# Dictionary Definition

space-time n : the 4-dimensional coordinate
system (3 dimensions of space and 1 of time) in which physical
events are located [syn: space-time
continuum]

# User Contributed Dictionary

## English

### Noun

spacetime uncountable- The four
dimensional continuum of the three
spatial dimensions plus time.
- An event is a point in spacetime, specified by the coordinates x,y,z and t.

#### Translations

four dimensional continuum

- Czech: časoprostor
- Finnish: aika-avaruus
- Greek: χωρόχρονος (choróchronos)
- Italian: spaziotempo
- Japanese: 時空 (じくう, jikū)
- Polish: czasoprzestrzeń
- Portuguese: espaço-tempo
- Russian: пространство-время
- Swedish: rumtid

# Extensive Definition

In physics, spacetime is any
mathematical
model that combines space and time
into a single construct called the spacetime 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
theories, 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 Euclidean space instead of spacetime is
appropriate, as time is treated as universal and constant, being
independent of the state of motion of an observer. In relativistic
contexts, however, time cannot be separated from the three
dimensions of space because the rate at which time passes depends
on an object's velocity
relative to the speed of
light, and also the strength of intense gravitational fields
which can slow the passage of time, and as such is dependent on the
state of motion of the observer and is therefore not
universal.

## Concept with dimensions

The concept of spacetime combines space and time within a single coordinate system, typically with 4 dimensions: length, width, height, and time. Dimensions are components of a coordinate grid typically used to locate a point in space, or on the globe, such as by latitude, longitude and planet (Earth). However, with spacetime, the coordinate grid is used to locate "events" (rather than just points in space), so time is added as another dimension to the grid.Formerly, from experiments at slow speeds, time
was believed to be a constant, which progressed at a fixed rate;
however, later high-speed experiments revealed that time slowed
down at higher speeds (with such slowing called "time
dilation"). Many experiments have confirmed the slowing from
time dilation, such as atomic
clocks onboard a Space
Shuttle running slower than synchronized Earth-bound clocks.
Since time varies, it is treated as a variable within the spacetime
coordinate grid, and time is no longer assumed to be a constant,
independent of the location in space.

Note that treating spacetime events with the 4
dimensions (including time) is the conventional view; however,
other invented coordinate grids treat time as 3 additional
dimensions, with length-time, width-time, and height-time, to
accompany the 3 dimensions of space. When dimensions are understood
as mere components of the grid system, rather than physical
attributes of space, it is easier to understand the alternate
dimensional views, such as: latitude, longitude, plus Greenwich
Mean Time (3 dimensions), or city, state, postal code, country,
and UTC time (5
dimensions). The various dimensions are chosen, depending on the
coordinate grid used.

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.

## Historical origin

The origins of this 20th century scientific
concept 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 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.”

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 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".

## 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.

A spacetime 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
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.

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.

### Time-like interval

- \begin \\

For two events separated by a time-like interval,
enough time passes between them for there to be a cause-effect
relationship between the two events. For a particle travelling less
than the speed of light, any two events which occur to or by the
particle must be separated by a time-like interval. Event pairs
with time-like separation define a positive squared spacetime
interval (s^2 > 0) and may be said to occur in each other's
future or past.

The measure of a time-like spacetime interval is
described by the proper
time:

\Delta\tau =
\sqrt (proper time). The
proper time interval would be measured by an observer with a clock
traveling between the two events in an inertial reference frame, when
the observer's path intersects each event as that event occurs.
(The proper time defines a real number,
since the interior of the square root is positive.)

### Light-like interval

- \begin

In a light-like interval, the spatial distance
between two events is exactly balanced by the time between the two
events. The events define a squared spacetime interval of zero (s^2
= 0).

Events which occur to or by a photon along its path (i.e.,
while travelling at c, the speed of light) all have light-like
separation. Given one event, all those events which follow at
light-like intervals define the propagation of a light cone,
and all the events which preceded from a light-like interval
defined a second light cone.

### Space-like interval

- \begin \\

When a space-like interval separates two events,
not enough time passes between their occurrences for there to exist
a causal relationship
crossing the spatial distance between the two events at the speed
of light or slower. Generally, the events are considered not to
occur in each other's future or past. There exists a reference
frame such that the two events are observed to occur at the
same time.

For these space-like event pairs with a negative
squared spacetime interval (s^2 ), the measurement of space-like
separation is the proper
distance:

\Delta\sigma =
\sqrt (proper distance).

Like the proper time of time-like intervals, the
proper distance (\Delta\sigma) of space-like spacetime intervals is
a real number value.

### Space-time intervals

As can be seen, neither spacelike nor timelike intervals are invariant, but it is desirable to have invariants that can be used where events are not on light-like intervals. Spacetime entails a new concept of distance. Whereas distances in Euclidean spaces are entirely spatial and always positive, in special relativity the concept of distance is quantified in terms of the space-time interval between two events, which occur in two locations at two times:s^2 = c^2\Delta t^2 - \Delta
r^2\, (spacetime interval),

where:

- c is the speed of light,
- \Delta t and \Delta r denote differences of the time and space coordinates, respectively, between the events.

(Note that the choice of signs for s^2 above
follows the Landau-Lifshitz
spacelike convention. Other treatments, including some within
Wikipedia, reverse the sign of s^2.)

Space-time intervals may be classified into three
distinct types based on whether the temporal separation (c^2 \Delta
t^2) or the spatial separation (\Delta r^2) of the two events is
greater:

For special
relativity, the spacetime interval is considered invariant
across inertial
reference frames.

Certain types of worldlines
(called geodesics of
the spacetime) are the shortest paths between any two events, with
distance being defined in terms of spacetime intervals. The concept
of geodesics becomes critical in general
relativity, since geodesic motion may be thought of as "pure
motion" (inertial
motion) in spacetime, 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
Lorentzian
manifold (M,g). This means the smooth Lorentz
metric g has signature \left(3,1\right). 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, t\right) 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 \left(x, y, z,
t\right) (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).

### 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.

### Space-time 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:

### Causal structure

The causal structure of a spacetime describes
causal relationships between pairs of points in the spacetime based
on the existence of certain types of curves joining the
points.

## Spacetime in special relativity

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 \eta and can be written as a
four-by-four matrix:

\eta_ \, = \operatorname(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.

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.

## 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."

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.

## 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 makes precise predictions about the geometry of spacetime
at the Planck scale.

## Spiralization and Compression Theory

A recent development in physics is the theory of the
spiralization and compression of space time, also known as the
"Jack-in-the-box" theory. This theory was first put forth in
2006 by a
group of scientists working in Portland,
Oregon. The theory speculates that over time, all the
dimensions of space spiral inward until reaching a state of
absolute compression. When complete compression is reached, space
springs outward and expands rapidly, as with the big bang, before
the cycle is begun again. The highlight of this theory is the
independence of time from the spiralization and compression of
space. The impact of this theory on relativity and attempts at a
unified
field theory are yet unknown. However, it has been predicted,
using the spiralization and compression theory, that the Large
Hadron Collider will produce micro-universes.

## Privileged character of 3+1 spacetime

A number of scientists and philosophers have written about spacetime, and concepts have evolved as more theories have been deduced and tested by mathematical analysis or experimentation.Other writers have been limited by the scientific
evidence available at the time. For example, in the latter 20th
century, experiments with "atom-smasher"
particle
accelerators had revealed that individual protons accelerated
to high speeds were gaining the mass equivalent to a car at rest,
requiring ever-increasing amounts of energy to accelerate the
protons even faster. While the passage of Time slowed at high
speeds, the mass of the particles increased. Writers from previous
eras were not aware of that evidence, so fanciful views are
sometimes expressed in the writings that are described below.

Let dimensions be of two kinds: spatial and
temporal. That spacetime, ignoring any undetectable compactified
dimensions, consists of three spatial (bidirectional) and one
temporal (unidirectional) dimensions can be explained by appealing
to the physical consequences of differing numbers of dimensions.
The argument is often of an anthropic
nature.

Immanuel
Kant argued that 3-dimensional Space was a consequence of the
inverse square
law of universal gravitation. While Kant's argument is
historically important, John D.
Barrow says of it 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, from Space having 3
dimensions, and from 3-dimensional solid objects having surface
area proportional to the square of their size in one chosen
dimension. In particular, a sphere of radius r has area of 4πr2. More
generally, in a Space of N dimensions, the strength of the
gravitational attraction between two bodies separated by a distance
of r would be inversely proportional to rN-1.

Fixing the number of temporal dimensions at 1 and
letting the number of spatial dimensions N 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. Likewise, F. R. Tangherlini showed in 1963
that when N>3, electrons would not form stable orbitals
around nuclei; they would either fall into the nucleus or
disperse. Ehrenfest also showed that if N is even, then the
different parts of a wave
impulse will travel at different speeds. If N is odd and greater
than 3, then wave impulses become distorted. Only when N=3 or 1 are
both problems avoided.

Max Tegmark
expands on the preceding argument in the following anthropic
manner. If the number of Time dimensions differed from 1, the
behavior of physical systems could not be predicted reliably from
knowledge of the relevant
partial differential equations. In such a universe, intelligent
life capable of manipulating technology could not emerge. In
addition, Tegmark maintains that protons and electrons would be unstable in
a universe with more than one Time dimension, as they can decay
into more massive particles (this is not a problem if the
temperature is sufficiently low). If N>3, Ehrenfest's above
argument holds; atoms as we know them (and probably more complex
structures as well) could not exist. If N<3, gravitation of any
kind becomes problematic, and the universe is probably too simple
to contain observers. For example, nerves must intersect and cannot
overlap.

In general, it is not clear how physical laws
could operate if the number of Time dimensions T differed from 1.
If T>1, individual subatomic particles, which decay after a
fixed period, would not have much predictability because timelike
geodesics would not be
necessarily maximal. N=1 and T=3 has the peculiar property that
that the speed of
light in a vacuum is a lower bound on the velocity of matter.
Hence anthropic arguments rule out all cases except 3 spatial and 1
temporal dimensions--the description of the world in which we
live.

Curiously, 3 and 4 dimensional spaces appear
richest geometrically and topologically. 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; for a deeper treatment, see Barrow and Tipler. Barrow
regularly cites Whitrow.

In string
theory, physicists are not constrained by notions limited to
3+1 dimensions, so coordinate grids of 10, or perhaps 26
dimensions, are used to describe the types and locations of the
vibrating strings. String theory follows the notion that the
"universe is wiggly" and considers matter and energy to be composed
of tiny vibrating strings of various types, specified by some of
the dimensions.

## See also

## References

- 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, Minkowski, 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.
- The Road to Reality Chpts. 17,18.
- Geometry of Time and Space

- Independent axioms for Minkowski Space-time

- Spacetime Physics

- The Time Machine (pp. 5; 6)

spacetime in Catalan: Espai-temps

spacetime in Czech: Časoprostor

spacetime in Danish: Rumtid

spacetime in German: Raumzeit

spacetime in Modern Greek (1453-):
Χωρόχρονος

spacetime in Spanish: Espacio-tiempo

spacetime in Persian: فضازمان

spacetime in French: Espace-temps

spacetime in Galician: Espazo-tempo

spacetime in Korean: 시공간

spacetime in Croatian: Prostorvrijeme

spacetime in Italian: Spaziotempo

spacetime in Hebrew: מרחב-זמן

spacetime in Latin: Spatium quattuor
dimensionum

spacetime in Latvian: Laiktelpa

spacetime in Lithuanian: Erdvėlaikis

spacetime in Hungarian: Téridő

spacetime in Dutch: Ruimte-tijd

spacetime in Japanese: 時空

spacetime in Norwegian: Romtid

spacetime in Polish: Czasoprzestrzeń

spacetime in Portuguese: Espaço-tempo

spacetime in Romanian: Spaţiu-timp

spacetime in Russian: Пространство-время

spacetime in Simple English: Spacetime

spacetime in Slovak: Priestoročas

spacetime in Slovenian: Prostor-čas

spacetime in Serbian: Простор-време

spacetime in Finnish: Aika-avaruus

spacetime in Swedish: Rumtid

spacetime in Tamil: வெளிநேரம்

spacetime in Vietnamese: Không-thời gian

spacetime in Turkish: Uzayzaman

spacetime in Ukrainian: Простір-час

spacetime in Urdu: زمان و مکاں

spacetime in Chinese: 时空