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Locally Inertial Frame


 

The difference between the locally inertial frame of general relativity and the inertial frame of special relativity is that the inertial frame of special relativity is able to span the whole flat Minkowski spacetime. But the inertial frame of general relativity is only valid locally. Exactly how locally depends upon the curvature of spacetime. If the spacetime is relatively flat, the inertial frame is valid over large distances and times. But if the spacetime is highly curved, the inertial frame is valid only over short distances and times.

 

Perhaps you have heard of experiments performed in an orbiting space shuttle or space station being referred to as micro-gravity experiments rather than zero-gravity experiments. This is because it is difficult to maintain a true zero-gravity environment for a prolonged period of time even over regions of space as small as a spaceship.

 

Consider, for example, two objects released perfectly at rest in an orbiting spaceship. If one object is located farther from the earth than the other, then the earth will pull slightly harder on the lower object than the higher object. Therefore, it is just a matter of time before the two objects drift apart. The non-uniformity of the gravitational field will eventually make itself known. In other words, the curvature of spacetime will eventually be distinguished from flat spacetime.

 

So when we say that curved space is locally flat or that an observer is in a locally inertial frame of reference, we assume that it is understood that the size of the locality depends upon the amount of curvature of spacetime and the amount of deviation from flatness one is willing to ignore.

 

 

 

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