The Equivalence Principle The Newtonian Version Gravitational mass is the charge to which gravity couples. Inertial mass is a measure of how fast an object accelerates--given the same force, increasing the inertial mass implies decreasing acceleration. The simplest way to state the equivalence principle is this: inertial mass and gravitational mass are the same thing. Then, gravitational force is proportional to inertial mass, and the proportionality is independent of the kind of matter. This implies the Universality of Free Fall(UFF): in a uniform gravitational field, all objects fall with the same acceleration, e.g. 9.8m/s2 near the surface of the earth. The Einsteinian Version All objects fall the same way under the influence of gravity; therefore, locally, one cannot tell the difference between an accelerated frame and an unaccelerated frame. Consider the famous example of a person in a falling elevator. The person floats in the middle of an elevator that is falling down a shaft. Locally, that is during any sufficiently small amount of time or over a sufficiently small space, the person falling in the elevator can make no distinction between being in the falling elevator or being in completely empty space, where there is no gravity. We could imagine two apples floating on either side of the person; as the elevator approached the earth, the apples would approach each other. This happens because their paths, both toward the center of the earth, eventually converge. But this is not an effect that can be detected in a local experiment. This statement of the equivalence principle makes an important suggestion. In special relativity--and all classical mechanics--we are used to the idea that objects travel at constant velocity unless a force acts on them. Now, if we cant locally tell the difference between falling in a gravitational field and travelling at constant velocity, then, locally, they must be the same thing. The paths of free bodies define what we mean by straight and if we observe an object deviate from constant velocity, it must be because spacetime itself is curved. Formally, we state the equivalence principle this way: in any and every locally Lorentz (inertial) frame, the laws of special relativity must hold. From this, we conclude that the only things which can define the geometric structure of spacetime are the paths of free bodies. The Strong and Weak Equivalence Principles Often, one finds references to the strong or weak equivalence principle. The weak equivalence principle has been stated, in the equality of gravitational and inertial mass and in the statement about special relativistic laws holding in every locally Lorentz frame, if we restrict that statement to the laws of freely falling bodies. The strong equivalence principle applies to all laws of nature, and implies that even gravitational self-energy must obey the equivalence principle.
Posted on: Sat, 15 Nov 2014 19:23:06 +0000
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