Theory of relativity

The theory of relativity usually encompasses two interrelated theories by Albert Einstein: special relativity and general relativity.[1] Special relativity applies to elementary particles and their interactions, describing all their physical phenomena except gravity. General relativity explains the law of gravitation and its relation to other forces of nature.[2] It applies to the cosmological and astrophysical realm, including astronomy.[3]

The theory transformed theoretical physics and astronomy during the 20th century, superseding a 200-year-old theory of mechanics created primarily by Isaac Newton.[3][4][5] It introduced concepts including spacetime as a unified entity of space and time, relativity of simultaneity, kinematic and gravitational time dilation, and length contraction. In the field of physics, relativity improved the science of elementary particles and their fundamental interactions, along with ushering in the nuclear age. With relativity, cosmology and astrophysics predicted extraordinary astronomical phenomena such as neutron stars, black holes, and gravitational waves.[3][4][5]

Spacetime curvature
Two-dimensional projection of a three-dimensional analogy of spacetime curvature described in general relativity

Development and acceptance

Albert Einstein published the theory of special relativity in 1905, building on many theoretical results and empirical findings obtained by Albert A. Michelson, Hendrik Lorentz, Henri Poincaré and others. Max Planck, Hermann Minkowski and others did subsequent work.

Einstein developed general relativity between 1907 and 1915, with contributions by many others after 1915. The final form of general relativity was published in 1916.[3]

The term "theory of relativity" was based on the expression "relative theory" (German: Relativtheorie) used in 1906 by Planck, who emphasized how the theory uses the principle of relativity. In the discussion section of the same paper, Alfred Bucherer used for the first time the expression "theory of relativity" (German: Relativitätstheorie).[6][7]

By the 1920s, the physics community understood and accepted special relativity.[8] It rapidly became a significant and necessary tool for theorists and experimentalists in the new fields of atomic physics, nuclear physics, and quantum mechanics.

By comparison, general relativity did not appear to be as useful, beyond making minor corrections to predictions of Newtonian gravitation theory.[3] It seemed to offer little potential for experimental test, as most of its assertions were on an astronomical scale. Its mathematics seemed difficult and fully understandable only by a small number of people. Around 1960, general relativity became central to physics and astronomy. New mathematical techniques to apply to general relativity streamlined calculations and made its concepts more easily visualized. As astronomical phenomena were discovered, such as quasars (1963), the 3-kelvin microwave background radiation (1965), pulsars (1967), and the first black hole candidates (1981),[3] the theory explained their attributes, and measurement of them further confirmed the theory.

Special relativity

Special relativity is a theory of the structure of spacetime. It was introduced in Einstein's 1905 paper "On the Electrodynamics of Moving Bodies" (for the contributions of many other physicists see History of special relativity). Special relativity is based on two postulates which are contradictory in classical mechanics:

  1. The laws of physics are the same for all observers in uniform motion relative to one another (principle of relativity).
  2. The speed of light in a vacuum is the same for all observers, regardless of their relative motion or of the motion of the light source.

The resultant theory copes with experiment better than classical mechanics. For instance, postulate 2 explains the results of the Michelson–Morley experiment. Moreover, the theory has many surprising and counterintuitive consequences. Some of these are:

  • Relativity of simultaneity: Two events, simultaneous for one observer, may not be simultaneous for another observer if the observers are in relative motion.
  • Time dilation: Moving clocks are measured to tick more slowly than an observer's "stationary" clock.
  • Length contraction: Objects are measured to be shortened in the direction that they are moving with respect to the observer.
  • Maximum speed is finite: No physical object, message or field line can travel faster than the speed of light in a vacuum.
    • The effect of Gravity can only travel through space at the speed of light, not faster or instantaneously.
  • Mass–energy equivalence: E = mc2, energy and mass are equivalent and transmutable.
  • Relativistic mass, idea used by some researchers.[9]

The defining feature of special relativity is the replacement of the Galilean transformations of classical mechanics by the Lorentz transformations. (See Maxwell's equations of electromagnetism).

General relativity

General relativity is a theory of gravitation developed by Einstein in the years 1907–1915. The development of general relativity began with the equivalence principle, under which the states of accelerated motion and being at rest in a gravitational field (for example, when standing on the surface of the Earth) are physically identical. The upshot of this is that free fall is inertial motion: an object in free fall is falling because that is how objects move when there is no force being exerted on them, instead of this being due to the force of gravity as is the case in classical mechanics. This is incompatible with classical mechanics and special relativity because in those theories inertially moving objects cannot accelerate with respect to each other, but objects in free fall do so. To resolve this difficulty Einstein first proposed that spacetime is curved. In 1915, he devised the Einstein field equations which relate the curvature of spacetime with the mass, energy, and any momentum within it.

Some of the consequences of general relativity are:

Technically, general relativity is a theory of gravitation whose defining feature is its use of the Einstein field equations. The solutions of the field equations are metric tensors which define the topology of the spacetime and how objects move inertially.

Experimental evidence

Einstein stated that the theory of relativity belongs to a class of "principle-theories". As such, it employs an analytic method, which means that the elements of this theory are not based on hypothesis but on empirical discovery. By observing natural processes, we understand their general characteristics, devise mathematical models to describe what we observed, and by analytical means we deduce the necessary conditions that have to be satisfied. Measurement of separate events must satisfy these conditions and match the theory's conclusions.[2]

Tests of special relativity

Relativity is a falsifiable theory: It makes predictions that can be tested by experiment. In the case of special relativity, these include the principle of relativity, the constancy of the speed of light, and time dilation.[11] The predictions of special relativity have been confirmed in numerous tests since Einstein published his paper in 1905, but three experiments conducted between 1881 and 1938 were critical to its validation. These are the Michelson–Morley experiment, the Kennedy–Thorndike experiment, and the Ives–Stilwell experiment. Einstein derived the Lorentz transformations from first principles in 1905, but these three experiments allow the transformations to be induced from experimental evidence.

Maxwell's equations—the foundation of classical electromagnetism—describe light as a wave that moves with a characteristic velocity. The modern view is that light needs no medium of transmission, but Maxwell and his contemporaries were convinced that light waves were propagated in a medium, analogous to sound propagating in air, and ripples propagating on the surface of a pond. This hypothetical medium was called the luminiferous aether, at rest relative to the "fixed stars" and through which the Earth moves. Fresnel's partial ether dragging hypothesis ruled out the measurement of first-order (v/c) effects, and although observations of second-order effects (v2/c2) were possible in principle, Maxwell thought they were too small to be detected with then-current technology.[12][13]

The Michelson–Morley experiment was designed to detect second-order effects of the "aether wind"—the motion of the aether relative to the earth. Michelson designed an instrument called the Michelson interferometer to accomplish this. The apparatus was more than accurate enough to detect the expected effects, but he obtained a null result when the first experiment was conducted in 1881,[14] and again in 1887.[15] Although the failure to detect an aether wind was a disappointment, the results were accepted by the scientific community.[13] In an attempt to salvage the aether paradigm, FitzGerald and Lorentz independently created an ad hoc hypothesis in which the length of material bodies changes according to their motion through the aether.[16] This was the origin of FitzGerald–Lorentz contraction, and their hypothesis had no theoretical basis. The interpretation of the null result of the Michelson–Morley experiment is that the round-trip travel time for light is isotropic (independent of direction), but the result alone is not enough to discount the theory of the aether or validate the predictions of special relativity.[17][18]

Kennedy-Thorndike experiment DE
The Kennedy–Thorndike experiment shown with interference fringes.

While the Michelson–Morley experiment showed that the velocity of light is isotropic, it said nothing about how the magnitude of the velocity changed (if at all) in different inertial frames. The Kennedy–Thorndike experiment was designed to do that, and was first performed in 1932 by Roy Kennedy and Edward Thorndike.[19] They obtained a null result, and concluded that "there is no effect ... unless the velocity of the solar system in space is no more than about half that of the earth in its orbit".[18][20] That possibility was thought to be too coincidental to provide an acceptable explanation, so from the null result of their experiment it was concluded that the round-trip time for light is the same in all inertial reference frames.[17][18]

The Ives–Stilwell experiment was carried out by Herbert Ives and G.R. Stilwell first in 1938[21] and with better accuracy in 1941.[22] It was designed to test the transverse Doppler effect – the redshift of light from a moving source in a direction perpendicular to its velocity—which had been predicted by Einstein in 1905. The strategy was to compare observed Doppler shifts with what was predicted by classical theory, and look for a Lorentz factor correction. Such a correction was observed, from which was concluded that the frequency of a moving atomic clock is altered according to special relativity.[17][18]

Those classic experiments have been repeated many times with increased precision. Other experiments include, for instance, relativistic energy and momentum increase at high velocities, experimental testing of time dilation, and modern searches for Lorentz violations.

Tests of general relativity

General relativity has also been confirmed many times, the classic experiments being the perihelion precession of Mercury's orbit, the deflection of light by the Sun, and the gravitational redshift of light. Other tests confirmed the equivalence principle and frame dragging.

Modern applications

Far from being simply of theoretical interest, relativitistic effects are important practical engineering concerns. Satellite-based measurement needs to take into account relativistic effects, as each satellite is in motion relative to an Earth-bound user and is thus in a different frame of reference under the theory of relativity. Global positioning systems such as GPS, GLONASS, and the forthcoming Galileo, must account for all of the relativistic effects, such as the consequences of Earth's gravitational field, in order to work with precision.[23] This is also the case in the high-precision measurement of time.[24] Instruments ranging from electron microscopes to particle accelerators would not work if relativistic considerations were omitted.

See also


  1. ^ Einstein A. (1916), Relativity: The Special and General Theory  (Translation 1920), New York: H. Holt and Company
  2. ^ a b Einstein, Albert (November 28, 1919). "Time, Space, and Gravitation" . The Times.
  3. ^ a b c d e f Will, Clifford M (2010). "Relativity". Grolier Multimedia Encyclopedia. Retrieved 2010-08-01.
  4. ^ a b Will, Clifford M (2010). "Space-Time Continuum". Grolier Multimedia Encyclopedia. Retrieved 2010-08-01.
  5. ^ a b Will, Clifford M (2010). "Fitzgerald–Lorentz contraction". Grolier Multimedia Encyclopedia. Retrieved 2010-08-01.
  6. ^ Planck, Max (1906), "Die Kaufmannschen Messungen der Ablenkbarkeit der β-Strahlen in ihrer Bedeutung für die Dynamik der Elektronen (The Measurements of Kaufmann on the Deflectability of β-Rays in their Importance for the Dynamics of the Electrons)" , Physikalische Zeitschrift, 7: 753–761
  7. ^ Miller, Arthur I. (1981), Albert Einstein's special theory of relativity. Emergence (1905) and early interpretation (1905–1911), Reading: Addison–Wesley, ISBN 978-0-201-04679-3
  8. ^ Hey, Anthony J.G.; Walters, Patrick (2003). The New Quantum Universe (illustrated, revised ed.). Cambridge University Press. p. 227. ISBN 978-0-521-56457-1. Extract of page 227
  9. ^ Greene, Brian. "The Theory of Relativity, Then and Now". Retrieved 2015-09-26.
  10. ^ Feynman, Richard Phillips; Morínigo, Fernando B.; Wagner, William; Pines, David; Hatfield, Brian (2002). Feynman Lectures on Gravitation. West view Press. p. 68. ISBN 978-0-8133-4038-8., Lecture 5
  11. ^ Roberts, T; Schleif, S; Dlugosz, JM (ed.) (2007). "What is the experimental basis of Special Relativity?". Usenet Physics FAQ. University of California, Riverside. Retrieved 2010-10-31.CS1 maint: Extra text: authors list (link)
  12. ^ Maxwell, James Clerk (1880), "On a Possible Mode of Detecting a Motion of the Solar System through the Luminiferous Ether" , Nature, 21 (535): 314–315, Bibcode:1880Natur..21S.314., doi:10.1038/021314c0
  13. ^ a b Pais, Abraham (1982). "Subtle is the Lord ...": The Science and the Life of Albert Einstein (1st ed.). Oxford: Oxford Univ. Press. pp. 111–113. ISBN 978-0-19-280672-7.
  14. ^ Michelson, Albert A. (1881). "The Relative Motion of the Earth and the Luminiferous Ether" . American Journal of Science. 22 (128): 120–129. Bibcode:1881AmJS...22..120M. doi:10.2475/ajs.s3-22.128.120.
  15. ^ Michelson, Albert A. & Morley, Edward W. (1887). "On the Relative Motion of the Earth and the Luminiferous Ether" . American Journal of Science. 34 (203): 333–345. Bibcode:1887AmJS...34..333M. doi:10.2475/ajs.s3-34.203.333.CS1 maint: Multiple names: authors list (link)
  16. ^ Pais, Abraham (1982). "Subtle is the Lord ...": The Science and the Life of Albert Einstein (1st ed.). Oxford: Oxford Univ. Press. p. 122. ISBN 978-0-19-280672-7.
  17. ^ a b c Robertson, H.P. (July 1949). "Postulate versus Observation in the Special Theory of Relativity" (PDF). Reviews of Modern Physics. 21 (3): 378–382. Bibcode:1949RvMP...21..378R. doi:10.1103/RevModPhys.21.378.
  18. ^ a b c d Taylor, Edwin F.; John Archibald Wheeler (1992). Spacetime physics: Introduction to Special Relativity (2nd ed.). New York: W.H. Freeman. pp. 84–88. ISBN 978-0-7167-2327-1.
  19. ^ Kennedy, R.J.; Thorndike, E.M. (1932). "Experimental Establishment of the Relativity of Time". Physical Review. 42 (3): 400–418. Bibcode:1932PhRv...42..400K. doi:10.1103/PhysRev.42.400.
  20. ^ Robertson, H.P. (July 1949). "Postulate versus Observation in the Special Theory of Relativity" (PDF). Reviews of Modern Physics. 21 (3): 381. Bibcode:1949RvMP...21..378R. doi:10.1103/revmodphys.21.378.
  21. ^ Ives, H.E.; Stilwell, G.R. (1938). "An experimental study of the rate of a moving atomic clock". Journal of the Optical Society of America. 28 (7): 215. Bibcode:1938JOSA...28..215I. doi:10.1364/JOSA.28.000215.
  22. ^ Ives, H.E.; Stilwell, G.R. (1941). "An experimental study of the rate of a moving atomic clock. II". Journal of the Optical Society of America. 31 (5): 369. Bibcode:1941JOSA...31..369I. doi:10.1364/JOSA.31.000369.
  23. ^ "Archived copy" (PDF). Archived from the original (PDF) on 2015-11-05. Retrieved 2015-12-09.CS1 maint: Archived copy as title (link)
  24. ^ Francis, S.; B. Ramsey; S. Stein; Leitner, J.; Moreau, J.M.; Burns, R.; Nelson, R.A.; Bartholomew, T.R.; Gifford, A. (2002). "Timekeeping and Time Dissemination in a Distributed Space-Based Clock Ensemble" (PDF). Proceedings 34th Annual Precise Time and Time Interval (PTTI) Systems and Applications Meeting: 201–214. Archived from the original (PDF) on 17 February 2013. Retrieved 14 April 2013.

Further reading

  • Einstein, Albert (2005). Relativity: The Special and General Theory. Translated by Robert W. Lawson (The masterpiece science ed.). New York: Pi Press. ISBN 978-0-13-186261-6.
  • Einstein, Albert. Relativity: The Special and General Theory (PDF). 1920: Henry Holt and Company.
  • Einstein, Albert; trans. Schilpp; Paul Arthur (1979). Albert Einstein, Autobiographical Notes (A Centennial ed.). La Salle, IL: Open Court Publishing Co. ISBN 978-0-87548-352-8.
  • Einstein, Albert (2009). Einstein's Essays in Science. Translated by Alan Harris (Dover ed.). Mineola, NY: Dover Publications. ISBN 978-0-486-47011-5.
  • Einstein, Albert (1956) [1922]. The Meaning of Relativity (5 ed.). Princeton University Press.
  • The Meaning of Relativity Albert Einstein: Four lectures delivered at Princeton University, May 1921
  • How I created the theory of relativity Albert Einstein, December 14, 1922; Physics Today August 1982
  • Relativity Sidney Perkowitz Encyclopædia Britannica

External links

Absolute space and time

Absolute space and time is a concept in physics and philosophy about the properties of the universe. In physics, absolute space and time may be a preferred frame.

Coordinate time

In the theory of relativity, it is convenient to express results in terms of a spacetime coordinate system relative to an implied observer. In many (but not all) coordinate systems, an event is specified by one time coordinate and three spatial coordinates. The time specified by the time coordinate is referred to as coordinate time to distinguish it from proper time.

In the special case of an inertial observer in special relativity, by convention the coordinate time at an event is the same as the proper time measured by a clock that is at the same location as the event, that is stationary relative to the observer and that has been synchronised to the observer's clock using the Einstein synchronisation convention.

Criticism of the theory of relativity

Criticism of the theory of relativity of Albert Einstein was mainly expressed in the early years after its publication in the early twentieth century, on scientific, pseudoscientific, philosophical, or ideological bases. Though some of these criticisms had the support of reputable scientists, Einstein's theory of relativity is now accepted by the scientific community.Reasons for criticism of the theory of relativity have included alternative theories, rejection of the abstract-mathematical method, and alleged errors of the theory. According to some authors, antisemitic objections to Einstein's Jewish heritage also occasionally played a role in these objections. There are still some critics of relativity today, but their opinions are not shared by the majority in the scientific community.

Die Grundlagen der Einsteinschen Relativitäts-Theorie

Die Grundlagen der Einsteinschen Relativitäts-Theorie (English: The Fundamentals of the Einsteinian Relativity Theory) is a 1922 German partly animated documentary film created with the goal of bringing Einstein's theory of relativity to the broad public. It premiered on April 2, 1922 at the Frankfurt Fair.

With more than 80,000 individual images, it is not only the first great science film, it is also the film with the longest trick sequences.

The original version of the film is lost. As part of the research carried out by the 3sat station, an English copy of the film was filmed in 2005 with the British Film Institute, which was provided with English and English language interludes and "speech bubbles". A companion to the English version is also available.

Part of the film was used to create Max Fleischer's The Einstein Theory of Relativity.

Eddington (spacecraft)

The Eddington mission was a European Space Agency (ESA) project that planned to search for Earth-like planets, but was cancelled in 2003. It was named for Arthur Eddington, a noted physicist who translated Einstein's work and carried out the first test (gravitational lensing) of the general theory of relativity. It was originally planned for operation in 2008, but was delayed. The ESA website now records its status as cancelled.

Ehrenfest paradox

The Ehrenfest paradox concerns the rotation of a "rigid" disc in the theory of relativity.

In its original formulation as presented by Paul Ehrenfest 1909 in relation to the concept of Born rigidity within special relativity, it discusses an ideally rigid cylinder that is made to rotate about its axis of symmetry. The radius R as seen in the laboratory frame is always perpendicular to its motion and should therefore be equal to its value R0 when stationary. However, the circumference (2πR) should appear Lorentz-contracted to a smaller value than at rest, by the usual factor γ. This leads to the contradiction that R = R0 and R < R0.

The paradox has been deepened further by Albert Einstein, who showed that since measuring rods aligned along the periphery and moving with it should appear contracted, more would fit around the circumference, which would thus measure greater than 2πR. This indicates that geometry is non-Euclidean for rotating observers, and was important for Einstein's development of general relativity.

Any rigid object made from real materials that is rotating with a transverse velocity close to the speed of sound in the material must exceed the point of rupture due to centrifugal force, because centrifugal pressure can not exceed the shear modulus of material.

where is speed of sound, is density and is shear modulus. Therefore, when considering velocities close to the speed of light, it is only a thought experiment. Neutron-degenerate matter allows velocities close to speed of light, because e.g. the speed of neutron-star oscillations is relativistic; however; these bodies cannot strictly be said to be "rigid" (per Born rigidity).

Event (relativity)

In physics, and in particular relativity, an event is the instantaneous physical situation or occurrence associated with a point in spacetime (that is, a specific place and time). For example, a glass breaking on the floor is an event; it occurs at a unique place and a unique time. Strictly speaking, the notion of an event is an idealization, in the sense that it specifies a definite time and place, whereas any actual event is bound to have a finite extent, both in time and in space.

Upon choosing a frame of reference, one can assign coordinates to the event: three spatial coordinates to describe the location and one time coordinate to specify the moment at which the event occurs. These four coordinates together form a four-vector associated to the event.

One of the goals of relativity is to specify the possibility of one event influencing another. This is done by means of the metric tensor, which allows for determining the causal structure of spacetime. The difference (or interval) between two events can be classified into spacelike, lightlike and timelike separations. Only if two events are separated by a lightlike or timelike interval can one influence the other.

General relativity

General relativity (GR, also known as the general theory of relativity or GTR) is the geometric theory of gravitation published by Albert Einstein in 1915 and the current description of gravitation in modern physics. General relativity generalizes special relativity and Newton's law of universal gravitation, providing a unified description of gravity as a geometric property of space and time, or 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. Examples of such differences include gravitational time dilation, gravitational lensing, the gravitational redshift of light, and the gravitational time delay. 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.

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.

Gravitational time dilation

Gravitational time dilation is a form of time dilation, an actual difference of elapsed time between two events as measured by observers situated at varying distances from a gravitating mass. The higher the gravitational potential (the farther the clock is from the source of gravitation), the faster time passes. Albert Einstein originally predicted this effect in his theory of relativity and it has since been confirmed by tests of general relativity.This has been demonstrated by noting that atomic clocks at differing altitudes (and thus different gravitational potential) will eventually show different times. The effects detected in such Earth-bound experiments are extremely small, with differences being measured in nanoseconds. Relative to Earth's age in billions of years, Earth's core is effectively 2.5 years younger than its surface. Demonstrating larger effects would require greater distances from the Earth or a larger gravitational source.

Gravitational time dilation was first described by Albert Einstein in 1907 as a consequence of special relativity in accelerated frames of reference. In general relativity, it is considered to be a difference in the passage of proper time at different positions as described by a metric tensor of space-time. The existence of gravitational time dilation was first confirmed directly by the Pound–Rebka experiment in 1959.

Jackiw–Teitelboim gravity

The R = T model, also known as Jackiw–Teitelboim gravity, is a theory of gravity with dilaton coupling in one spatial and one time dimension. It should not be confused with the CGHS model or Liouville gravity. The action is given by

where Φ is the dilaton, denotes the covariant derivative and the equation of motion is

The metric in this case is more amenable to analytical solutions than the general 3+1D case though a canonical reduction for the latter has recently been obtained. For example, in 1+1D, the metric for the case of two mutually interacting bodies can be solved exactly in terms of the Lambert W function, even with an additional electromagnetic field (see quantum gravity and references for details).

Light cone

In special and general relativity, a light cone is the path that a flash of light, emanating from a single event (localized to a single point in space and a single moment in time) and traveling in all directions, would take through spacetime.

Minkowski diagram

The Minkowski diagram, also known as a spacetime diagram, was developed in 1908 by Hermann Minkowski and provides an illustration of the properties of space and time in the special theory of relativity. It allows a qualitative understanding of the corresponding phenomena like time dilation and length contraction without mathematical equations.

Minkowski diagrams are two-dimensional graphs that depict events as happening in a universe consisting of one space dimension and one time dimension. Unlike a regular distance-time graph, the distance is displayed on the horizontal axis and time on the vertical axis. Additionally, the time and space units of measurement are chosen in such a way that an object moving at the speed of light is depicted as following a 45° angle to the diagram's axes.

In this way, each object, like an observer or a vehicle, traces a certain line in the diagram, which is called its world line. Also, each point in the diagram represents a certain position in space and time, and is called an event, regardless of whether anything relevant happens there.

Nonsingular black hole models

A nonsingular black hole model is a mathematical theory of black holes that avoids certain theoretical problems with the standard black hole model, including information loss and the unobservable nature of the black hole event horizon.

Philosophical presentism

Philosophical presentism is the view that neither the future nor the past exist. In some versions of presentism, this view is extended to timeless objects or ideas (such as numbers). According to presentism, events and entities that are wholly past or wholly future do not exist at all. Presentism contrasts with eternalism and the growing block theory of time which hold that past events, like the Battle of Waterloo, and past entities, like Alexander the Great's warhorse Bucephalus, really do exist, although not in the present. Eternalism extends to future events as well.

Principle of relativity

In physics, the principle of relativity is the requirement that the equations describing the laws of physics have the same form in all admissible frames of reference.

For example, in the framework of special relativity the Maxwell equations have the same form in all inertial frames of reference. In the framework of general relativity the Maxwell equations or the Einstein field equations have the same form in arbitrary frames of reference.

Several principles of relativity have been successfully applied throughout science, whether implicitly (as in Newtonian mechanics) or explicitly (as in Albert Einstein's special relativity and general relativity).

Proper length

Proper length or rest length refers to the length of an object in the object's rest frame.

The measurement of lengths is more complicated in the theory of relativity than in classical mechanics. In classical mechanics, lengths are measured based on the assumption that the locations of all points involved are measured simultaneously. But in the theory of relativity, the notion of simultaneity is dependent on the observer.

A different term, proper distance, provides an invariant measure whose value is the same for all observers.

Proper distance is analogous to proper time. The difference is that the proper distance is defined between two spacelike-separated events (or along a spacelike path), while the proper time is defined between two timelike-separated events (or along a timelike path).

Special relativity

In physics, special relativity (SR, also known as the special theory of relativity or STR) is the generally accepted and experimentally well-confirmed physical theory regarding the relationship between space and time. In Albert Einstein's original pedagogical treatment, it is based on two postulates:

the laws of physics are invariant (i.e. identical) in all inertial systems (i.e. non-accelerating frames of reference); and

the speed of light in a vacuum is the same for all observers, regardless of the motion of the light source.Special relativity was originally proposed by Albert Einstein in a paper published 26 September 1905 titled "On the Electrodynamics of Moving Bodies". The inconsistency of Newtonian mechanics with Maxwell's equations of electromagnetism and the lack of experimental confirmation for a hypothesized luminiferous aether led to the development of special relativity, which corrects mechanics to handle situations involving all motions and especially those at a significant fraction of the speed of light (known as relativistic velocities). Today, special relativity is the most accurate model of motion at any speed when gravitational effects are negligible. Even so, the Newtonian mechanics model is still valid as a simple and high accuracy approximation at low velocities relative to the speed of light.

Special relativity implies a wide range of consequences, which have been experimentally verified, including length contraction, time dilation, relativistic mass, mass–energy equivalence, a universal speed limit, the speed of causality and relativity of simultaneity. It has replaced the conventional notion of an absolute universal time with the notion of a time that is dependent on reference frame and spatial position. Rather than an invariant time interval between two events, there is an invariant spacetime interval. Combined with other laws of physics, the two postulates of special relativity predict the equivalence of mass and energy, as expressed in the mass–energy equivalence formula E = mc2, where c is the speed of light in a vacuum.A defining feature of special relativity is the replacement of the Galilean transformations of Newtonian mechanics with the Lorentz transformations. Time and space cannot be defined separately from each other. Rather, space and time are interwoven into a single continuum known as "spacetime". Events that occur at the same time for one observer can occur at different times for another.

Not until Einstein developed general relativity, introducing a curved spacetime to incorporate gravity, was the phrase "special relativity" employed. A translation that has often been used is "restricted relativity"; "special" really means "special case".The theory is "special" in that it only applies in the special case where the spacetime is flat, i.e., the curvature of spacetime, described by the energy-momentum tensor and causing gravity, is negligible. In order to correctly accommodate gravity, Einstein formulated general relativity in 1915. Special relativity, contrary to some outdated descriptions, is capable of handling accelerations as well as accelerated frames of reference.As Galilean relativity is now accepted to be an approximation of special relativity that is valid for low speeds, special relativity is considered an approximation of general relativity that is valid for weak gravitational fields, i.e. at a sufficiently small scale (for example, for tidal forces) and in conditions of free fall. Whereas general relativity incorporates noneuclidean geometry in order to represent gravitational effects as the geometric curvature of spacetime, special relativity is restricted to the flat spacetime known as Minkowski space. As long as the universe can be modeled as a pseudo-Riemannian manifold, a Lorentz-invariant frame that abides by special relativity can be defined for a sufficiently small neighborhood of each point in this curved spacetime.

Galileo Galilei had already postulated that there is no absolute and well-defined state of rest (no privileged reference frames), a principle now called Galileo's principle of relativity. Einstein extended this principle so that it accounted for the constant speed of light, a phenomenon that had been observed in the Michelson–Morley experiment. He also postulated that it holds for all the laws of physics, including both the laws of mechanics and of electrodynamics.

The Einstein Theory of Relativity

The Einstein Theory of Relativity (1923) is a silent short film directed by Dave Fleischer and released by Fleischer Studios.


A wormhole (or Einstein–Rosen bridge) is a speculative structure linking disparate points in spacetime, and is based on a special solution of the Einstein field equations solved using a Jacobian matrix and determinant. A wormhole can be visualized as a tunnel with two ends, each at separate points in spacetime (i.e., different locations or different points of time). More precisely it is a transcendental bijection of the spacetime continuum, an asymptotic projection of the Calabi–Yau manifold manifesting itself in Anti-de Sitter space.

Wormholes are consistent with the general theory of relativity, but whether wormholes actually exist remains to be seen.

A wormhole could connect extremely long distances such as a billion light years or more, short distances such as a few meters, different universes, or different points in time.

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