# theory of relativity

The theory of relativity deals with the structure of space and time as well as with the nature of gravity . It consists of two physical theories mainly created by Albert Einstein , the special theory of relativity published in 1905 and the general theory of relativity, completed in 1916 . The special theory of relativity describes the behavior of space and time from the point of view of observers who move relative to one another and the associated phenomena. Building on this, the general theory of relativity leads back gravity to a curvature of space and time, which is caused, among other things, by the masses involved.

The term relativistic , which is often used in the technical jargon , usually means that a speed is not negligibly small compared to the speed of light ; the limit is often drawn at 10 percent. At relativistic speeds, the effects described by the special theory of relativity become increasingly important; the deviations from classical mechanics can then no longer be neglected.

This article provides a summary of the basic structures and phenomena. For explanations and details see the articles Special Theory of Relativity and General Theory of Relativity as well as the references in the text. For the concept of relativity as such, see Relativity .

## meaning

The theory of relativity has revolutionized the understanding of space and time and uncovered interrelationships that cannot be clearly imagined . However, these can be expressed mathematically precisely in formulas and confirmed through experiments. The theory of relativity contains Newtonian physics as a limiting case. It thus fulfills the correspondence principle .

The standard model of particle physics is based on the union of the special relativity theory with the quantum theory to form a relativistic quantum field theory .

The general theory of relativity is, alongside quantum physics, one of the two pillars of the theoretical building of physics . It is generally accepted that a union of these two pillars into a Theory of Everything is possible in principle. Despite great efforts, however, such a union has not yet fully succeeded. It is one of the great challenges of basic physical research .

## The special theory of relativity

### The principle of relativity

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

Both observers measure the same numerical value for the speed of light, although the one on the left is moving relative to the light source.
• If different observers measure the speed of a light beam relative to their location, they will arrive at the same result regardless of their own state of motion. This is the so-called principle of the constancy of the speed of light .
• The physical laws have the same form for all observers who move relative to each other at constant speed, i.e. not subject to acceleration. This fact is called the principle of relativity .

The principle of relativity in itself is not very spectacular, because it also applies to Newtonian mechanics. It immediately follows from this that there is no possibility of determining an absolute speed of an observer in space and thus defining an absolutely stationary reference system. Such a rest system would have to be different from all others in some way, in contradiction to the principle of relativity, according to which the laws of physics have the same shape in all reference systems. Before the development of the theory of relativity, electrodynamics was based on the assumption that aether was the carrier of electromagnetic waves . If such an ether were to fill space as a rigid structure, then it would define a reference system in which, contrary to the principle of relativity, the physical laws would have a particularly simple form and which would also be the only system in which the speed of light is constant. However, all attempts to prove the existence of the ether failed, such as the famous Michelson-Morley experiment of 1887.

By abandoning the conventional ideas of space and time and rejecting the ether hypothesis, Einstein succeeded in resolving the apparent contradiction between the principle of relativity and the constancy of the speed of light resulting from electrodynamics. It was not by chance that experiments and considerations on electrodynamics led to the discovery of the theory of relativity. That was the inconspicuous title of Einstein's 1905 publication, which founded the special theory of relativity, On the electrodynamics of moving bodies .

### Relativity of space and time

In the theory of relativity, space and time specifications are not universally valid structures of order. Rather, the spatial and temporal distance between two events or their simultaneity are assessed differently by observers with different states of motion. In comparison to the state of rest, moving objects turn out to be shortened in the direction of movement and moving clocks to be slowed down. However, since all observers who are uniformly moved relative to one another can equally take the position that they are at rest, these observations are based on reciprocity, that is, two observers who move relatively to one another see each other's clocks going slower. In addition, from their point of view, each other's yardstick is shorter than a meter when they are aligned along the direction of movement. The question of who describes the situation more correctly cannot be answered in principle and is therefore pointless.

This length contraction and time dilation can be understood comparatively clearly using Minkowski diagrams . In the mathematical formulation they result from the Lorentz transformation , which describes the relationship between the space and time coordinates of the various observers. This transformation can be derived directly from the two axioms above and the assumption that it is linear .

Most of these relativistically explainable phenomena only become noticeable at speeds that are appreciably large compared to the speed of light. Such speeds are not even close to being reached by masses in everyday life.

### Speed ​​of light as a limit

No object and no information can move faster than light in a vacuum . If the speed of a material object approaches the speed of light, the energy expenditure strives for a further acceleration beyond all limits, because the kinetic energy increases more and more steeply with increasing approach to the speed of light. To reach the speed of light, an infinite amount of energy would have to be applied.

This circumstance is a consequence of the structure of space and time and not a property of the object, such as a merely imperfect spaceship . If an object were to move from A to B at faster than light speed , there would always be an observer moving relative to it who would perceive a movement from B to A, again without the question of who is describing the situation more correctly. The principle of causality would then be violated, since the sequence of cause and effect would no longer be defined. Incidentally, such an object would move faster than light for any observer.

### Union of space and time into space-time

In the basic equations of the theory of relativity, space and time appear formally almost equal and can therefore be combined into a four-dimensional space-time. That space and time appear in different ways is a peculiarity of human perception. Mathematically, the difference can be traced back to a single sign by which the definition of a distance in Euclidean space differs from the definition of the distance in four-dimensional space-time. Ordinary vectors in three-dimensional space become so-called four - vectors .

In spacetime there are three clearly distinguishable areas for every observer due to the relativity of lengths and time spans:

• All points that the observer can reach by means of a signal with the maximum speed of light are located in the future light cone.
• The past light cone includes all points from which a signal can reach the observer at the maximum speed of light.
• All remaining points are called “spatially separated by the observer”. In this area the chosen observer cannot define the future and the past.

The space-time four-vectors find practical application, for example, in calculations of the kinematics of fast particles.

### Equivalence of mass and energy

An energy E can be assigned to a system with the mass m even in the stationary state , namely according to

${\ displaystyle E = m \ cdot c ^ {2}}$,

where c is the speed of light. This formula is one of the most famous in physics. It is often misleadingly claimed that it made possible the development of the atomic bomb . The action , however, the atomic bomb can not be explained with it. However, as early as 1939, shortly after the discovery of nuclear fission, Lise Meitner was able to estimate the enormous release of energy with this formula and the already known masses of the atoms . This decrease in mass also occurs in chemical reactions, but because of its small size it could not be determined with the measurement methods of the time, unlike in the case of nuclear reactions.

### Magnetic fields in the theory of relativity

The existence of magnetic forces is inextricably linked with the theory of relativity. An isolated existence of Coulomb's law for electrical forces would not be compatible with the structure of space and time. An observer who is at rest relative to a system of static electrical charges does not see a magnetic field, unlike an observer who moves relative to him. If one translates the observations of the stationary observer via a Lorentz transformation into those of the moving one, it turns out that he perceives another magnetic force in addition to the electrical force. The existence of the magnetic field in this example can therefore be traced back to the structure of space and time. From this point of view, the structure of the comparable Biot-Savartian law for magnetic fields, which is complicated compared to the Coulomb law and, at first glance, implausible . In the mathematical formalism of the theory of relativity, the electric and magnetic fields are combined into one unit, the four-dimensional electromagnetic field strength tensor , analogous to the union of space and time to form four-dimensional space-time.

## The general theory of relativity

### Gravitation and the curvature of spacetime

The general theory of relativity traces gravity back to the geometric phenomenon of curved spacetime by stating:

• Energy bends space-time in its environment.
• An object on which only gravitational forces act, always moves between two points in space-time on a so-called geodesic .

If the four-dimensional space-time of the special theory of relativity eludes a vivid imaginability, this is even more true for an additionally curved space-time. However, to illustrate, one can consider situations with a reduced number of dimensions. In the case of a 2-dimensional curved landscape, a geodesic corresponds to the path that a vehicle would take with the steering fixed straight ahead. If two such vehicles were to start next to each other at the equator of a sphere, exactly parallel to each other, heading north, then they would meet at the North Pole. An observer who would not see the spherical shape of the earth would conclude that there is an attraction between the two vehicles. However, it is a purely geometric phenomenon. Gravitational forces are therefore sometimes referred to as pseudo-forces in general relativity .

Since the geodetic path through space-time depends on its geometry and not on the mass or other properties of the falling body, all bodies in the gravitational field fall at the same speed, as Galileo already established. This fact is described in Newtonian mechanics by the equivalence of inert and heavy mass , which is also the basis of the general theory of relativity.

### The mathematical structure of general relativity

While many aspects of the special theory of relativity in their simplest formulation can be understood even with little mathematical knowledge, the mathematics of general relativity is much more demanding. The description of a crooked spacetime is carried out with the methods of differential geometry , which includes and extends the Euclidean geometry of the flat space we are familiar with.

To describe curvature, a curved object is usually embedded in a higher-dimensional space. For example, one usually imagines a two-dimensional spherical surface in a three-dimensional space. However, curvature can be described without the assumption of such an embedding space, which also happens in the general theory of relativity. For example, it is possible to describe curvature by saying that the sum of the angles of triangles does not correspond to 180 °.

The origin of the curvature is described by Einstein's field equations . These are differential equations of a tensor field with ten components, which can only be solved analytically in special cases, i.e. in the form of a mathematical equation. For complex systems, approximation mechanisms are therefore usually used.

### Clocks in the gravitational field

In the general theory of relativity, the rate of clocks depends not only on their relative speed, but also on their location in the gravitational field . A clock on a mountain goes faster than one in the valley. Although this effect is only slight in the terrestrial gravitational field, it is taken into account in the GPS navigation system to avoid errors in the position determination via a corresponding frequency correction of the radio signals .

### cosmology

While the special theory of relativity is only valid in areas of space-time that are so small that the curvature can be neglected in the presence of masses, the general theory of relativity manages without this restriction. It can therefore also be applied to the universe as a whole and therefore plays a central role in cosmology . The expansion of the universe observed by astronomers is adequately described by Friedmann's solutions of Einstein's field equations in combination with a so-called cosmological constant . After that, this expansion began with the Big Bang , which, according to the most recent studies, took place 13.7 billion years ago. It can also be seen as the beginning of space and time, when the entire universe was concentrated in an area of ​​space the diameter of Planck's length .

### Black holes

Another prediction of general relativity is black holes . These objects have such strong gravity that they can even “trap” light so that it cannot come out of the black hole. Einstein could not get used to this idea and said that there must be a mechanism that prevents the creation of such objects. Today's observations, however, show that such black holes actually exist in the universe, namely as the final stage of stellar evolution in very massive stars and in the centers of galaxies .

### Gravitational waves

The general theory of relativity allows the existence of gravitational waves , local deformations of space-time that propagate at the speed of light. They arise when masses accelerate, but they are only very small. For a long time, gravitational waves could therefore only be confirmed indirectly, for example by observing binary star systems with pulsars . Russell Hulse and Joseph Taylor received the 1993 Nobel Prize in Physics for this. It was not until the LIGO experiment, on September 14, 2015 at 11:51 CEST, that direct evidence was found.

## History of origin

### Special theory of relativity

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

• the Michelson-Morley experiment (1887), which could not show any relative movement 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 by Lorentz (1892, 1899) and Joseph Larmor (1897), which included a change in the time variables and which should generally be used to explain the negative ether drift experiments;
• 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 , who, however, stuck to the etheric idea;
• as well as the achievement of the full covariance of the electrodynamic basic equations by Lorentz (1904) and Poincaré (1905) in the Lorentzian ether theory .

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

### general theory of relativity

While a number of scientists were involved in the development of the special theory of relativity - Einstein's 1905 work being both an end and a new beginning - the development of general relativity was virtually Einstein's sole achievement in terms of its fundamental physical statements.

This development began in 1907 with the principle of equivalence , according to which inertial and heavy mass are equivalent. From this he derived the gravitational redshift and found that light is deflected in the gravitational field, taking into account the resulting delay, the so-called Shapiro delay . In 1911 he continued these basic ideas with refined methods. This time he also suspected that the deflection of light can be measured in the gravitational field. However, the value he predicted at that time was still too small by a factor of 2.

In the further course, Einstein recognized that Minkowski's four-dimensional space-time formalism, which Einstein had been skeptical about up to now, had a very important role in the new theory. It also now became clear to him that the means of Euclidean geometry were insufficient to be able to continue his work. In 1913, with the mathematical support of Marcel Grossmann , he was able to integrate the non-Euclidean geometry developed in the 19th century into his theory, but without the complete covariance, i.e. H. to achieve the agreement of all natural laws in the reference systems. In 1915, after a few failures, these problems were overcome and Einstein was finally able to derive the correct field equations for gravity. David Hilbert succeeded in doing this almost at the same time . Einstein calculated the correct value for the perihelion rotation of Mercury, and for the light deflection twice the value obtained in 1911. In 1919 this value was confirmed for the first time, which initiated the triumph of the theory in physicists' circles and also in public.

After that, many physicists tried to find exact solutions to the field equations, which resulted in the establishment of various cosmological models and theories such as that of black holes .

### More geometric theories

After the explanation of gravity as a geometric phenomenon, it was obvious to trace back the other basic forces known at the time , the electrical and the magnetic, to geometric effects. Theodor Kaluza (1921) and Oskar Klein (1926) assumed an additional, self-contained dimension of space with such a small, namely subatomic, length that this dimension remains hidden from us. However, they were unsuccessful with their theory. Einstein also worked in vain for a long time to create such a unified field theory .

After the discovery of other basic 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 the theory of relativity and the quantum theory of this kind, the string theory , assumes six or seven hidden dimensions of the size of the Planck length and thus a ten- or eleven-dimensional space-time.

## Experimental confirmations

The first success of the special theory of relativity was the resolution of the contradiction that can be seen as the reason for its discovery: the contradiction between the result of the Michelson-Morley experiment and the theory of electrodynamics. Since then, the special theory of relativity has proven itself in the interpretation of countless experiments. A convincing example is the detection of muons in cosmic radiation , which, due to their short lifespan, could not reach the earth's surface if the time did not go slower for them due to their high speed, or they experience the flight path contracted in length. This evidence was partly achieved during the balloon flights into the stratosphere of the Swiss physicist Auguste Piccard in 1931 and 1932, which were prepared with the help of Einstein.

On the other hand, at the time of the publication of the general theory of relativity, there was only one indication of its correctness, the perihelion of Mercury . In 1919 Arthur Stanley Eddington noticed a shift in the apparent position of the stars near the sun during a solar eclipse and provided further confirmation of the theory with this very direct indication of a curvature of space.

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

The theory of relativity has been able to assert itself in the form given by Einstein against all alternatives that were proposed in particular for his theory of gravitation. The most important was the Jordan-Brans-Dicke theory , but it was more complex. Their validity has not yet been refuted. However, the range that the decisive parameter can occupy according to today's experimental status is very limited.

## Reception and interpretation

### Public perception

The new view of the theory of relativity with regard to space and time also caused a sensation in the general public after its discovery. Einstein became a celebrity and the theory of relativity received significant media coverage. Shortened to the winged word Everything is relative , it has sometimes been brought into the vicinity of a philosophical relativism .

In April 1922, a film entitled The Basics of Einstein's Theory of Relativity was premiered, in which Einstein's special theory of relativity should be made understandable to the audience with many animations .

Criticism of the theory of relativity was fed by various sources, such as incomprehension, rejection of the advancing mathematization of physics and, in some cases, resentment against Einstein's Jewish ancestry. From the 1920s onwards, a few openly anti-Semitic physicists in Germany, namely Nobel Prize winners Philipp Lenard and Johannes Stark , tried to counter the theory of relativity with German physics . A few years after the National Socialist seizure of power, Stark went on the offensive with an article in the SS newspaper Das Schwarze Korps on July 15, 1937, against the supporters of relativity and quantum theory who remained in the country. Among other things, he denounced Werner Heisenberg and Max Planck as white Jews . Heisenberg turned directly to Himmler and achieved his full rehabilitation; not least with a view to the needs of armaments development, the theory of relativity was allowed.

Many leading proponents of traditional physics also rejected Einstein's theory of relativity, including Lorentz and Poincaré themselves and experimental physicists such as Michelson.

### Scientific recognition

The meaning of the theories of relativity was initially controversial . The 1921 Nobel Prize in Physics was awarded to Einstein in 1922 for his interpretation of the photoelectric effect . However, in his award speech he spoke about the theories of relativity.

## Literature and film

### 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 search 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 .
• Rüdiger Vaas : Beyond Einstein's Universe - From Relativity Theory to Quantum Gravity . Kosmos, Stuttgart 2015, ISBN 978-3-440-14883-9 .

### Philosophical introductions and discussion

• Julian Barbour: The End of Time . Weidenfeld & Nicolson, London 1999, ISBN 0-297-81985-2 .
• Ernst Cassirer : On Einstein's theory of relativity. Epistemological considerations . Meiner, Hamburg 2001, ISBN 3-7873-1410-5 .
• John Earman : World Enough and Space-Time. Absolute versus relational theories of space and time . MIT, Cambridge, Mass. 1989, ISBN 0-262-05040-4 .
• 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 spacetime explains. 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 1915–1925 . 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 .
• Werner Bernhard Sendker: The very different theories of space and time. The transcendental idealism of Kant in relation to Einstein's theory of relativity . Osnabrück 2000, ISBN 3-934366-33-3 .

as well as overview presentations in most manuals on natural philosophy , philosophy of physics and often also philosophy of science .

### Movie

• Einstein's big idea . France, Great Britain 2005, ARTE France, directed by Gary Johnstone. (The script is based on the bestseller Bis Einstein Came by David Bodanis.)