space-time

space-time, central concept in the theory of relativity that replaces the earlier concepts of space and time as separate absolute entities. In relativity one cannot uniquely distinguish space and time as elements in descriptions of events. Space and time are joined together in an intimate combination in which time becomes the "fourth dimension." The mathematical formulation of the theory by H. Lorentz (see Lorentz contraction) preceded the interpretation by A. Einstein that space and time are not absolute. The abstract description of space-time was made by H. Minkowski. In space-time, events in the universe are described in terms of a four-dimensional continuum in which each observer locates an event by three spacelike coordinates (position) and one timelike coordinate. The choice of the timelike coordinate in space-time is not unique; hence, time is not absolute but is relative to the observer. A striking consequence is that simultaneity is no longer an intrinsic relation between two events; it exists only as a relation between two events and a particular observer. In general, events at different locations that are simultaneous for one observer will not be simultaneous for another observer. Other relativistic effects, such as the Lorentz contraction and time dilation, are due to the structure of space-time.

Bibliography

See E. F. Taylor and J. A. Wheeler, Spacetime Physics (1966); N. D. Mermin, Space and Time in Special Relativity (1968).

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space-time

Single entity that relates space and time in a four-dimensional structure, postulated by Albert Einstein in his theories of relativity. In the Newtonian universe it was supposed that there was no connection between space and time. Space was thought to be a flat, three-dimensional arrangement of all possible point locations, which could be expressed by Cartesian coordinates; time was viewed as an independent one-dimensional concept. Einstein showed that a complete description of relative motion requires equations that include time as well as the three spatial dimensions. He also showed that space-time is curved, which allowed him to account for gravitation in his general theory of relativity.

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space-time, space-time continuum

Physics the four-dimensional continuum having three spatial coordinates and one time coordinate that together completely specify the location of a particle or an event

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space-time [′spās ′tīm]

(relativity)

A four-dimensional space used to represent the universe in the theory of relativity, with three dimensions corresponding to ordinary space and the fourth to time. Also known as space-time continuum.

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Space-time

A term used to denote the geometry of the physical universe as suggested by the theory of relativity. It is also called space-time continuum. Whereas in Newtonian physics space and time had been considered quite separate entities, A. Einstein and H. Minkowski showed that they are actually intimately intertwined.

Einstein showed that in general two observers, each using the same techniques of observation but being in motion relative to each other, will disagree concerning the simultaneity of distant events. But if they do disagree, they are also unable to compare unequivocally the rates of clocks moving in different ways, or the lengths of scales and measuring rods. Instead, clock rates and scale lengths of different observers and different frames of reference must be established so as to assure the principal observed fact. Each observer, using his or her own clocks and scales, must measure the same speed of propagation of light. This requirement leads to a set of relationships known as the Lorentz transformations.

In accordance with the Lorentz transformations, both the time interval and the spatial distance between two events are relative quantities, depending on the state of motion of the observer who carries out the measurements. There is, however, a new absolute quantity that takes the place of the two former quantities. It is known as the invariant, or proper, space-time interval τ and is defined by Eq. (1), where T is the ordi

(1) 

nary time interval, R the distance between the two events, and c the speed of light in empty space. Whereas T and R are different for different observers, τ has the same value. In the event that Eq. (1) would render τ imaginary, its place may be taken by σ, defined by Eq. (2). If both τ and σ are zero,

(2) 

then a light signal leaving the location of one event while it is taking place will reach the location of the other event precisely at the instant the signal from the latter is coming forth.

The existence of a single invariant interval led the mathematician Minkowski to conceive of the totality of space and time as a single four-dimensional continuum, which is often referred to as the Minkowski universe. In this universe, the history of a single space point in the course of time must be considered as a curve (or line), whereas an event, limited both in space and time, represents a point. So that these geometric concepts in the Minkowski universe may be distinguished from their analogs in ordinary three-dimensional space, they are referred to as world curves (world lines) and world points, respectively. See Gravitation, Relativity