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Encyclopedia > Spacetime
Two-dimensional analogy of space-time distortion. The presence of matter changes the geometry of spacetime, this (curved) geometry being interpreted as gravity. Note that the white lines do not represent the curvature of space, but instead represent the coordinate system imposed on the curved spacetime which would be rectilinear in a flat spacetime
Two-dimensional analogy of space-time distortion. The presence of matter changes the geometry of spacetime, this (curved) geometry being interpreted as gravity. Note that the white lines do not represent the curvature of space, but instead represent the coordinate system imposed on the curved spacetime which would be rectilinear in a flat spacetime

In physics, spacetime is any mathematical model that combines space and time into a single construct called the space-time continuum. Spacetime is usually interpreted with space being three-dimensional and time playing the role of the fourth dimension. According to Euclidean space perception, the universe has three dimensions of space, and one dimension of time. By combining space and time into a single manifold, physicists have significantly simplified a large amount of physical theory, as well as described in a more uniform way the workings of the universe at both the supergalactic and subatomic levels. Spacetime may refer to: Spacetime - in physics, refers to the mathematical union of 3-dimensional space and time as a 4-dimensional manifold. ... Illustration of spacetime curvature. ... Illustration of spacetime curvature. ... In physics, matter is commonly defined as the substance of which physical objects are composed, not counting the contribution of various energy or force-fields, which are not usually considered to be matter per se (though they may contribute to the mass of objects). ... Calabi-Yau manifold Geometry (Greek γεωμετρία; geo = earth, metria = measure) is a part of mathematics concerned with questions of size, shape, and relative position of figures and with properties of space. ... Gravity is a force of attraction that acts between bodies that have mass. ... In mathematics as applied to geometry, physics or engineering, a coordinate system is a system for assigning a tuple of numbers to each point in an n-dimensional space. ... Rectilinear: Characterized by straight lines, as opposed to curvilinear which is characterized by curved lines. ... This is a discussion of a present category of science. ... A mathematical model is an abstract model that uses mathematical language to describe the behaviour of a system. ... Space has been an interest for philosophers and scientists for much of human history. ... A pocket watch, a device used to tell time Look up time in Wiktionary, the free dictionary. ... This article does not cite any references or sources. ... Around 300 BC, the Greek mathematician Euclid laid down the rules of what has now come to be called Euclidean geometry, which is the study of the relationships between angles and distances in space. ... The Universe is defined as the summation of all particles and energy that exist and the space-time in which all events occur. ... 2-dimensional renderings (ie. ... On a sphere, the sum of the angles of a triangle is not equal to 180° (see spherical trigonometry). ... Theoretical physics employs mathematical models and abstractions of physics, as opposed to experimental processes, in an attempt to understand nature. ... This article is about the physics subject. ... Fig. ...


In classical mechanics, the use of spacetime over Euclidean space is optional, as time is independent of mechanical motion in three dimensions. In relativistic contexts, however, time cannot be separated from the three dimensions of space as it depends on an object's velocity relative to the speed of light. Classical mechanics (also called Newtonian mechanics) is used for describing the motion of macroscopic objects, from projectiles to parts of machinery, as well as astronomical objects, such as spacecraft, planets, stars, and galaxies. ... Two-dimensional analogy of space-time curvature described in General Relativity. ... In physics, velocity is defined as the rate of change of displacement or the rate of displacement. ... Cherenkov effect in a swimming pool nuclear reactor. ...


The term spacetime has taken on a generalized meaning with the advent of higher-dimensional theories. How many dimensions are needed to describe the universe is still an open question. Speculative theories such as string theory predict 10 or 26 dimensions (With M-theory predicting 11 dimensions, 10 spatial and 1 temporal), but the existence of more than four dimensions would only appear to make a difference at the subatomic level. Interaction in the subatomic world: world lines of pointlike particles in the Standard Model or a world sheet swept up by closed strings in string theory String theory is a model of fundamental physics whose building blocks are one-dimensional extended objects called strings, rather than the zero-dimensional point... M-theory is a solution proposed for the unknown theory of everything which would combine all five superstring theories and 11-dimensional supergravity together. ... Helium atom (not to scale) Showing two protons (red), two neutrons (green) and a probability cloud (gray) of two electrons (yellow). ...

Contents

Historical origin

The origins of this 20th century scientific theory began in the 19th century with fiction writers. Edgar Allan Poe stated in his essay on cosmology titled Eureka (1848) that "space and duration are one." This is the first known instance of suggesting space and time to be different perceptions of one thing. Poe arrived at this conclusion after approximately 90 pages of reasoning but employed no mathematics. In 1895, in his novel, The Time Machine, H.G. Wells wrote, “There is no difference between Time and any of the three dimensions of Space except that our consciousness moves along it.” He added, “Scientific people…know very well that Time is only a kind of Space.” Edgar Allan Poe (January 19, 1809 – October 7, 1849) was an American poet, short story writer, playwright, editor, literary critic, essayist and one of the leaders of the American Romantic Movement. ... Eureka is a prose poem by Edgar Allan Poe from (1848) in which he describes his illumination about the universe. ... The Time Machine is a novel by H. G. Wells, first published in 1895, later made into two films of the same title. ... H. G. Wells at the door of his house at Sandgate Herbert George Wells (September 21, 1866 - August 13, 1946) was an English writer best known for his science fiction novels such as The War of the Worlds and The Time Machine. ...


While spacetime can be viewed as a consequence of Albert Einstein's 1905 theory of special relativity, it was first explicitly proposed mathematically by one of his teachers, the mathematician Hermann Minkowski, in a 1908 essay [1] building on and extending Einstein's work. His concept of Minkowski space is the earliest treatment of space and time as two aspects of a unified whole, the essence of special relativity. The idea of Minkowski space also led to special relativity being viewed in a more geometrical way, this geometric viewpoint of spacetime being important in general relativity too. (For an English translation of Minkowski's article, see Lorentz et al. 1952.) The 1926 thirteenth edition of the Encyclopedia Britannica included an article by Einstein titled "space-time".[2] “Einstein” redirects here. ... 1905 (MCMV) was a common year starting on Sunday (link will display the full calendar). ... For a less technical and generally accessible introduction to the topic, see Introduction to special relativity. ... Hermann Minkowski. ... In physics and mathematics, Minkowski space (or Minkowski spacetime) is the mathematical setting in which Einsteins theory of special relativity is most conveniently formulated. ... For a less technical and generally accessible introduction to the topic, see Introduction to special relativity. ... Year 1926 (MCMXXVI) was a common year starting on Friday (link will display the full calendar) of the Gregorian calendar. ... 1913 advertisement for the 11th edition, with the slogan When in doubt — look it up in the Encyclopædia Britannica The Encyclopædia Britannica (properly spelled with æ, the ae-ligature) was first published in 1768–1771 as The Britannica was an important early English-language general encyclopedia and is still...


Basic concepts

Spacetimes are the arenas in which all physical events take place — an event is a point in spacetime specified by its time and place. For example, the motion of planets around the Sun may be described in a particular type of spacetime, or the motion of light around a rotating star may be described in another type of spacetime. The basic elements of spacetime are events. In any given spacetime, an event is a unique position at a unique time. Examples of events include the explosion of a star or the single beat of a drum. The eight planets and three dwarf planets of the Solar System. ... The Sun (Latin: ) is the star at the center of the Solar System. ... This article does not cite any references or sources. ... STAR is an acronym for: Organizations Society of Ticket Agents and Retailers], the self-regulatory body for the entertainment ticket industry in the UK. Society for Telescopy, Astronomy, and Radio, a non-profit New Jersey astronomy club. ...


A space-time is independent of any observer.[3] However, in describing physical phenomena (which occur at certain moments of time in a given region of space), each observer chooses a convenient coordinate system. Events are specified by four real numbers in any coordinate system. The worldline of a particle or light beam is the path that this particle or beam takes in the spacetime and represents the history of the particle or beam. The worldline of the orbit of the Earth is depicted in two spatial dimensions x and y (the plane of the Earth orbit) and a time dimension orthogonal to x and y. The orbit of the Earth is an ellipse in space alone, but its worldline is a helix in spacetime. In mathematics as applied to geometry, physics or engineering, a coordinate system is a system for assigning a tuple of numbers to each point in an n-dimensional space. ... Please refer to Real vs. ... A world line of an object or person is the sequence of events labeled with time and place, that marks the history of the object or person. ... A helix (pl: helices), from the Greek word έλικας/έλιξ, is a twisted shape like a spring, screw or a spiral (correctly termed helical) staircase. ...


The unification of space and time is exemplified by the common practice of expressing distance in units of time, by dividing the distance measurement by the speed of light. The former Weights and Measures office in Middlesex, England. ... Various meters Measurement is an observation that reduces an uncertainty expressed as a quantity. ... A line showing the speed of light on a scale model of Earth and the Moon, about 1. ...


Space-time intervals

Spacetime entails a new concept of distance. Whereas distances are always positive in Euclidean spaces, the distance between any two events in spacetime (called an "interval") may be real, zero, or even imaginary. The spacetime interval quantifies this new distance (in Cartesian coordinates x,y,z,t): In mathematics, Euclidean geometry is the familiar kind of geometry on the plane or in three dimensions. ... Fig. ...


s^2 = , c^2t^2 - r^2


where c is the speed of light, differences of the space and time coordinates of the two events are denoted by r and t, respectively and r2 = x2 + y2 + z2. (Note that the choice of signs above follows the Landau-Lifshitz spacelike convention. Other treatments, including some within Wikipedia, reverse the order of the arguments on the right-hand side. If this alternate convention is chosen, the relationships in the next two paragraphs are reversed.) In physics, a sign convention is a choice of the signs (plus or minus) of a set of quantities, in a case where the choice of sign is arbitrary. ...


Pairs of events in spacetime may be classified into 3 distinct types based on 'how far' apart they are:

  • time-like (more than enough time passes for there to be a cause-effect relationship between the two events; there exists a reference frame such that the two events occur at the same place; s2 > 0).
  • light-like (the space between the two events is exactly balanced by the time between the two events; s2 = 0).
  • space-like (not enough time passes for there to be a cause-effect relationship between the two events; there exists a reference frame such that the two events occur at the same time; s2 < 0).

Events with a positive space-time interval are in each other's future or past, and the value of the interval defines the proper time measured by an observer traveling between them. Events with a spacetime interval of zero are separated by the propagation of a light signal. In relativity, proper time is time measured by a single clock between events that occur at the same place as the clock. ... In special relativity, a light cone is the pattern describing the temporal evolution of a flash of light in Minkowski spacetime. ...


For special relativity, the space-time interval is considered invariant across inertial reference frames. For a less technical and generally accessible introduction to the topic, see Introduction to special relativity. ... In physics, invariants are usually quantities conserved (unchanged) by the symmetries of the physical system. ... In physics, an inertial frame of reference, or inertial frame for short (also descibed as absolute frame of reference), is a frame of reference in which the observers move without the influence of any accelerating or decelerating force. ...


Certain types of worldlines (called geodesics of the space-time) are the shortest paths between any two events, with distance being defined in terms of space-time intervals. The concept of geodesics becomes critical in general relativity, since geodesic motion may be thought of as "pure motion" (inertial motion) in space-time, that is, free from any external influences. In physics, the world line of an object is the unique path of that object as it travels through 4-dimensional spacetime. ... In mathematics, a geodesic is a generalization of the notion of a straight line to curved spaces. In presence of a metric, geodesics are defined to be (locally) the shortest path between points on the space. ... For a less technical and generally accessible introduction to the topic, see Introduction to general relativity. ... A fictitious force is an apparent force that acts on all masses in a non-inertial frame of reference, e. ...


Mathematics of space-times

For physical reasons, a space-time continuum is mathematically defined as a four-dimensional, smooth, connected pseudo-Riemannian manifold together with a smooth Lorentz metric of signature left(3,1right). The metric determines the geometry of spacetime, as well as determining the geodesics of particles and light beams. About each point (event) on this manifold, coordinate charts are used to represent observers in reference frames. Usually, Cartesian coordinates left(x, y, z, tright) are used. Moreover, for simplicity's sake, the speed of light 'c' is usually assumed to be unity. In differential geometry, a pseudo-Riemannian manifold is a smooth manifold equipped with a smooth, symmetric, tensor which is nondegenerate at each point on the manifold. ... In differential geometry, a pseudo-Riemannian manifold is a smooth manifold equipped with a smooth, symmetric, tensor which is nondegenerate at each point on the manifold. ... In mathematics, a geodesic is a generalization of the notion of a straight line to curved spaces. In presence of a metric, geodesics are defined to be (locally) the shortest path between points on the space. ... In topology, an atlas describes how a complicated space is glued together from simpler pieces. ...


A reference frame (observer) can be identified with one of these coordinate charts; any such observer can describe any event p. Another reference frame may be identified by a second coordinate chart about p. Two observers (one in each reference frame) may describe the same event p but obtain different descriptions. A frame of reference in physics is a set of axes which enable an observer to measure the aspect, position and motion of all points in a system relative to the reference frame. ...


Usually, many overlapping coordinate charts are needed to cover a manifold. Given two coordinate charts, one containing p (representing an observer) and another containing q (another observer), the intersection of the charts represents the region of spacetime in which both observers can measure physical quantities and hence compare results. The relation between the two sets of measurements is given by a non-singular coordinate transformation on this intersection. The idea of coordinate charts as 'local observers who can perform measurements in their vicinity' also makes good physical sense, as this is how one actually collects physical data - locally. In mathematics, a singular point of an algebraic variety V is a point P that is special (so, singular), in the geometric sense that V is not locally flat there. ...


For example, two observers, one of whom is on Earth, but the other one who is on a fast rocket to Jupiter, may observe a comet crashing into Jupiter (this is the event p). In general, they will disagree about the exact location and timing of this impact, i.e., they will have different 4-tuples left(x, y, z, tright) (as they are using different coordinate systems). Although their kinematic descriptions will differ, dynamical (physical) laws, such as momentum conservation and the first law of thermodynamics, will still hold. In fact, relativity theory requires more than this in the sense that it stipulates these (and all other physical) laws must take the same form in all coordinate systems. This introduces tensors into relativity, by which all physical quantities are represented. For more technical Wiki articles on tensors, see the section later in this article. ...


Geodesics are said to be timelike, null, or spacelike if the tangent vector to one point of the geodesic is of this nature. The paths of particles and light beams in spacetime are represented by timelike and null (light-like) geodesics (respectively).


Space-time topology

The assumptions contained in the definition of a spacetime are usually justified by the following considerations.


The connectedness assumption serves two main purposes. First, different observers making measurements (represented by coordinate charts) should be able to compare their observations on the non-empty intersection of the charts. If the connectedness assumption were dropped, this would not be possible. Second, for a manifold, the property of connectedness and path-connectedness are equivalent and one requires the existence of paths (in particular, geodesics) in the spacetime to represent the motion of particles and radiation. In mathematics, a geodesic is a generalization of the notion of a straight line to curved spaces. In presence of a metric, geodesics are defined to be (locally) the shortest path between points on the space. ...


Every spacetime is paracompact. This property, allied with the smoothness of the spacetime, gives rise to a smooth linear connection, an important structure in general relativity. Some important theorems on constructing spacetimes from compact and non-compact manifolds include the following: In mathematics, a paracompact space is a topological space in which every open cover admits an open locally finite refinement. ... An affine connection is a connection on the tangent bundle of a differentiable manifold. ...

  • A compact manifold can be turned into a spacetime if, and only if, its Euler characteristic is 0.
  • Any non-compact 4-manifold can be turned into a spacetime.

In mathematics, a subset of Euclidean space Rn is called compact if it is closed and bounded. ... It has been suggested that Vertex/Face/Edge relation in a convex polyhedron be merged into this article or section. ...

Space-time symmetries

Main article: Spacetime symmetries

Often in relativity, space-times that have some form of symmetry are studied. As well as helping to classify spacetimes, these symmetries usually serve as a simplifying assumption in specialised work. Some of the most popular ones include: The role of symmetry in physics is important, for example, in simplifying solutions to many problems. ...

A spherically symmetric spacetime is one whose isometry group contains a subgroup which is isomorphic to the (rotation) group and the orbits of this group are 2-dimensional spheres (2-spheres). ... In general relativity, a spacetime is said to be static if it admits a global, nowhere zero, timelike hypersurface orthogonal Killing vector field. ... In general relativity, a spacetime is said to be stationary if it admits a global, nowhere zero timelike Killing vector field. ...

Causal structure

Main article: Causal spacetime structure

This article does not cite any references or sources. ...

Spacetime in special relativity

Main article: Minkowski space

The geometry of spacetime in special relativity is described by the Minkowski metric on R4. This spacetime is called Minkowski space. The Minkowski metric is usually denoted by η and can be written as a four-by-four matrix: In physics and mathematics, Minkowski space (or Minkowski spacetime) is the mathematical setting in which Einsteins theory of special relativity is most conveniently formulated. ... In physics and mathematics, Minkowski space (or Minkowski spacetime) is the mathematical setting in which Einsteins theory of special relativity is most conveniently formulated. ...


eta_{ab} , = operatorname{diag}(1, -1, -1, -1)


where the Landau-Lifshitz spacelike convention is being used. A basic assumption of relativity is that coordinate transformations must leave spacetime intervals invariant. Intervals are invariant under Lorentz transformations. This invariance property leads to the use of four-vectors (and other tensors) in describing physics. In physics, a sign convention is a choice of the signs (plus or minus) of a set of quantities, in a case where the choice of sign is arbitrary. ... Lorentz covariance is a term in physics for the property of space time, that in two different frames of reference, located at the same event in spacetime but moving relative to each other, all non-gravitational laws must make the same predictions for identical experiments. ... A Lorentz transformation (LT) is a linear transformation that preserves the spacetime interval between any two events in Minkowski space, while leaving the origin fixed (=rotation of Minkowski space). ... In relativity, a four-vector is a vector in a four-dimensional real vector space, whose components transform like the space and time coordinates (ct, x, y, z) under spatial rotations and boosts (a change by a constant velocity to another inertial reference frame). ...


Strictly speaking, one can also consider events in Newtonian physics as a single spacetime. This is Galilean-Newtonian relativity, and the coordinate systems are related by Galilean transformations. However, since these preserve spatial and temporal distances independently, such a space-time can be decomposed into spatial coordinates plus temporal coordinates, which is not possible in the general case. In general, the principle of relativity is the requirement that the laws of physics be the same for all observers. ... The Galilean transformation is used to transform between the coordinates of two reference frames which differ only by constant relative motion within the constructs of Newtonian physics. ...


Spacetime in general relativity

In general relativity, it is assumed that spacetime is curved by the presence of matter (energy), this curvature being represented by the Riemann tensor. In special relativity, the Riemann tensor is identically zero, and so this concept of "non-curvedness" is sometimes expressed by the statement "Minkowski spacetime is flat." For a less technical and generally accessible introduction to the topic, see Introduction to general relativity. ... In differential geometry, the Riemann curvature tensor is the most standard way to express curvature of Riemannian manifolds, or more generally, any manifold with an affine connection, torsionless or with torsion. ...


Many space-time continua have physical interpretations which most physicists would consider bizarre or unsettling. For example, a compact spacetime has closed, time-like curves, which violate our usual ideas of causality (that is, future events could affect past ones). For this reason, mathematical physicists usually consider only restricted subsets of all the possible spacetimes. One way to do this is to study "realistic" solutions of the equations of general relativity. Another way is to add some additional "physically reasonable" but still fairly general geometric restrictions, and try to prove interesting things about the resulting spacetimes. The latter approach has led to some important results, most notably the Penrose-Hawking singularity theorems. In mathematics, a subset of Euclidean space Rn is called compact if it is closed and bounded. ... This article or section is in need of attention from an expert on the subject. ...


Quantized space-time

In general relativity, space-time is assumed to be smooth and continuous- and not just in the mathematical sense. In the theory of quantum mechanics, there is an inherent discreteness present in physics. In attempting to reconcile these two theories, it is sometimes postulated that spacetime should be quantized at the very smallest scales. Current theory is focused on the nature of space-time at the Planck scale. Causal sets, loop quantum gravity, string theory, and black hole thermodynamics all predict a quantized space-time with agreement on the order of magnitude. Loop quantum gravity even makes precise predictions about the geometry of spacetime at the Planck scale. In physics, Planck units are physical units of measurement originally proposed by Max Planck. ... The causal sets programme is an approach to quantum gravity. ... Loop quantum gravity (LQG), also known as loop gravity and quantum geometry, is a proposed quantum theory of spacetime which attempts to reconcile the seemingly incompatible theories of quantum mechanics and general relativity. ... Interaction in the subatomic world: world lines of pointlike particles in the Standard Model or a world sheet swept up by closed strings in string theory String theory is a model of fundamental physics whose building blocks are one-dimensional extended objects called strings, rather than the zero-dimensional point... This article or section is in need of attention from an expert on the subject. ... Generally, quantization is the state of being constrained to a set of discrete values, rather than varying continuously. ...


Other uses of the word 'spacetime'

Spacetime has taken on meanings different from the four-dimensional one given above. For example, when drawing a graph of the distance a car has travelled for a certain time, it is natural to draw a two-dimensional spacetime diagram. As drawing four-dimensional spacetime diagrams is impossible, physicists often resort to drawing three-dimensional spacetime diagrams. For example, the Earth orbiting the Sun is a helical shape traced out in the direction of the time axis.


In higher-dimensional theories of physics such as string theory, the assumption that our universe has more than four dimensions is frequently made. For example, Kaluza-Klein theory was an attempt to unify the two fundamental forces of gravitation and electromagnetism and used four space dimensions with one of time. Modern theories use as many as ten or more spacetime dimensions. These theories are highly speculative, as there has been no experimental evidence to support them. To explain why the extra dimensions are not observed, it is assumed that they are compactified, so that they loop around over a very short distance (usually around the Planck length). Interaction in the subatomic world: world lines of pointlike particles in the Standard Model or a world sheet swept up by closed strings in string theory String theory is a model of fundamental physics whose building blocks are one-dimensional extended objects called strings, rather than the zero-dimensional point... In physics, Kaluza-Klein theory (or KK theory, for short) is a model that seeks to unify the two fundamental forces of gravitation and electromagnetism. ... A fundamental interaction or fundamental force is a mechanism by which particles interact with each other, and which cannot be explained in terms of another interaction. ... “Gravity” redirects here. ... Electromagnetism is the physics of the electromagnetic field: a field which exerts a force on particles that possess the property of electric charge, and is in turn affected by the presence and motion of those particles. ... In physics, compactification plays an important part in string theory. ...


Privileged character of 3+1 spacetime

Dimensions are of two kinds: spatial and temporal. That spacetime, ignoring any undetectable compactified dimensions, consists of 3+1 dimensions (ie three spatial (bidirectional) and one temporal (unidirectional)), is often explained by appeal to the mathematical and physical effects of differing numbers of dimensions. Most often this takes the form of an anthropic argument. In physics and cosmology, the anthropic principle is an umbrella term for various dissimilar attempts to explain the structure of the universe by way of coincidentally balanced features that are necessary and relevant to the existence of observers (usually assumed to be carbon-based life or even specifically human beings). ...


Immanuel Kant argued that space having 3 dimensions followed from the inverse square law of universal gravitation. Kant's argument is historically important, but John D. Barrow has stated that "we would regard this as getting the punch-line back to front: it is the three-dimensionality of space that explains why we see inverse-square force laws in Nature, not vice-versa." (Barrow 2002) This is because the law of gravitation (or any other inverse-square law) follows from the concept of flux and the fact that space has 3 dimensions and 3-dimensional solid objects have surface area proportional to the square of their size in one chosen dimension (particularly a sphere has area of 4πr2 with r as the radius of the sphere). More generally, in a space with N dimensions, the strength of the gravitational attraction between two bodies separated by a distance of r would be inversely proportional to rN-1. “Kant” redirects here. ... It has been suggested that this article or section be merged into Gravity. ... John David Barrow FRS (born November 29, 1952, London) is an English cosmologist, theoretical physicist, and mathematician. ... This diagram shows how the law works. ... flux in science and mathematics. ...


Fixing the number of temporal dimensions at 1 and letting the number of spatial dimensions exceed 3, Paul Ehrenfest showed in 1920 that the orbit of a planet about its sun cannot remain stable, and that the same holds for a star's orbit around its galactic center.[4] Likewise, in 1963, F. R. Tangherlini showed that electrons would not form stable orbitals around nuclei; they would either fall into the nucleus or disperse. Ehrenfest also showed that if space has an even number of dimensions, then the different parts of a wave impulse will travel at different speeds. If the number of dimensions is odd and greater than 3, wave impulses become distorted. Only with three dimensions (or one dimension) are both problems avoided. Paul Ehrenfest Paul Ehrenfest (Vienna, January 18, 1880 – Amsterdam, September 25, 1933) was an Austrian physicist and mathematician, who obtained Dutch citizenship on March 24, 1922. ... Two bodies with a slight difference in mass orbiting around a common barycenter. ... The eight planets and three dwarf planets of the Solar System. ... In chemistry, an atomic orbital is the region in which an electron may be found around a single atom. ... The nucleus of an atom is the very small dense region, of positive charge, in its centre consisting of nucleons (protons and neutrons). ... A wave is a disturbance that propagates through space or spacetime, transferring energy and momentum and sometimes angular momentum. ...


Another anthropic argument, expanding upon the preceding one, is due to Tegmark.[5] If the number of time dimensions differed from 1, Tegmark argues, the behavior of physical systems could not be predicted reliably from knowledge of the relevant partial differential equations. In such a universe, intelligent life manipulating technology could not emerge. In addition, he argues that protons and electrons would be unstable in a universe with more than one time dimension, as they can decay into more massive particles. However, he also argues that this phenomenon would be suppressed if the temperature is sufficiently low. If space had more than 3 dimensions, atoms as we know them (and probably more complex structures as well) could not exist (following Ehrenfest's argument). If space had fewer than 3 dimensions, gravitation of any kind becomes problematic, and the universe is probably too simple to contain observers. For example, nerves cannot overlap; they must intersect. In physics and cosmology, the anthropic principle is an umbrella term for various dissimilar attempts to explain the structure of the universe by way of coincidentally balanced features that are necessary and relevant to the existence of observers (usually assumed to be carbon-based life or even specifically human beings). ... In mathematics, a partial differential equation (PDE) is a relation involving an unknown function of several independent variables and its partial derivatives with respect to those variables. ... In physics, the proton (Greek proton = first) is a subatomic particle with an electric charge of one positive fundamental unit (1. ... e- redirects here. ...


In general, it is not clear how physical laws should operate in the presence of more than one temporal dimension, or in the absence of time. If there was more than one time dimension, individual subatomic particles which decay after a fixed period would not have such predictability because timelike geodesics would not be necessarily maximal.[6] Three time and one space dimensions has the peculiar property that that the speed of light in a vacuum is a lower bound on the velocity of matter. The only remaining case, 3 spatial and 1 temporal dimensions, is the world we live in. Hence anthropic arguments require a universe with 3 spatial and 1 temporal dimensions. In mathematics, a geodesic is a generalization of the notion of a straight line to curved spaces. In presence of a metric, geodesics are defined to be (locally) the shortest path between points on the space. ... A line showing the speed of light on a scale model of Earth and the Moon, about 1. ...


Curiously, 3 and 4 dimensional spaces appear to be the mathematically richest. For example, there are geometric statements whose truth or falsity is known for any number of spatial dimensions except 3, 4, or both.


For a more detailed introduction to the privileged status of 3 spatial and 1 temporal dimensions, see Barrow [7]; for a deeper treatment, see Barrow and Tipler.[8] Barrow regularly cites Whitrow.[9]


References

  1. ^ Hermann Minkowski, "Raum und Zeit", 80. Versammlung Deutscher Naturforscher (Köln, 1908). Published in Physikalische Zeitschrift 10 104-111 (1909) and Jahresbericht der Deutschen Mathematiker-Vereinigung 18 75-88 (1909). For an English translation, see Lorentz et al. (1952).
  2. ^ Einstein, Albert, 1926, "Space-Time," Encyclopedia Britannica, 13th ed.
  3. ^ Matolcsi, Tamás (1994). Spacetime Without Reference Frames. Budapest: Akadémiai Kiadó. 
  4. ^ Ehrenfest, Paul, "How do the fundamental laws of physics make manifest that space has 3 dimensions?", Annalen der Physik 61: 440
  5. ^ Tegmark, Max (April 1997). "On the dimensionality of spacetime". Classical and Quantum Gravity 14 (4): L69-L75. DOI:10.1088/0264-9381/14/4/002. Retrieved on [[16 December 2006]]. 
  6. '^ Dorling, J. (1970) "The Dimensionality of Time" American Journal of Physics '38(4): 539-40.
  7. ^ Barrow, J. D. (2002). The Constants of Nature. Pantheon Books.  (chpt. 6, esp. Fig. 10.12)
  8. ^ Barrow, J. D.; Tipler, Frank J. (1986). The Anthropic Cosmological Principle. Oxford: Oxford University Press.  (4.8) Chpt. 6 is a good survey of modern cosmology, which builds on spacetime.
  9. ^ Whitrow, James Gerald (1959). The Structure and Evolution of the Universe. London: Hutchinson. 
  • Ehrenfest, Paul, 1920, "How do the fundamental laws of physics make manifest that space has 3 dimensions?" Annalen der Physik 61: 440.
  • Kant, Immanuel, 1929, "Thoughts on the true estimation of living forces" in J. Handyside, trans., Kant's Inaugural Dissertation and Early Writings on Space. Univ. of Chicago Press.
  • Lorentz, H. A., Einstein, Albert, Minkowksi, Hermann, and Weyl Hermann, 1952. The Principle of Relativity: A Collection of Original Memoirs. Dover.
  • Lucas, John Randolph, 1973. A Treatise on Time and Space. London: Methuen.
  • Penrose, Roger (2004). The Road to Reality. Oxford: Oxford University Press.  Chpts. 17,18.
  • Robb, A. A. (1936). Geometry of time and space. University Press. 
  • Schutz, J. W. (1997). Independent axioms for Minkowski Space-time. Addison-Wesley Longman. 
  • Tangherlini, F. R. (1963). "Atoms in Higher Dimensions". Nuovo Cimento 14 (27): 636. 

Hermann Minkowski. ... “Einstein” redirects here. ... Paul Ehrenfest Paul Ehrenfest (Vienna, January 18, 1880 – Amsterdam, September 25, 1933) was an Austrian physicist and mathematician, who obtained Dutch citizenship on March 24, 1922. ... Max Tegmark Max Tegmark born 1967 in Sweden to Karin Tegmark and Harold S Shapiro, is a cosmologist formerly at the University of Pennsylvania and now at the Massachusetts Institute of Technology as an Associate Professor. ... A digital object identifier (or DOI) is a standard for persistently identifying a piece of intellectual property on a digital network and associating it with related data, the metadata, in a structured extensible way. ... is the 350th day of the year (351st in leap years) in the Gregorian calendar. ... Year 2006 (MMVI) was a common year starting on Sunday of the Gregorian calendar. ... John David Barrow FRS (born November 29, 1952, London) is an English cosmologist, theoretical physicist, and mathematician. ... John David Barrow FRS (born November 29, 1952, London) is an English cosmologist, theoretical physicist, and mathematician. ... Frank J. Tipler (born in 1947 in Andalusia, Alabama) is a professor of mathematical physics at Tulane University in New Orleans, Louisiana. ... Gerald James Whitrow (died June 2nd, 2000). ... Paul Ehrenfest Paul Ehrenfest (Vienna, January 18, 1880 – Amsterdam, September 25, 1933) was an Austrian physicist and mathematician, who obtained Dutch citizenship on March 24, 1922. ... “Kant” redirects here. ... Hendrik Antoon Lorentz (July 18, 1853, Arnhem – February 4, 1928, Haarlem) was a Dutch physicist who shared the 1902 Nobel Prize in Physics with Pieter Zeeman for the discovery and elucidation of the Zeeman effect. ... “Einstein” redirects here. ... Hermann Minkowski. ... Hermann Klaus Hugo Weyl (November 9, 1885 – December 9, 1955) was a German mathematician. ... John Randolph Lucas (born 18 June 1929) is a British philosopher. ... Sir Roger Penrose, OM, FRS (born 8 August 1931) is an English mathematical physicist and Emeritus Rouse Ball Professor of Mathematics at the Mathematical Institute, University of Oxford and Emeritus Fellow of Wadham College. ... The Road to Reality is a book by the British mathematical physicist Roger Penrose, published in 2004. ... Edgar Allan Poe (January 19, 1809 – October 7, 1849) was an American poet, short story writer, playwright, editor, literary critic, essayist and one of the leaders of the American Romantic Movement. ... Eureka is a prose poem by Edgar Allan Poe from (1848) in which he describes his illumination about the universe. ... John Archibald Wheeler (born 1911) is an American theoretical physicist. ... H. G. Wells at the door of his house at Sandgate Herbert George Wells (September 21, 1866 - August 13, 1946) was an English writer best known for his science fiction novels such as The War of the Worlds and The Time Machine. ... The Time Machine is a novel by H. G. Wells, first published in 1895, later made into two films of the same title. ...

See also

Wikibooks
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Image File history File links Wikibooks-logo-en. ... Wikibooks logo Wikibooks, previously called Wikimedia Free Textbook Project and Wikimedia-Textbooks, is a wiki for the creation of books. ... Dimensional analysis is a conceptual tool often applied in physics, chemistry, and engineering to understand physical situations involving a mix of different kinds of physical quantities. ... In relativity, a four-vector is a vector in a four-dimensional real vector space, whose components transform like the space and time coordinates (ct, x, y, z) under spatial rotations and boosts (a change by a constant velocity to another inertial reference frame). ... This article does not cite any references or sources. ... This article or section does not cite its references or sources. ... This article or section does not cite its references or sources. ... Lorentz covariance is a term in physics for the property of space time, that in two different frames of reference, located at the same event in spacetime but moving relative to each other, all non-gravitational laws must make the same predictions for identical experiments. ... On a sphere, the sum of the angles of a triangle is not equal to 180° (see spherical trigonometry). ... For a less technical introduction to this topic, please see Introduction to mathematics of general relativity. ... In mathematics, a metric space is a set where a notion of distance between elements of the set is defined. ... Simultaneity is the property of two events happening at the same time in at least ONE Reference frame. ... This article is on the minimal body of mathematics necessary to understand general relativity. ... According to Albert Einsteins theory of general relativity, space and time get pulled out of shape near a rotating body in a phenomenon referred to as frame-dragging. ...

External links

  • Spacetime - Summary and collection of links to academic sites.

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