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The Principle of Equivalence |
The principle of equivalence is an assertion that Einstein made to guide him in his understanding of gravitation. Just like the principle of relativity guided him in his development of special relativity, the principle of equivalence guided him in his development of general relativity. Just like the principle of relativity asserts that it is impossible to distinguish one inertial frame from another, the principle of equivalence asserts that it is impossible to distinguish one accelerating frame from another.
More explicitly, the principle of equivalence asserts that it is impossible to distinguish experimentally between a spaceship at rest in a gravitational field and one accelerating uniformly in free space. Conversely, it is impossible to distinguish experimentally between a spaceship falling freely in a gravitational field and one floating freely in space.
Another way to express the principle of equivalence is to say that the spacetime of a uniform gravitational field is identical to the spacetime of special relativity. Therefore, if you want to understand the properties of gravity, simply view Minkowski spacetime from an accelerated frame of reference.
Therefore, general relativity is not necessary to accommodate accelerated observers or to understand many of the properties of gravity. Special relativity is perfectly adequate. Not only can special relativity be applied to accelerating observers but it must apply to accelerating frames. Otherwise, the principle of equivalence would be completely worthless.
However, only the properties of a uniform gravitational field can be deduced from the flat Minkowski spacetime. To understand the properties of non-uniform gravitational fields, curved spacetimes must be considered. In this case, the principle of equivalence requires that the curved spacetime of general relativity must be locally Minkowski. Not only must curved space be locally flat, but the relationship between space and time in general relativity must be the same as their relationship in special relativity. All the equations and relationships derived for special relativity must carry over into general relativity, at least on the local level.
Therefore, an observer falling freely under the influence of gravity is in a locally inertial frame of reference. There is no local experiment a free-falling observer can perform to distinguish his frame of reference from that of an inertial observer located in free space. Of course, if he extends his experiment very far outside of his local environment, he will be able to detect the non-uniformity of the gravitational field – the curvature of spacetime.
Questions:
Q1. Which are true? (A) Einstein
used the correspondence principle to guide him in the development of general
relativity. (B) The principle of equivalence asserts that it is impossible to
distinguish experimentally between a spaceship at rest in a gravitational field
and one floating freely in free space (C) The principle of equivalence requires
that the curved spacetime of general relativity must be locally Minkowski. (D)
Two of these. (E) Three of these.
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