Spacetime

Spacetime is an extension of the Cartesian spatial reference frame to include time as a coordinate. It is a four-dimensional combination of a single time dimension and three space dimensions. A set of three numbers ${x, y, z}$ characterizes points in space, and one number, $t$ , selects a point in time. Their combination is the set of the general spacetime coordinates: ${t, x, y, z}$ that characterizes events.

The idea is that every possible physical event in the universe has a ‘space-time location’, and this coordinate system provides a numerical description of the system of these possible locations. Newtonian mechanics, special relativity, general relativity, and quantum mechanics all require the set of all events to form a four-dimensional continuum.

Usually in classical physics, the coordinate values measure distances along the coordinate axis, with the meter (or some part of it) as the measurement unit. If events are to be described, then a fourth axis for time is needed, but its units would be temporal and not spatial units. However, the S.I. meter is defined as the fraction 1/299.792.458 of the light-second (i.e., the distance traversed by a photon in vacuo in one second). Thus, without losing consistency we can replace the time coordinate $t$ by a new ‘time’ coordinate $x^{0} : = c t$ having a spatial dimension as have the three spatial coordinates, in relativity often denoted as $x^{1} : = x, x^{2} : = y, x^{3} : = z$ .

Points of spacetime are specified uniquely by the set of four spacetime coordinates ${x^{μ}; μ = 0, 1, 2, 3}$ .
In relativity, the measurement units of ‘time’ and ‘distance’ are commonly chosen to be the light second (or any convenient fraction), with the speed of light a dimensionless constant equal to one $(c = 1)$ .