What actually is space-time?

Question

I have heard of it nit have no idea what purpose and point it has in space in general.

Answer 1

The four-dimensional continuum of one temporal and three spatial coordinates in which any event or physical object is located.

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.

Answer 2

In physics, spacetime is a mathematical model that combines space and time into a single construct called the space-time continuum. Spacetime is usually interpreted as a four-dimensional object with space being three-dimensional and time playing the role of the 4th dimension. According to Euclidean space perception, our 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 good deal of physical theory, as well as described in a more uniform way the workings of the universe at both the supergalactic and subatomic levels.

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.

The term spacetime has taken on a generalised 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 from 10 to 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.

Spacetimes are the arenas in which all physical events take 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.

A space-time is independent of any observer. 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 world line 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.

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.

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."

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.

Answer 3

Short answer: without time, when you drive to the store, your car would be both at home AND at the store. Time allows movement of physical 3D objects.

Answer 4

Space and time coordinate system: a four-dimensional system consisting of three spatial coordinates and one for time, in which it is possible to locate events. In physics, spacetime is a mathematical model that combines space and time into a single construct called the space-time continuum. Spacetime is usually interpreted as a four-dimensional object with space being three-dimensional and time playing the role of the 4th dimension. According to Euclidean space perception, our 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 good deal of physical theory, as well as described in a more uniform way the workings of the universe at both the supergalactic and subatomic levels.

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.

The term spacetime has taken on a generalised 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 from 10 to 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. Historical origin
While spacetime can be viewed as consequence of Albert Einstein's 1905 theory of special relativity, it was first explicitly proposed by one of his teachers, the mathematician Hermann Minkowski, in an admiring 1908 essay building on and extending Einstein's work. His Minkowski space is the earliest treatment of space and time as two aspects of a unified whole, the essence of special relativity. (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".

H.G. Wells's 1895 novel The Time Machine refers to time as the "fourth dimension".
Basic concepts
Spacetimes are the arenas in which all physical events take 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.

A space-time is independent of any observer. 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 world line 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.

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.

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):



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.

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; 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; s2 > 0).
Events with a negative 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.

For special relativity, the space-time interval is considered invariant across inertial reference frames.

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.
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 . 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 are used. Moreover, for simplicity's sake, the speed of light 'c' is usually assumed to be unity.

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.

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.

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 (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.

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.

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:

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.
Often in general relativity, space-time continua that have some form of symmetry are studied. Some of the most popular ones include:

Axially symmetric spacetimes
Spherically symmetric spacetimes
Static spacetimes
Stationary spacetimes

Hope my answer kills all your curiousness!