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The principle of equivalence may be summarized by the following statement:
Whenever an observer detects the presense of a force that acts of all objects
in direct proportion to the inertial mass of the object, that observer is in
an accelerated frame of reference.
The Equivalance Principle is therefore a rule for determining if one is in an accelerated frame of reference.
Since inertial mass is equivalent to gravitational mass in gravitational fields, this shows that a local gravitational fields represent accelerated frames of reference.
History of the Equivalance Principle
The Equivalence Principle was introduced by Albert Einstein in 1911. In that article, he made the observation that the unfirm acceleration of bodies towards the center of the Earth is basically that effect as one would observe if one was on a rocket in free space, being accelerated at a rate of 1g. This observation was the start of a process that eventually led to the development of general relativity
Weak vs. Strong Equivalnce Principles
There are two flavors of the Equivalence Principle: Weak and Strong. The weak equivlance principle is what was stated above. The strong equivalance 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 is not uniform nor does 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, the variations in both the strength and direction of the gravitational fields for massive object between neighboring positions create measurable tidal effects. So the tides themselves are in fact observational repudiations of the strong equivalence principle.
So only the weak equivalance principle is valid. It should be noted that the being in an accelerated frame of reference is enough to explain the downward acceleration of massive objects due and the bending of light 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 is the theory that relates that curvature to the presense of mass, energy, and momentum.)
Validation of the Equivalence Principle
| Researcher
| Method
| Result
|
| Isaac Newton
| measure the period of pendulums of different mass but identical length
| no measurable difference
|
| Friedrich Wilhelm Bessel
| measure the period of pendulums of different mass but identical length
| no measurable difference
|
| Roland von Eötvos
| 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
|
This principle, enunciated by Albert Einstein, 1907 as the equivalence of gravitational and inertial mass, is a central tenet of his theory of general relativity.
In summary, the principle of equivalence entails the following assumptions:
Being in free fall in a volume of curved space-time is profoundly similar to floating in zero-curvature space-time. Locally, curved space-time is fundamentally indistinguishable from zero-curvature space-time.
- If the surface of a gravitating body is pushing against you, keeping you from moving along the geodesic, that is: causing you to deviate from moving along the geodesic, then that surface is accelerating you in your local volume of space-time.
- If you are in a space-ship and you engage your thrusters, then this force will make you deviate from moving along the geodesic.
- If you are in a pilot training centrifuge, or rollercoaster ride, or in any situation making curves, a force is necessary to make you deviate from moving along the geodesic.
Note: Einstein used the principle of equivalence to guide his explorations in search for General Relativity. But Einstein did not view the principle of equivalence in the way it is described in this section of the article, this description draws heavily on the benefit of hindsight. The description in this section of the article presents a modernized principle of equivalance, not a historical one.
See also
References
- Steven Weinberg Gravitation and Cosmology ISBN 0-471-92567-5, pp. 188-190 (for bending of light in a gravitational field), 342-348 (for time dilation during gravitational collapse).
External links
