Theory of relativity

The theory of relativity is concerned with the structure of space and time as well as with the nature of gravity. It consists of two largely created by Albert Einstein theories in physics, the special theory of relativity, published in 1905 and in 1916 completed general relativity. The special theory of relativity describes the behavior of space and time from the perspective of observers moving relative to each other, and the associated phenomena. Building on results in the general theory of relativity the gravitational back to a curvature of space and time that is caused among other things by the masses involved.

In this article, the basic structures and phenomena are merely listed in summary. For explanations and details see the article special relativity and general relativity, and the references in the text. The concept of relativity as such see relativity.

The frequent in the physical jargon relativistic expression usually means that a speed relative to the speed of light is not negligibly small ( as the limit is often 10% solid); therefore be considered instead of classical mechanics, the relationships of the special theory of relativity.

3.1 Gravity and the curvature of space-time
3.2 The mathematical structure of general relativity
3.3 clocks in a gravitational field
3.4 cosmology
3.5 Black Holes
3.6 gravitational waves

4.1 Special Theory of Relativity
4.2 General Theory of Relativity
4.3 Other geometric theories

6.1 Public perceptions

7.1 Physical introductions and discussion
7.2 Popular Literature
7.3 Philosophical introductions and discussion
7.4 movie

Fundamental importance

The theory of relativity revolutionized the understanding of space and time and revealed natural phenomena that are beyond the intuitive idea. The relevant processes and properties can however describe mathematically precise and are experimentally confirmed.

The theory of relativity is one of the two pillars of the theoretical structure of physics represents the union with the quantum theory, which represents the second pillar, is not yet fully succeeded and one of the greatest challenges facing the fundamental physics research. Both theories contain their predecessors, the Newtonian physics, as a limiting case and thus fulfill the so-called correspondence principle.

The current standard model of physics is based on the unification of special relativity with quantum theory in the relativistic quantum field theories. A quantum theory, which takes account of the general theory of relativity, is called quantum gravity.

The special theory of relativity

The principle of relativity

The following two observations can be interpreted as axioms of the theory of relativity, from which everything else can be derived:

Different observers measuring the speed of a light beam relative to their location, so they are independent of their own state of motion to the same result. This is called the principle of the constancy of the speed of light.
The laws of physics have for all observers moving at constant speed, so are not subject to acceleration, the same shape. This circumstance is called the principle of relativity. This is called inertial frames, in which those observers.

The principle of relativity itself is not very spectacular, because it also applies to the Newtonian mechanics. From it immediately follows that there is no possibility to determine an absolute velocity of an observer in the room and so as to define a resting absolute reference system. Such a system would have to rest in some form from all others differ in contradiction with the principle of relativity, according to which the laws of physics in all reference systems have the same shape. Well rested prior to the development of the theory of relativity, electrodynamics on the assumption of the ether as a carrier of electromagnetic waves. Would such ether fill the space as a rigid structure, it would define a reference system, the laws of physics would have a particularly simple form in the contrary to the principle of relativity and which, moreover, would be the only system in which the speed of light is constant. However, all attempts to prove the existence of the ether, such as the famous Michelson - Morley experiment of 1887.

By giving up the conventional notions of space and time and the rejection of the ether hypothesis Einstein managed to resolve the apparent contradiction between the principle of relativity and the following from electrodynamics constancy of the speed of light. Not coincidentally, there were experiments and considerations for electrodynamics that led to the discovery of the theory of relativity. That was the unassuming title of Einstein's publication of 1905, which established the special theory of relativity, On the Electrodynamics of Moving Bodies.

Relativity of space and time

Space and time are in the theory of relativity is no universally valid order structures, but the spatial and temporal distance between two events, and thus their simultaneity are judged differently by observers with different motion states. Moving objects are found to be shortened in the direction of movement compared to rest and moving clocks as slowed down. However, since each uniformly moving observer can argue that he is at rest, these observations are based on reciprocity, that is, two relatively moving observers see the clocks of the other go slower. Moreover, in their view, the meter-lengths of each other are shorter than a meter when they are aligned along the direction of motion. The question of who describes the situation is correct, this principle can not be answered and therefore pointless.

This length contraction and time dilation can be relatively clearly understood by means of Minkowski diagrams and using the well-known twin paradox. In the mathematical formulation it will be apparent from the Lorentz transformation which describes the relationship between the space and time coordinates of the different observers. This transformation can be directly from the above two axioms and the assumption that it is linear, derive.

Most of these relativistic phenomena explainable make only noticeable at speeds which appreciably compared to the speed of light are great. Such speeds are achieved not nearly everyday.

Speed of light as a limit

No object and no information can travel faster than light in a vacuum. Approaches the speed of a material object, the speed of light, so the intention of the energy required for further acceleration beyond all limits, because the kinetic energy always increases more steeply with increasing proximity to the speed of light with increasing speed. To achieve the speed of light infinite amount of energy would have to be applied.

This fact is a consequence of the structure of space and time and not a property of the object, such as a merely imperfect spaceship. An object would move faster than light from A to B, so there would always be a moving relative to him observer would perceive a movement from B to A, again without the question of who describes the situation correctly, would make sense. The principle of causality would be violated, since the order of cause and effect would no longer be defined. Such an object would move the way for each observer with superluminal velocity.

Association of time and space for space time

Space and time appear formally broadly equivalent to the basic equations of the theory of relativity together and leave unite to form a four-dimensional space-time therefore. The fact that space and time occur at all as different phenomena in appearance, can be ultimately traced back to a single sign, by the way, as a distance in Euclidean space is defined by determining the distance in the four-dimensional space-time differs. There are so-called four-vectors from ordinary vectors in three-dimensional space.

In the space-time there, because of the relativity of lengths and times, only three clearly distinct regions for each observer:

In the future light cone are all points that can reach the observer with a maximum speed of light or to which it can send a light signal.
The past light cone includes all points from which a signal with a maximum velocity of light can reach the observer.
All remaining points are called " space-like separated from the observer ." In this area, future and past can not define.

Equivalence of mass and energy

A system of mass m can be assigned to an energy E in the stationary state, after

Where c is the speed of light. This formula is one of the most famous in physics. It is often misleading claims that it allows the development of the atomic bomb. However, the effect of the atomic bomb can not be explained to her. However, the enormous release of energy could be estimated as early as 1939, shortly after the discovery of nuclear fission with this formula and the already known masses of the atoms by Lise Meitner. This mass loss also occurs already in chemical reactions, but there was not determinable with the former measurement methods, unlike in the case of nuclear reactions.

Magnetic fields in the theory of relativity

The existence of magnetic forces is inextricably linked to the theory of relativity. An isolated existence of the Coulomb law for electric forces would not be compatible with the structure of space and time. This is what an observer who is at rest relative to a system of static electric charges, no magnetic field, unlike an observer moving relative to him. If we translate the observations of the observer at rest on a Lorentz transformation into the moved, so it turns out that this addition to the electrical power exercised a further, magnetic, force. The existence of the magnetic field in this example can therefore be attributed to the structure of space and time. From this perspective, the complicated compared to the Coulomb and at first glance a rather plausible structure of the Biot- Savart law for comparable magnetic fields seems less surprising. In the mathematical formalism of the theory of relativity, the electric and magnetic field are combined into one unit, the four-dimensional electromagnetic field strength tensor, analogous to the union of space and time for the four-dimensional space-time.

The general theory of relativity

Gravity and the curvature of space-time

The general relativity theory attributes the gravity on a geometric phenomenon in a curved space-time, by determining:

Energy curves spacetime in their vicinity.

An object, act on the only gravitational forces, moves between two points in space-time always on a so-called geodesic.

The four-dimensional space-time of special relativity Revokes already a philosophical conceivability, so this is true for an additional curved spacetime even more so. To illustrate, consider situations may, however, with a reduced number of dimensions. So corresponds to the case of a two -dimensional curved landscape a geodesic the path that would take a vehicle with fixed straight ahead steering. If two such vehicles run exactly parallel north at the equator of a sphere next to each other, then they would meet at the North Pole. An observer, the spherical shape of the earth would remain hidden, would infer a force of attraction between the two vehicles. It is a purely geometrical phenomenon. Gravitational forces are therefore sometimes referred to in the general theory of relativity as image forces.

Since the geodesic path through space-time of their geometry and not from Earth, or other properties of the falling body depends, every body in the gravitational field fall equally fast, as Galileo found. This situation is described in the Newtonian mechanics by the equivalence of inertial and gravitational mass, which is also the general theory of relativity is based.

The mathematical structure of general relativity

While many aspects of special relativity is understandable even with low mathematical knowledge in its simplest formulation, the mathematics of general relativity is much more demanding. The description of a curved space-time is done using the methods of differential geometry, which replaces the Euclidean geometry of our familiar flat space.

For a description of curvature usually a curved object is embedded in a higher-dimensional space for contemplation. For example, a two-dimensional spherical surface usually one imagines in a three dimensional space. Curvature can, however, be described without the adoption of such embedding space, which also happens in the general theory of relativity. It is for example possible to describe curvature characterized in that the angular sum of triangles not equivalent to 180 °.

The origin of the curvature is described by the Einstein's field equations. It is a tensor differential equations with ten components that analytically only in special cases, ie in the form of a mathematical equation, are detachable. For complex systems is therefore usually worked with proximity mechanisms.

Clocks in a gravitational field

In general relativity, the passage of clocks depends not only on their relative speed, but also on their location in a gravitational field. A clock on a mountain faster than in the valley. Although this effect is only slight in the terrestrial gravitational field, but is considered in the GPS navigation system to avoid errors in determining the position of a corresponding frequency correction of the radio signals.

Cosmology

While the special theory of relativity applies in the presence of masses only in regions of spacetime that are so small that the curvature can be neglected, the general theory of relativity does not require this restriction. It can thus be applied to the universe as a whole, and therefore plays a central role in cosmology. Thus, the expansion of the universe, watch the astronomers adequately described by the friedmann between solutions of Einstein's field equations in combination with a so-called cosmological constant. After this expansion began with the Big Bang, which took place after the recent investigations 13.7 billion years ago. It can also be regarded as the beginning of time and space, in which the entire universe was concentrated on a space area on the diameter of the Planck length.

Black Holes

Another prediction of general relativity are black holes. These objects have such strong gravity that they even can "capture" light, so that it can not again come out of the black hole. Einstein could not make friends with this thought, and thought there must be a mechanism that prevents the formation of such objects. Todays but observational evidence suggests that there is indeed such black holes in the universe, as a final stage of stellar evolution at very massive stars and in the centers of galaxies.

Gravitational waves

The general theory of relativity allows for the existence of gravitational waves, local deformations of space-time, which propagate at the speed of light. They should be formed in the acceleration of masses. However, these deformations are so small that they have eluded direct detection until now one. A relatively nearby supernova explosion in 1987 should have generated gravitational waves that would be detectable with present-day (2011) detectors. However, were the two detectors, which were at that time in use, is not accurate enough to provide a clear confirmation. After all, it could be confirmed indirectly from observations of binary systems with pulsar the existence of gravitational waves. Russell Hulse and Joseph Taylor received for 1993 Nobel Prize in Physics.

Genesis

Special Theory of Relativity

Based on the problems of the various ether theories of the 19th century and the Maxwell 's equations sat a continuous development with the following main stations one:

The Michelson - Morley experiment (1887 ), which failed to show relative motion between Earth and ether (ether drift);
The contraction hypothesis of George FitzGerald (1889 ) and Hendrik Antoon Lorentz (1892 ) with which the Michelson - Morley experiment should be explained;
The Lorentz transformation of Lorentz (1892, 1899) and Joseph Larmor (1897 ), which included a change in the time variable, and in general the negative aether drift experiments should be explained by the;
The principle of relativity (1900, 1904), the constancy of the speed of light ( 1898, 1904), and the relativity of simultaneity (1898, 1900) by Henri Poincaré, however, which held the ether of thought;
And reaching the full covariance of the electrodynamic basic equations by Lorentz (1904) and Poincaré (1905 ) in the Lorentz ether theory between.

This culminated in the special theory of relativity Albert Einstein (1905 ) through a transparent derivation of the whole theory of the postulates of the principle of relativity and the constancy of the speed of light, and the final overcoming of the ether concept by reformulation of the concepts of space and time. The dynamic view of Lorentz and Poincaré was replaced by the kinematic Einstein. Finally, the mathematical reformulation of the theory followed by the inclusion of time as a fourth dimension by Hermann Minkowski (1907).

General Theory of Relativity

During the development of the special theory of relativity, a number of scientists was involved - where Einstein's work constituted of 1905 both an end and a new beginning - was the development of the general theory of relativity, what their basic physical statements were concerned, practically the sole achievement of Einstein.

This development began in 1907 with the equivalence principle that inertial and gravitational mass are equivalent. From this he derived the gravitational redshift and found that light is deflected in a gravitational field, where he gave the resulting delay, called the Shapiro delay. In 1911, he led with refined methods these basic ideas further. This time he also suspected that the light deflection in the gravitational field can be measured. However, at that time predicted value of it was still a factor of 2 too small.

Later Einstein realized that Minkowski's four-dimensional space-time formalism, which he previously faced skeptical played a very important role in the new theory. He was also now clear that the means of Euclidean geometry was not sufficient to continue his work. In 1913 he was able to integrate the developed non-Euclidean geometry in the 19th century in his theory with the mathematical support Marcel Grossmann's, but without the full covariance, ie, to achieve the compliance of all laws of nature in the reference systems. 1915, these problems were overcome after a few failures, and Einstein could finally derive the correct field equations of gravitation. Almost simultaneously, managed this David Hilbert. Einstein calculated the correct value for the perihelion advance of Mercury, and the deflection of light twice the value obtained in 1911. 1919 this value was first confirmed what initiated the triumph of theory among physicists and also in public.

After that, many physicists tried on the exact solution of the field equations, which resulted in the formation of various cosmological models and theories such as black holes.

Other geometric theories

After the explanation of gravity as a geometric phenomenon it was obvious the other then-known fundamental forces, the electric and magnetic, due to geometrical effects. Theodor Kaluza (1921) and Oskar Klein (1926 ) took this to an additional self-contained dimension of space with sub-atomic length such that it remains hidden from us. However, they were unsuccessful with their theory. Even Einstein worked long in vain out to create such a unified field theory.

After the discovery of other fundamental forces of nature, these so-called Kaluza-Klein theories experienced a renaissance - albeit on the basis of quantum theory. Today's most promising theory for the unification of relativity and quantum theory of this type, the string theory is based on six or seven hidden dimensions of the size of the Planck length and thus of a ten - or elfdimensionalen spacetime.

Experimental confirmations

The first success of the special theory of relativity was the resolution of the contradiction between the result of the Michelson -Morley experiment and the theory of electrodynamics, which can be viewed at all as a reason for their discovery. Since then, the theory of special relativity has been proven in the interpretation of numerous experiments. A convincing example is the detection of muons in the cosmic radiation that could not reach the earth's surface due to their short lifetime, if not because of its high speed, the time would slow down for them, or they would learn contracted in length the route. Evidence for this comes partly from the balloon flights into the stratosphere of the Swiss physicist Auguste Piccard in 1931 and 1932, which were prepared with the involvement of Einstein.

In contrast, there was at the time of publication of the general theory of relativity a single clue as to its accuracy, the perihelion of Mercury. In 1919, Arthur Stanley Eddington during a solar eclipse a shift in the apparent position of stars near the sun -proof and supplied with this very direct reference to a curvature of space, a further confirmation of the theory.

Further experimental tests are described in the article on the general theory of relativity.

The theory of relativity has been able in the form prescribed by Einstein, argue against all alternatives that have been proposed in particular to his theory of gravitation today. The most significant was the Jordan - Brans Dicke theory, which, however, was more complex. Their validity has not yet been disproved. The area that is the decisive parameter can assume, according to current experimental status is, however, very limited.

Reception and interpretation

Perception by the public

The new view of the theory of relativity with respect to space and time aroused after their discovery in the general stir. Einstein became a celebrity and the theory of relativity experienced a significant media coverage. Cuts to the saying everything is relative, it was sometimes moved into the vicinity of a philosophical relativism.

Criticism of the theory of relativity was fed by various sources, such as misunderstanding, rejection of progressive mathematization of physics and partly resentment against Einstein's Jewish ancestry. From the 1920s tried in Germany a few overtly anti -Semitic physicists, including Nobel laureates Philipp Lenard and Johannes Stark, the theory of relativity to oppose a German physics. A few years after the Nazi seizure of power Stark went with an article in the SS newspaper Das Schwarze Korps from July 15, 1937 against the remaining in the country supporters of relativity and quantum theory in the offensive. Among other things, he denounced Werner Heisenberg and Max Planck as white Jews. Heisenberg turned directly to Himmler and reached its full rehabilitation; not least in view of the needs of armaments development was allowed the theory of relativity.

Many leaders of the traditional classical physics rejected Einstein's relativity theory, including Lorentz and Poincaré themselves and also experimental physicist as Michelson.

Literature and Film

Physical introductions and discussion

Max Born: the theory of relativity of Einstein. Edited by Jürgen Ehlers and Mark Pössel. Springer, Berlin 2003, ISBN 3-540-67904-9.
Albert Einstein, Leopold Infeld: The Evolution of Physics. Zsolnay, Hamburg 1950, Rowohlt, Reinbek 1987, ISBN 3-499-18342-0. ,
Albert Einstein: Fundamentals of the theory of relativity. Springer, Berlin 2002, ISBN 3-540-43512-3. ( Original title Meaning of relativity )
Jürgen Freund: Relativity for Beginners - a textbook. vdf Hochschulverlag, Zurich 2004, ISBN 3-7281-2993-3.
Hubert backers: Special relativity and the classical field theory. Elsevier - Spektrum Akademischer Verlag, Munich 2004, ISBN 3-8274-1434-2.
Holger Müller, Achim Peters: Einstein's theory on the optical bench - Special Theory of Relativity. In: Physics in our time. Wiley -VCH, Weinheim 35.2004,2, p.70 - 75th ISSN 0031-9252
Wolfgang Nolting: Basic Course of Theoretical Physics. Volume 4 Special Theory of Relativity, Thermodynamics. Springer, Berlin 2003, ISBN 3-540-42116-5.
Hans Stephani: General Theory of Relativity. German Academic Publishers, Berlin, 1991, ISBN 3-326-00083-9.
Torsten Fließbach: General Theory of Relativity '. Spektrum Akademischer Verlag, Heidelberg 2006, ISBN 3-8274-1685- X.

Popular literature

Julian Schwinger: Einstein's legacy. The unity of space and time. Spectrum, Heidelberg, 2000. ISBN 3-8274-1045-2.
David Bodanis: Until Einstein came. The adventurous quest for the secret of the world. Fischer, Frankfurt am Main, 2003. ISBN 3-596-15399-9.
Gerald Kahan: Einstein's theory of relativity - for easy understanding for everyone. Dumont, Cologne, 1987, 2005. ISBN 3-7701-1852-9.

Philosophical introductions and discussion

Julian Barbour: The End of Time. Weidenfeld & Nicolson, London 1999, ISBN 0-297-81985-2.
Ernst Cassirer: For Einstein 's theory of relativity. Epistemological considerations. Meiner, Hamburg 2001, ISBN 3-7873-1410-5.
John Earman (ed.): Foundations of space -time theories. University of Minnesota Press, Minneapolis, Minn. 1977, ISBN 0-8166-0807-5.
Lawrence Sklar: Space, Time, and Spacetime. University of California Press 1977, ISBN 0-520-03174-1.
R. Torretti: Relativity and Geometry. Pergamon, Oxford 1983, ISBN 0-08-026773-4.
M. Friedman: Foundations of Space-Time Theories. Relativistic physics and philosophy of science. Princeton University Press, Princeton, NJ, 1983, ISBN 0-691-07239-6.
John Earman: Bangs, crunches, whimpers and shrieks. Singularities and acausalities in relativistic spacetimes. Oxford University Press, Oxford 1995, ISBN 0 - 19-509591 -X.
H. Brown: Physical Relativity. Space -time structure from a dynamical perspective. Clarendon, Oxford 2005, ISBN 978-0-19-927583-0.
Graham Nerlich: What Explains spacetime. Metaphysical essays on space and time. Cambridge University Press, Cambridge 1994, ISBN 0-521-45261-9.
T. Ryckman: The Reign of Relativity. Philosophy in physics from 1915 to 1925. Oxford University Press, New York 2005, ISBN 0-19-517717-7.
R. DiSalle: Understanding space -time. The philosophical development of physics from Newton to Einstein. Cambridge University Press, Cambridge 2007, ISBN 978-0-521-85790-1.
Sendker, Werner Bernhard: The so different theories of space and time. The transcendental idealism of Kant in relation to the theory of relativity of Einstein, Osnabrück, 2000 ISBN 3-934366-33-3

And overviews in most manuals of natural philosophy, philosophy of physics and philosophy of science often

Film

Einstein's Big Idea, France, Great Britain 2005, ARTE F, directed by Gary Johnstone. The screenplay is based on the bestselling Until Einstein came from David Bodanis.

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