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2007-09-12 07:14:10 · 5 answers · asked by chimsy 2 in Science & Mathematics Physics

5 answers

(GR) (aka general theory of relativity (GTR)) is the geometrical theory of gravitation published by Albert Einstein in 1915/16. It unifies special relativity, Newton's law of universal gravitation, and the insight that gravitational acceleration can be described by the curvature of space and time. General relativity further calls for the curvature of space-time to be produced by the mass-energy and momentum content of the matter in space-time. General relativity is distinguished from other metric theories of gravitation by its use of the Einstein field equations to relate space-time content and space-time curvature.

General relativity is currently the most successful gravitational theory, being almost universally accepted and well-supported by observations. The first success of general relativity was in explaining the anomalous perihelion precession of Mercury. Then in 1919, Sir Arthur Stanley Eddington announced that observations of stars near the eclipsed Sun confirmed general relativity's prediction that massive objects bend light. Since then, many other observations and experiments have confirmed many of the predictions of general relativity, including gravitational time dilation, the gravitational redshift of light, signal delay, and gravitational radiation. In addition, numerous observations are interpreted as confirming one of general relativity's most mysterious and exotic predictions, the existence of black holes.

In the mathematical formalism of general relativity, the Einstein field equations are a system of partial differential equations whose solution represents the metric tensor (or the metric) of space-time, describing its "shape". Some important solutions of the Einstein field equations are the Schwarzschild solution (for the space-time surrounding a spherically symmetric uncharged and non-rotating massive object), the Reissner-Nordström solution (for a charged spherically symmetric massive object), and the Kerr metric (for a rotating massive object). An object moving inertially in a gravitational field follows a geodesic path that may be found using the Christoffel symbol of the metric.

In spite of its overwhelming success, there is discomfort with general relativity in the scientific community due to its being incompatible with quantum mechanics and the reachable singularities of black holes (at which the mathematics of general relativity breaks down). Because of this, numerous other theories have been proposed as alternatives to general relativity. An early and still-popular class of modifications is Brans-Dicke theory, which, although not solving the problems of singularities and quantum gravity, appeared to have observational support in the 1960s. However, those observations have since been refuted and modern measurements indicate that any Brans-Dicke type of deviation from general relativity must be very small if it exists at all.

The justification for creating general relativity came from the equivalence principle, which dictates that free-falling observers are the ones in inertial motion. Roughly speaking, the principle states that the most obvious effect of gravity – things falling down – can be eliminated by making the transition to a reference frame that is in free fall, and that in such a reference frame, the laws of physics will be approximately the same as in special relativity. A consequence of this insight is that inertial observers can accelerate with respect to each other. For example, a person in free fall in an elevator whose cable has been cut will experience weightlessness: objects will either float alongside him or her, or drift at constant speed. In this way, the experiences of an observer in free fall will be very similar to those of an observer in deep space, far away from any source of gravity, and in fact to those of the privileged ("inertial") observers in Einstein's theory of special relativity. Albert Einstein realized that the close connection between weightlessness and special relativity represented a fundamental property of gravity.

Einstein's key insight was that there is no fundamental difference between the constant pull of gravity we know from everyday experience and the fictitious forces felt by an accelerating observer (in the language of physics: an observer in a non-inertial reference frame). So what people standing on the surface of the Earth perceive as the 'force of gravity' is a result of their undergoing a continuous physical acceleration which could just as easily be imitated by placing an observer within a rocket accelerating at the same rate as gravity (9.81 m/s²).

This redefinition is incompatible with Newton's first law of motion, and cannot be accounted for in the Euclidean geometry of special relativity. To quote Einstein himself:
“ If all accelerated systems are equivalent, then Euclidean geometry cannot hold in all of them." ”

Thus the equivalence principle led Einstein to develop a gravitational theory which involves curved space-times. Paraphrasing John Wheeler, Einstein's geometric theory of gravity can be summarized thus: spacetime tells matter how to move; matter tells spacetime how to curve.

Another motivating factor was the realization that relativity calls for the gravitational potential to be expressed as a symmetric rank-two tensor, and not just a scalar as was the case in Newtonian physics (An analogy is the electromagnetic four-potential of special relativity). Thus, Einstein sought a rank-two tensor means of describing curved space-times surrounding massive objects. This effort came to fruition with the discovery of the Einstein field equations in 1915.

General relativity is a metric theory of gravitation. For this class of theory, the main defining feature is the concept of gravitational 'force' being replaced by spacetime geometry. Phenomena that in classical mechanics are ascribed to the action of the force of gravity (such as free-fall, orbital motion, and spacecraft trajectories) are taken in general relativity to represent inertial motion within a curved geometry of spacetime.

General relativity (and all other metric theories of gravitation) are predicated upon several underlying assumptions. The general principle of relativity states that the laws of physics must be the same for all observers (accelerated or not). The principle of general covariance states the laws of physics must take the same form in all coordinate systems. General relativity also requires equivalence between inertial and geodesic motion because the world lines of particles unaffected by physical forces are timelike or null geodesics of spacetime. The principle of local Lorentz invariance requires that the laws of special relativity apply locally for all inertial observers. Finally there is the principle that the curvature and of spacetime and its energy-momentum content are related. (As mentioned above, this relationship between curvature and spacetime content is specifically dictated by the Einstein field equations in general relativity.)

The equivalence principle, which was the starting point for the development of general relativity, ended up being a consequence of the general principle of relativity and the principle that inertial motion is geodesic motion.

The requirements of the mathematics of general relativity are further modified by the other principles. Local Lorentz Invariance requires that the manifolds described in GR be 4-dimensional and Lorentzian instead of Riemannian. In addition, the principle of general covariance requires that mathematics to be expressed using tensor calculus. Tensor calculus permits a manifold as mapped with a coordinate system to be equipped with a metric tensor of spacetime which describes the incremental (spacetime) intervals between coordinates from which both the geodesic equations of motion and the curvature tensor of the spacetime can be ascertained.

2007-09-12 07:21:44 · answer #1 · answered by James M 3 · 2 4

The layman's version:

Einstein's Special Theory of Relativity (STR) postulates that the speed of light in a particular medium is constant - that the speed is the same in any observer's frame of reference, regardless of the observer's own speed.

2007-09-12 07:26:57 · answer #2 · answered by fed up woman 6 · 0 0

Top marks to eyeonthescreen, the best layman's description I've seen for a long time. I feel sad for whoever gave him the thumbs down!

2007-09-13 00:45:55 · answer #3 · answered by andy muso 6 · 0 0

I don't know about you, but my eyes glazed over when trying to read the copied and pasted very long answer above. Here's the short and sweet of it.

What we see is relative to the framework we are seeing it from. That's why it is called relativity...everything is relative to the context (the framework) of the observer.

Here are some examples:

Assume two frameworks...a spaceship going at velocity v ~ c relative to us on Earth, the second framework. c is light speed in a vacuum.

Relative to an observer in the spaceship, time T, length L, and mass M are not changed. That is, these three things look just like they looked before the spaceship took off on its star trek at close to the speed of light. Thus we call T, L, and M rest time, length, and mass because these are what we have when the spaceship framework is at rest.

On the other hand, we on Earth (the at-rest framework) see some remarkable things happen to the spaceship as it approaches light speed. First, we Earthlings see time dilate on the spaceship. That is, time slows down; so that, clocks on the ship get slower and slower as the ship speeds up relative to Earth. In the extreme, at really close to light speed, time on the ship, relative to Earth, could come almost to a stop. Centuries or millennia could pass on Earth, while but a second or two passes for the spaceship crew because relative to the ship framework everything is still at rest.

Second, the length of the spaceship, relative to Earth's dimensions, will shrink in the direction of travel as people on
Earth see it. Yet, on board, the ship's cabin, desks, galley, etc. have not changed size at all as far as the crew is concerned.

Third, and final, on Earth, we see the mass of the spaceship grow to unimaginable levels of inertia. That is, the effect on the ship's inertia is as though its physical mass had grown. So, if there is an external force causing the ship to accelerate, that force has to get bigger and bigger just to keep the ship accelerating at the same rate. This comes from f = ma; where m is that relative inertial mass that is growing as the ship's velocity approaches c.

It should be noted that Einstein's theory has been validated in the particle accelerators. When subatomic particles are accelerated to nearly light speed, their rates of decay slow way down, indicating time dilating for the particle as we see it from outside the accelerator.

Also, as the particles get closer to light speed, it takes more and more umph from the accelerator to keep them accelerating. This shows the inertial mass of the particles is also increasing according to Einstein's theory. Because the particles are so tiny, I don't believe anyone has observed the shortening of the particle lengths, but two out of three ain't bad.

Wraping up...relativity is about effects observed relative to the framework the observer is in. If the observer is in the framework that's moving at close to light speed, he or she will see no changes because he or she is at rest relative to that moving framework. On the other hand, an observer outside that moving framework will see all kinds of changes in time, length, and mass.

One fiinal note...because inertial mass approaches infinitiy as the moving frame approaches light speed, the speed of light cannot be reached or exceeded. This results again from f = ma or f/m = a.

As m --> infinity, acceleration a --> 0 unless f grows as fast as m or faster. In the end, we'd need close to an infinite amount of force to accelerate the moving framework (e.g., the starship Enterprise) that last increment to reach c, the speed of light. There is not an infinite force in the whole universe; so we cannot accelerate up to and including the speed of light if we have mass of any kind. On the other hand, massless things, like photons have no such limit; so they can go at v = c light speed.

2007-09-12 08:15:34 · answer #4 · answered by oldprof 7 · 3 2

Start here...

2007-09-12 07:19:01 · answer #5 · answered by gebobs 6 · 0 1

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