The Special And General Theory By Albert Einstein Pdf

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The theory of special relativity explains how space and time are linked for objects that are moving at a consistent speed in a straight line. One of its most famous aspects concerns objects moving at the speed of light.

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Relativity: The Special and the General Theory

General relativity , also known as the general theory of relativity , is the geometric theory of gravitation published by Albert Einstein in and is the current description of gravitation in modern physics.

General relativity generalizes special relativity and refines Newton's law of universal gravitation , providing a unified description of gravity as a geometric property of space and time or four-dimensional spacetime. In particular, the curvature of spacetime is directly related to the energy and momentum of whatever matter and radiation are present. The relation is specified by the Einstein field equations , a system of partial differential equations.

Some predictions of general relativity differ significantly from those of classical physics , especially concerning the passage of time, the geometry of space, the motion of bodies in free fall , and the propagation of light. The predictions of general relativity in relation to classical physics have been confirmed in all observations and experiments to date.

Although general relativity is not the only relativistic theory of gravity , it is the simplest theory that is consistent with experimental data. However, unanswered questions remain, the most fundamental being how general relativity can be reconciled with the laws of quantum physics to produce a complete and self-consistent theory of quantum gravity ; and how gravity can be unified with the three non-gravitational forces— strong , weak , and electromagnetic forces.

Einstein's theory has important astrophysical implications. For example, it implies the existence of black holes—regions of space in which space and time are distorted in such a way that nothing, not even light, can escape—as an end-state for massive stars.

There is ample evidence that the intense radiation emitted by certain kinds of astronomical objects is due to black holes. For example, microquasars and active galactic nuclei result from the presence of stellar black holes and supermassive black holes , respectively.

The bending of light by gravity can lead to the phenomenon of gravitational lensing, in which multiple images of the same distant astronomical object are visible in the sky. General relativity also predicts the existence of gravitational waves , which have since been observed directly by the physics collaboration LIGO.

In addition, general relativity is the basis of current cosmological models of a consistently expanding universe. Widely acknowledged as a theory of extraordinary beauty , general relativity has often been described as the most beautiful of all existing physical theories.

Soon after publishing the special theory of relativity in , Einstein started thinking about how to incorporate gravity into his new relativistic framework. In , beginning with a simple thought experiment involving an observer in free fall, he embarked on what would be an eight-year search for a relativistic theory of gravity. After numerous detours and false starts, his work culminated in the presentation to the Prussian Academy of Science in November of what are now known as the Einstein field equations, which form the core of Einstein's general theory of relativity.

The Einstein field equations are nonlinear and very difficult to solve. Einstein used approximation methods in working out initial predictions of the theory. But in , the astrophysicist Karl Schwarzschild found the first non-trivial exact solution to the Einstein field equations, the Schwarzschild metric.

This solution laid the groundwork for the description of the final stages of gravitational collapse, and the objects known today as black holes.

In line with contemporary thinking, he assumed a static universe, adding a new parameter to his original field equations—the cosmological constant —to match that observational presumption. This is readily described by the expanding cosmological solutions found by Friedmann in , which do not require a cosmological constant.

During that period, general relativity remained something of a curiosity among physical theories. It was clearly superior to Newtonian gravity , being consistent with special relativity and accounting for several effects unexplained by the Newtonian theory.

Einstein showed in how his theory explained the anomalous perihelion advance of the planet Mercury without any arbitrary parameters " fudge factors " , [11] and in an expedition led by Eddington confirmed general relativity's prediction for the deflection of starlight by the Sun during the total solar eclipse of May 29, , [12] instantly making Einstein famous.

Over the years, general relativity has acquired a reputation as a theory of extraordinary beauty. It juxtaposes fundamental concepts space and time versus matter and motion which had previously been considered as entirely independent. Chandrasekhar also noted that Einstein's only guides in his search for an exact theory were the principle of equivalence and his sense that a proper description of gravity should be geometrical at its basis, so that there was an "element of revelation" in the manner in which Einstein arrived at his theory.

General relativity can be understood by examining its similarities with and departures from classical physics. The first step is the realization that classical mechanics and Newton's law of gravity admit a geometric description.

The combination of this description with the laws of special relativity results in a heuristic derivation of general relativity. At the base of classical mechanics is the notion that a body 's motion can be described as a combination of free or inertial motion, and deviations from this free motion.

Such deviations are caused by external forces acting on a body in accordance with Newton's second law of motion , which states that the net force acting on a body is equal to that body's inertial mass multiplied by its acceleration.

In modern parlance, their paths are geodesics , straight world lines in curved spacetime. Conversely, one might expect that inertial motions, once identified by observing the actual motions of bodies and making allowances for the external forces such as electromagnetism or friction , can be used to define the geometry of space, as well as a time coordinate. However, there is an ambiguity once gravity comes into play. Given the universality of free fall, there is no observable distinction between inertial motion and motion under the influence of the gravitational force.

This suggests the definition of a new class of inertial motion, namely that of objects in free fall under the influence of gravity. This new class of preferred motions, too, defines a geometry of space and time—in mathematical terms, it is the geodesic motion associated with a specific connection which depends on the gradient of the gravitational potential.

Space, in this construction, still has the ordinary Euclidean geometry. However, space time as a whole is more complicated. As can be shown using simple thought experiments following the free-fall trajectories of different test particles, the result of transporting spacetime vectors that can denote a particle's velocity time-like vectors will vary with the particle's trajectory; mathematically speaking, the Newtonian connection is not integrable.

From this, one can deduce that spacetime is curved. The resulting Newton—Cartan theory is a geometric formulation of Newtonian gravity using only covariant concepts, i. As intriguing as geometric Newtonian gravity may be, its basis, classical mechanics, is merely a limiting case of special relativistic mechanics. The differences between the two become significant when dealing with speeds approaching the speed of light , and with high-energy phenomena. With Lorentz symmetry, additional structures come into play.

They are defined by the set of light cones see image. The light-cones define a causal structure: for each event A , there is a set of events that can, in principle, either influence or be influenced by A via signals or interactions that do not need to travel faster than light such as event B in the image , and a set of events for which such an influence is impossible such as event C in the image.

These sets are observer-independent. In mathematical terms, this defines a conformal structure [32] or conformal geometry. Special relativity is defined in the absence of gravity, so for practical applications, it is a suitable model whenever gravity can be neglected. Bringing gravity into play, and assuming the universality of free fall motion, an analogous reasoning as in the previous section applies: there are no global inertial frames.

Instead there are approximate inertial frames moving alongside freely falling particles. Translated into the language of spacetime: the straight time-like lines that define a gravity-free inertial frame are deformed to lines that are curved relative to each other, suggesting that the inclusion of gravity necessitates a change in spacetime geometry.

A priori, it is not clear whether the new local frames in free fall coincide with the reference frames in which the laws of special relativity hold—that theory is based on the propagation of light, and thus on electromagnetism, which could have a different set of preferred frames. But using different assumptions about the special-relativistic frames such as their being earth-fixed, or in free fall , one can derive different predictions for the gravitational redshift, that is, the way in which the frequency of light shifts as the light propagates through a gravitational field cf.

The actual measurements show that free-falling frames are the ones in which light propagates as it does in special relativity. The same experimental data shows that time as measured by clocks in a gravitational field— proper time , to give the technical term—does not follow the rules of special relativity. In the language of spacetime geometry, it is not measured by the Minkowski metric. As in the Newtonian case, this is suggestive of a more general geometry.

At small scales, all reference frames that are in free fall are equivalent, and approximately Minkowskian. Consequently, we are now dealing with a curved generalization of Minkowski space. The metric tensor that defines the geometry—in particular, how lengths and angles are measured—is not the Minkowski metric of special relativity, it is a generalization known as a semi- or pseudo-Riemannian metric.

Furthermore, each Riemannian metric is naturally associated with one particular kind of connection, the Levi-Civita connection , and this is, in fact, the connection that satisfies the equivalence principle and makes space locally Minkowskian that is, in suitable locally inertial coordinates , the metric is Minkowskian, and its first partial derivatives and the connection coefficients vanish.

Having formulated the relativistic, geometric version of the effects of gravity, the question of gravity's source remains. In Newtonian gravity, the source is mass.

In special relativity, mass turns out to be part of a more general quantity called the energy—momentum tensor , which includes both energy and momentum densities as well as stress : pressure and shear. Drawing further upon the analogy with geometric Newtonian gravity, it is natural to assume that the field equation for gravity relates this tensor and the Ricci tensor , which describes a particular class of tidal effects: the change in volume for a small cloud of test particles that are initially at rest, and then fall freely.

In special relativity, conservation of energy —momentum corresponds to the statement that the energy—momentum tensor is divergence -free. This formula, too, is readily generalized to curved spacetime by replacing partial derivatives with their curved- manifold counterparts, covariant derivatives studied in differential geometry. With this additional condition—the covariant divergence of the energy-momentum tensor, and hence of whatever is on the other side of the equation, is zero—the simplest set of equations are what are called Einstein's field equations:.

In particular,. The Ricci tensor itself is related to the more general Riemann curvature tensor as. All tensors are written in abstract index notation. In general relativity, the world line of a particle free from all external, non-gravitational force is a particular type of geodesic in curved spacetime. In other words, a freely moving or falling particle always moves along a geodesic.

The geodesic equation is:. The quantity on the left-hand-side of this equation is the acceleration of a particle, and so this equation is analogous to Newton's laws of motion which likewise provide formulae for the acceleration of a particle. This equation of motion employs the Einstein notation , meaning that repeated indices are summed i.

The Christoffel symbols are functions of the four spacetime coordinates, and so are independent of the velocity or acceleration or other characteristics of a test particle whose motion is described by the geodesic equation.

In the general relativity , the effective gravitational potential energy of an object of mass m rotating around a massive central body M is given by [40] [41]. A conservative total force can then be obtained as [ citation needed ]. The first term represents the Newton's force of gravity , which is described by the inverse-square law. The second term represents the centrifugal force in the circular motion.

The third term is related to the Coriolis force in the rotating reference frame , which includes the inverse of the distance to the fourth power. The derivation outlined in the previous section contains all the information needed to define general relativity, describe its key properties, and address a question of crucial importance in physics, namely how the theory can be used for model-building.

General relativity is a metric theory of gravitation. At its core are Einstein's equations , which describe the relation between the geometry of a four-dimensional pseudo-Riemannian manifold representing spacetime, and the energy—momentum contained in that spacetime.

Instead, gravity corresponds to changes in the properties of space and time, which in turn changes the straightest-possible paths that objects will naturally follow. Paraphrasing the relativist John Archibald Wheeler , spacetime tells matter how to move; matter tells spacetime how to curve.

While general relativity replaces the scalar gravitational potential of classical physics by a symmetric rank -two tensor , the latter reduces to the former in certain limiting cases. For weak gravitational fields and slow speed relative to the speed of light, the theory's predictions converge on those of Newton's law of universal gravitation.

As it is constructed using tensors, general relativity exhibits general covariance : its laws—and further laws formulated within the general relativistic framework—take on the same form in all coordinate systems. It thus satisfies a more stringent general principle of relativity , namely that the laws of physics are the same for all observers.

The core concept of general-relativistic model-building is that of a solution of Einstein's equations.

Physics: One hundred years of general relativity

General relativity is a theory of gravitation developed by Albert Einstein between and The theory of general relativity says that the observed gravitational effect between masses results from their warping of spacetime. By the beginning of the 20th century, Newton's law of universal gravitation had been accepted for more than two hundred years as a valid description of the gravitational force between masses. In Newton's model, gravity is the result of an attractive force between massive objects. Although even Newton was troubled by the unknown nature of that force, the basic framework was extremely successful at describing motion. Experiments and observations show that Einstein's description of gravitation accounts for several effects that are unexplained by Newton's law, such as minute anomalies in the orbits of Mercury and other planets.


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Einstein's Theory of Special Relativity

A handsome annotated edition of Einstein's celebrated book on relativity After completing the final version of his general theory of relativity in November , Albert Einstein wrote Relativity. Intended for a popular audience, the book remains one of the most lucid explanations of the special and general theories ever written. Providing invaluable insight into one of the greatest scientific minds of all time, the book also includes a unique survey of the introductions from past editions, covers from selected early editions, a letter from Walther Rathenau to Einstein discussing the book, and a revealing sample from Einstein's original handwritten manuscript.

David Tong: Lectures on Dynamics and Relativity

General relativity , also known as the general theory of relativity , is the geometric theory of gravitation published by Albert Einstein in and is the current description of gravitation in modern physics. General relativity generalizes special relativity and refines Newton's law of universal gravitation , providing a unified description of gravity as a geometric property of space and time or four-dimensional spacetime.

General relativity

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Из почты Танкадо Сьюзан знала также, что цепные мутации, обнаруженные Чатрукьяном, безвредны: они являются элементом Цифровой крепости. - Когда я впервые увидел эти цепи, сэр, - говорил Чатрукьян, - я подумал, что фильтры системы Сквозь строй неисправны. Но затем я сделал несколько тестов и обнаружил… - Он остановился, вдруг почувствовав себя не в своей тарелке.  - Я обнаружил, что кто-то обошел систему фильтров вручную. Эти слова были встречены полным молчанием.


A handsome annotated edition of Einstein's celebrated book on relativity After completing the final version of his general theory of relativity in November.


Мы решили уйти. Я не видела смысла впутывать моего спутника, да и самой впутываться в дела, связанные с полицией. Беккер рассеянно кивнул, стараясь осмыслить этот жестокий поворот судьбы.

Соши развела руками. Она села за терминал Джаббы и перепечатала все группы, а закончив, подбежала к Сьюзан. Все посмотрели на экран.

 Похоже, ты облажался, приятель.

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    ALBERT EINSTEIN, Ph.D. PROFESSOR OF PHYSICS IN THE UNIVERSITY OF BERLIN. TRANSLATED BY. ROBERT W. LAWSON, M.