General relativity (GR) is the geometrical theory of gravitation published by Albert Einstein in 1915. It unifies Einstein's earlier special relativity with Isaac Newton's law of universal gravitation. This is done with the insight that gravitation is not due to a force but rather is a manifestation of curved space and time.
In the early 1920s Arthur Eddington claimed that there were only 3 people in the world who understood general relativity
Einstein's treatment of gravitation
The equivalence principle
Einstein was uncomfortable with the equations he had for gravitation as a force. Then he noticed something. A person free falling in an elevator will notice that he is floating, something very similar to an inertial system in the space.
He postulated that a free falling system is a privileged system, similar to the inertial systems of special relativity, but while an inertial system follows a straight line in space-time (see special relativity), these free-falling systems follow bent lines.
He postulated that the presence of the earth bends the space-time inertial paths in some way, making the straight lines of the inertial systems a curve. With this in mind, we can explain usual things in a different way:
A satellite circling the earth is following an inertial path, with that the path being curved by the presence of the earth.
If we throw a stone it will make something close to a parabola, but in fact is like an ellipse. The stone is following an inertial path like the one of the satellite.
And when we are sitting on a chair, we are trying to follow an inertial path or orbit, but the chair does not allow us to do it. Therefore we are accelerated with respect to the inertial path of free fall. This explains the sensation of acceleration or gravity when living on earth.
Therefore, the gravitational field we feel at the surface of the earth is really a fictitious force like those of other non-inertial frames of reference. From this moment, we will use in this article the word "gravitational" to refer to any fictitious field.
Extension of special relativity to non-inertial frames of reference
Though initially general relativity was intended as an extension of special relativity to non-inertial frames, nowadays only the theory of gravitation is considered GR, and non-inertial frames are considered just an introduction, because Accelerated frames of reference can be examined in special relativity by considering the instantaneous inertial frame of reference that an accelerated observer is in at a given event.
This consideration leads to two related effects: gravitational time dilation and gravitational red shift.
For example consider two people in an accelerating rocket ship with one being above the other (in the direction of acceleration) in the rocket ship. If the "lower" person emits a beam of light towards the "upper" person, during the time the light is traveling the upper will accelerate from the inertial frame in which the light was emitted to one which is moving away from the source of the light. As a result, the light will be red-shifted for the upper person. This is the gravitational red shift effect. Similarly, the light emitted by the upper person will be blue shifted for the lower person (since the lower person is being accelerated towards the source of the light).
The red-shifting being continuous reveals another effect for accelerated observers: gravitational time dilation. Since the red-shift means that the light is not vibrating as fast, it must follow that time for the lower person runs slow in the perception of the upper person.
Another effect is the bending of light. For an accelerated observer, a beam of light which is initially traveling horizontally will be bent "downwards" over time as the observers accelerate into "upwards" moving frames of reference.
By virtue of the equivalence principle as described above, all of these effects should be observable in the gravitational fields of the Earth and the stars. For example:
The gravitational red-shift of light was confirmed by Pound and Rebka in 1959
The Hafele-Keating experiment validated gravitational time dilation. An even more rigorous confirmation was done by the GPS system.
In 1919, Eddington verified the bending of light by the Sun's gravitational field.
The Einstein field equations
As orbital motion and free-fall are dependent on the presence of a massive object, it follows in general relativity and related metric theories of gravitation that the presence of mass somehow curves spacetime. Furthermore, mass is a form of energy in relativity (due to E=mc2), and energy and momentum are intertwined in relativity (just as space and time are intertwined). So it follows that presence of mass, energy, and momentum (or "matter") causes spacetime to be curved.
In general relativity, this relationship between matter and curvature is described by the Einstein field equations. These equations were discovered by Einstein in late 1915. The Einstein field equations are expressed using tensor calculus, and are a collection of up to 10 independent simultaneous differential equations. These field equations are solved to create metrics of spacetime. (A metric of spacetime describes the invariant intervals squared between neighboring positions in spacetime whose coordinates differ by an infinitesimal amount. The simplest metric of spacetime is the Minkowski metric.) These metrics described the shape of the spacetime, and the curvature of spacetime and equations of motion for inertially moving objects can be obtained from it.
The actual shapes of spacetime are described by solutions of the Einstein field equations. In particular, the Schwarzschild solution (1916) describes the gravitational field around a spherically symmetric massive object. The geodesics of the Schwarzschild solution describe the observed behavior of objects being acted on gravitationally, including the anomalous perihelion precession of Mercury and the bending of light as it passes the Sun.
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2006-07-16 13:12:12
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answer #4
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answered by Sherlock Holmes 6
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