вторник, 29 декември 2009 г.

THE GENERAL THEORY OF RELATIVITY

The general theory of relativity derives its origin from the need to extend the new space and time concepts of the special theory of relativity from the domain of electric and magnetic phenomena to all of physics and, particularly, to the theory of gravitation. As space and time relations underlie all physical phenomena, it is conceptually intolerable to have to use mutually contradictory notions of space and time in dealing with different kind of interactions, particularly in view of the fact that the same particles may interact with each other in several different ways-electromagnetically, gravitationally, and by way of so-called nuclear forces.

Newton's explanation of gravitational interactions must be considered one of the most successful physical theories of all times. It accounts for the motions of all the constituents of the solar system with uncanny accuracy, permitting, for instance, the prediction of eclipses hundreds of years ahead. But Newton's theory visualizes the gravitational pull that the sun exerts on the planets and the pull that the planets in turn exerts on their moons and on each other as taking place instantaneously over the vast distances of interplanetary space, whereas according to relativistic notions of space and time any and all interactions cannot spread faster than the speed of light. The difference may be unimportant, for practical reasons, as all of the members of the solar system move at relative speeds far less than 1/1000 of the speed of light; nevertheless, relativistic space-time and Newton's instantaneous action at a distance are fundamentally incompatible. Hence Einstein set out to develop a theory of gravitation that would be consistent with relativity.

Proceeding on the basis of the experience gained from Maxwell's theory of the electric field, Einstein postulated the existence of gravitational field that propagates at the speed of light, c, and that will mediate an attraction as closely as possible equal to the attraction obtained from Newton's theory. From the outset it was clear that mathematically a field theory of gravitation would be more involved than that of electricity and magnetism. whereas the source of the electric field, the electric charges of particles, have values independent of the state of motion of the instruments by which these charges are measured, the source of the gravitational field, the mass of a particle, varies with the speed of the particle relative to the frames of reference in which it is determined and hence will have different values in different frames of reference. This complicating factor introduces into the task of constructing a relativistic theory of the gravitational field a measure of ambiguity, which Einstein resolved eventually by invoking the principle of equivalence.

THE PRINCIPLE OF EQUIVALENCE. Everyday experience indicates that in a given field of gravity, such as the field caused by the Earth, the greater the mass of abody the greater the force acting on it. That is to say, the more massive a body the more effectively will it tend to fall toward the Earth; in fact, in order to determine the mass of a body one weighs it-that is to say, one really measures the force by which it is attracted to the Earth, whereas the mass is properly defined as the body's resistance to acceleration. Newton noted that the radio of the attractive forces to a body's mass in a given field is the same for all bodies, irrespective of their chemical constitution and other characteristics, and that they all undergo the same acceleration in free fall; this common rate of acceleration on the surface of the Earth amounts to an increase in speed by approximately 32 feet (about 9.8 metres) per second every second.

This common rate of gravitationally caused acceleration is illustrated dramatically in space travel during periods of coasting. The vehicle, the astronauts, and all other objects within the space capsule undergo the same acceleration, hence no acceleration relative to each other. The result is apparent weightlessness; no force holds the astronaut to the floor of his cabin or a liquid in an open container. To this extent, the behaviour of objects within the freely coasting space capsule is indistinguishable from the condition that would be encountered if the space capsule were outside all gravitational fields in interstellar space and moved in accordance with the law of inertia. Conversely, if a space capsule were to be accelerated upward by its rocket engines in the absence of gravitation, all objects inside would behave exactly as if the capsule were at rest but in a gravitational field. The principle of equivalence states formally the equivalence, in terms of local experiment, of gravitational forces and reactions to an accelerated noninertial frame of reference (e.g., the capsule while the rockets are being fired) and the equivalence between inertial frames of reference and local freely falling frames of reference. Of course, the principle of equivalence refers strictly to local effects: looking out of his window and performing navigational observations, the astronaut can tell how he is moving relative to the planets and moons of the solar system.

Einstein argued, however, that in the presence of gravitational fields there is no unambiguous way to separate gravitational pull from the effects occasioned by the noninertial character of one's chosen frame of reference; hence one cannot identify an inertial frame of reference with complete precision. Thus the principle of equivalence renders the gravitational field fundamentally different from all other force fields encountered in nature. The new theory of gravitation, the general theory of relativity, adopts this characteristic of the gravitational field as its foundation.

Curved space-time. The principles. In terms of Minkowski's space-time, inertial frames of reference are the analogues of rectilinear (straight-line) Cartesian coordinate systems in Euclidean geometry. In a plan these coordinate systems always exist, but they do not exist on the surface of a sphere: any attempt to cover a spherical surface with a grid of squares breaks down when the grid is extended over a significant fraction of the soherical surface. Thus a plane is a flat surface, whereas the surface of a sphere is curved. This distinction, based entirely on internal properties of the surface itself, classifies the surface of a cylinder as flat, as it can be rolled off on a plane and thus is capable of being covered by agrid of squares.

Einstein conjectured that the presence of a gravitationalfield causes space-time to be curved (whereas in the absence of gravitation it is flat), and that this is the reason that inertial frames cannot be constructed. The curved trajectory of a particle in space and time resulting from the effects of gravitation would then represent not a sraight line (which exists only in flat spaces and space-time) but the straightest curve possible in a curvedspace-time, a geodesic. Geodesics on a sphere (such as the surface of the Earth) are the great circles. (The plane of any great circle goes through the centre of the Earth.) They are the least curved lines one can construct on the surface of a sphere, and they are the shortest curves connecting any two points. The geodesics of space-time connect two events(of two instanta in the history of one particle) with the greatest lapse of proper time, as was indicated in theearlier discussion of the twin paradox.

If the presence of a gravitational field amounts to a curvature of space-time, then the description of the gravitational field in turn hinges on a mathematical elucrdaton of the curvature of four-dimensional space-time. Before Einstein, the German mathematician Bernfars Riemannn (1826-66) had deveoped methods related directly to the failure of any attempt to construct square grids. If one were to construct within any small piece of (two-dimensional) surface a quadrilateral whose sides are geodesics, if the surface were flat, the sum of the angels at the four corners would be 360. If the surface is not flat, the sum of the angles will not be 360. The deviation of the actual sum of the angles from 360 will be proportional to the area of the quadrilateral; the amount of deviation per unit of surface will be a measure of the curvature of that surface. If the surface is imbedded in a higher dimensional continum, then one can consider similary unavoidable angles between vectors constructed as parallel as possible to each other at the four corners of the quadrilateral, and thus associate several distinct components of curvature with one surface. And, of course, there are several independent possible orientations of two-dimensional surfaces, for instance, six in a four-dimensional continuum. such as space-time. Altogether there are 20 distinct and independent components of curvatured defined at each point of of space-time; in mathematics these are referred to the 20 components of Riemann's curvature tension.

The mathematical expression. Einstein discovered that he could relate 10 of these components in a natural way to the sources of the gravitational field, mass (or energy), density, momentum density, and stress, if he were to duplicate approximately Newton's equations of the gravitational field and, at the same time, formulate laws that would take the same form regardless of the choice of frame of reference. The remaining 10 components may be chosen arbitrarily at any one point but are related to each other by partial differential equations at neighbouring points. Einstein derived a field equation that, along with the rule that a freely falling body moves along a geodesic, forms the comprehensive treatment of gravitation known as the general theory of relativity.
In contrast to some vulgarized popular nontions of it, which confuse it with moral and other forms of relativism, Einstein's theory does not argue that "all is relative."On the contrary, it is largely a theory based upon those physical attributes that do not change, or, in the language of the theory,that are invariant.

In the begining of my essay I've mentioned about the famous German-American physicist A. Einstein. He was born on March 14 1870 Wurttember, Germany and died on 18 April 1955, Princeton N.J., U.S. He developed the theories of relativity, the equivalence of mass and energy, and the foton theory of light. In 1921 Einstein was awarded the Nobel Prize for his photoelectric law and work in theoretical physics.

There are actually two distinct theories of relativity known in physics, one called the special theory of relativity, the other - the general theory of relativity. Einstein proposed the first in 1905, the second in 1916. Whereas the special theory of relativity is concerned primarily with electric and magnetic phenomena and with their propagation in space and time, the general theoryof relativity was developed primarily in order to deal with gravitation. Both theories centre on new approaches to space and time, approaches that differ profoundly from those useful in everyday life; but relativistic notions of space and time are inextricably woven into any contemporary interpretation of physical phenomena ranging from the atom to the universe as a whole.
Relativity is concerned with measurements made by different observers moving relative to one another. in classical physics it was assumed that all observers anywhere in the universe, whehter moving or not, obtained identical measurements of space and time intervals. According to relativity theory, this is not so, but their resolts depend on their relative motions.

The general theory of relativity derives it's origin from the need to extend the new space and time concepts of the special theory of relativity from the domain of electric and magnetic phenomena to all of physics and, particularly, to the theory of gravitation. As space and time relations underlie all physical phenomena, it is conceptually intolerable to have to use mutually contradictory notions of space and time in dealing with different kind of interactions, particularly in view of the fact that the same particles may interact with each other in several different ways-electromagnetically, gravitationally, and by way of so-called nuclear forces.


EINSTEIN'S GENERAL THEORY OF RELATIVITY

The theory of relativity forms the background of all modern cosmological theories. It was created by Albert Einstein.
A. Einstein was born on March 14 1870 Wurttember, Germany and died on 18 April 1955 ,Princeton N.J., U.S. He is German-American physicist who developed the special and general theories of relativity. The equivalence of mass and energy, and the foton theory of light.

Einstein earned a doctorate at the Polytechnic Academy in Zurich in 1905. And in the same year he published four research papers each containing a great discovery in physics. International fame came to Einstein in 1919 with the announcement that a prediction of his general theory of relativity was verified. Two years later he was awarded the Nobel Prize for his photoelectric law and work in theoretical physics Einstein continued his work in general relativity, the unified field theories, and the critical discussion of the interpretation of quantum theory. In 1945 Einstein retired from his position at the Institute for Advanced Study in Princeton but continued to work there until his death in 1955.

Relativity is concerned with measurements made by different observers moving relative to one another. in classical physics it was assumed that all observers anywhere in the universe, whehter moving or not, obtained identical measurements of space and time intervals. According to relativity theory, this is not so, but their results depend on their relative motions.

There are actually two distinct theories of relativity known in physics, one called the special theory of relativity, the other the other the general theory of relativity. Albert Einstein proposed the first in 1905, the second in 1916. Whereas the special theory of relativity is concerned primarily with electric and magnetic phenomena and with their propagation in space and time, the general theory relativity was developed primarily in order to deal with gravitation. Both theories centre on new approaches to space and time, approaches that differ profoundly from those useful in everyday life; but relativistic notions of space and time are inextricably woven into any contemporary interpretation of physical phenomena ranging from the atom to the universe as a whole.

Specific and unusual relativistic effects flow directly from Einstein's two basic postulates, which are formulated in terms of so-called inertial reference frames. These are reference systems that move in such a way that in them Newton's first law, the law of inertia, is valid. The set of inertial frames consists of all those that move with constant velocity with respect to each other (accelerating frames therefore being excluded). Einstein's postulates are:

(1) All observers, whatever their state of motion relative to a light source, measure the same speed for light;
(2) The laws of physics are the same in all inertial frames.

The first postulate, the constancy of the speed of the light, is an experimental fact from which follows the distinctive relatevistic phenomena of space contraction, time dilation, and the relativity of simultaneity: as measured by an observer assumed to be at rest, an object in motion is contracted along the direction of its motion, and moving clock run slow; two spatially separated events that are simultaneous for a stationary observer occur sequentially for amoving observer. As a consequence, space intervals in three-dimensional space are related to time intervals, thus forming so-called four-dimensional space-time.

The second postulate is called the principle of relativity. It is equally valid in classical mechanics (but not in classical electrodynamics until Einstein reinterpreted it). This postulate implies, for example, that table tennis played on a train moving with constant velocity is just like table tennis played with the train at rest, the states of rest and motion being physically indistinguishable. In relativity theory, mechanical quantities such as momentum and energy have forms that are different from their classical counterparts but give the same values for speed that are small compared to the speed of light, the maximum permissible speed in nature (about 300000 kilometres per second). According to relativity, mass and energy are equivalent and interchangeable quantities, the equivalence being expressed by Einstein's famous equation E=mc2(c.c), where m is the mass of the object and c is the speed of light.

The general theory of relativity is Einstein's theory of gravitation, which uses the principle of the equivalence of gravitation and locally accelerating frames of reference. Einstein's theory has special mathematical beauty; it generalizes the "flat" space-time concept of special relativity to one of curvature.

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