### spacetime

(four dimensions: time and the three space dimensions)

**Spacetime** is three-dimensional space with time as a fourth
dimension. For an event, such as snapping your fingers in
your living room, its position in space might be described
by distances from the floor and two walls, and its time by
the time on the clock, i.e., four numbers.

The concept is discussed in relativity because
to some extent, what seems like space to one person could
be time to another, which is what happens when they are
moving in relation to each other. (The effect is too
slight to be noticed, but with extreme speeds, becomes
significant.) There are still four dimensions, but,
in effect, the time dimensions of the two people are
at an angle with each other.

**Minkowski space** is a particular mathematical model
of spacetime which fits very well with the
Lorentz transformation used in the
equations of **special relativity**.
It treats time as a dimension made up of
imaginary numbers, i.e., real numbers multiplied by
*i*, the square root of minus 1.
The advantage is that measuring distances
using the Pythagorean theorem naturally
extend to time: whereas a distance across
a plane is √(x²+y²) for
coordinates across the plane, spacetime "distances"
(**spacetime intervals**, such as between two events at different times)
are √(d²-t²)
for d as the distance between the events and
t as time expressed as (c × our concept of time).
This can be expressed as the normal Pythagorean-theorem form
√(d²+t²) if t includes *i*
(*i* × c × our concept of time).

Both space and spacetime conceivably can be curved, and
are now assumed to be so in such a slight manner that detecting it
is a challenge.

(*physics,relativity*)
**Further reading:**

http://en.wikipedia.org/wiki/Spacetime

http://en.wikipedia.org/wiki/Minkowski_space

**Referenced by pages:**

curvature

geodesic

gravitational wave (GW)

holographic duality

mathematical field

relativistic invariance

spacetime diagram

worldline

Index