Minkowski spacetime provides a lucid pictorial representation for the special theory of relativity. An

*event* occurring at a time

at the location

in three-dimensional space is described by a point

in a four-dimensional manifold known as Minkowski spacetime.The factor

m/s, the speed of light, gives

the dimensions of length, to match those of

. The fundamental principle of special relativity can be expressed as the invariance of the

*interval* as measured by observers in

*all* inertial frames. This differs dramatically from Galilean relativity, the foundational postulate of Newtonian mechanics, in that both time and space intervals become

*relative*, or dependent on the velocity of the observer.

For simplicity, this Demonstration considers just a single space dimension

that, along with the time variable

, gives a two-dimensional projection of Minkowski space. A stationary observer measures variables denoted

and

, while an observer in another inertial frame moving at a constant speed

measures variables denoted

' and

'. For ease of visualization, the primed variables are shown in red. These alternative variables are related by a

*Lorentz transformation*,

'

and

'

. Here

is the

*rapidity*, defined by

. The velocity can also be expressed in dimensionless form as

. In accordance with this hyperbolic transformation, the primed (red) coordinate axes are skewed at angles

relative to the stationary axes. The origin represents an event in which

momentarily for

*both* observers. You can move the locator to determine another event, for which the two observers no longer agree on values of

and

. The two sets of values of

and

are represented by the black and red projections on their respective axes. Their numerical values are given at the bottom of the graphic. The constancy of the interval is shown by the relation

. In the cases

,

, and

, the interval is called

*timelike*,

*spacelike,* or

*lightlike* (or

*null*), respectively. Timelike intervals lie within the future or past lightcones, projected as yellow triangles in the graphic. The red lines meeting at the event point are parallel to their respective red axes. Note that time is not ordered in a spacelike event: past and future are not invariant; nor is space ordered in a timelike event: left and right are not invariant.