isaac Newton | |~1680 | |measure the period 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 | | Roland Etvs | |1908 | |measure the torsion on a wire, suspending a balance beam, between two nearly identical masses under the acceleration of gravity and the rotation of the Earth | |difference is less than 1 part in a billion | | Neil Armstrong | |1969 | |Dropped an eagle feather and a hammer at the same time on the Moon | |no detectable difference (Not a very good experiment, but it was the first lunar one.) | | Branginsky and Panov | |1971 | |torsion balance with effects of the Sun's gravitation accounted for | |difference is less than 1 part in a trillion (most accurate to date) | See also References - Hans Ohanian and Remo Ruffini Gravitation and Spacetime 2nd edition ISBN 0-393-96501-5, Chapter 1.
- Albert Einstein On the influence of gravitation on the propagation of light, Annalen der Physik, 35 (1911), as translated in The Principle of Relativity ISBN 0-486-60081-5, pp 99-108.
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