Relativity, General Theory of

Meaning of Relativity

As in special relativity (SR), the term relativity corresponds to two or more observers who make measurements with respect (relative) to each other. This means that there exists no absolute point or frame to which measurements can be referred. To picture this, consider a passenger inside a train that passes by a station. This passenger observes a trolley travel inside the train with a velocity of about 0.3 meters per second. To an observer standing at the station, that trolley appears to have the velocity of the train plus the 0.3 meters per second. The two measurements of the velocity of the same object differ, depending on the position of the observer. This example demonstrates that there is no independent point from which the observations appear to be the same; they can only be regarded relative to each other. In terms of physics, there is no absolute preferred frame (position) in which physical processes are measured and described. Every observer located at an arbitrary position, like the train or the platform, describes the movement correctly. The most important aspect is that, for all freely moving observers, without the presence of any other forces the physical laws are the same independent of their respective relative velocity. Another fundamental fact of SR and GR is the constancy of the speed of light. In each frame, it has the same value.

The Equivalence Principle

In GR, the argument of relativity is extended further in order to include gravity. Einstein's realization was in understanding that the gravitational force is equivalent to an inertial force and in thereby concluding his principle of equivalence. (An inert force appears if movements are described in accelerated frames, like standing in an accelerated subway.) Imagine a free-falling elevator in a building. To a person standing within it, it seems that there is no gravity, because the inert force counterbalances the gravitational force. However, to an observer standing outside, it is clear that the elevator is accelerated toward the ground by the gravity field of the earth. Inside the elevator, the person does not feel the gravitational field, and all physical laws within this frame are written without considering gravity.

A further example to demonstrate this equivalence is given by the picture of an astronaut inside a spaceship. Let us consider two special cases, one with the spaceship standing on the surface of the earth and one with the spaceship being constantly accelerated. In the latter case, the astronaut will feel the inert force due to the acceleration, and with that a certain weight, as if a gravitational force is acting. On the surface of the earth, however, gravitational force is exerted on the astronaut inside. But the astronaut is not able to distinguish whether he or she is at rest within a gravitational field, or experiencing an inertial force due to the acceleration. Hence, gravitation can be seen either as the attracting force or the inertial force. This means that gravity can be “switched off” locally by going into a frame in which the inert force cancels the gravitational force. Such a system could be a free-falling elevator or a satellite in orbit.

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