Space-time is relativistic 3D space + 1D time. It obscures the 3D nature of time. The opposite is time-space with 3D time + 1D space, which obscures the 3D nature of space. Both of these have their advantages and disadvantages.

To avoid the disadvantage of obscuring 3D space or 3D time use 3D space + 3D time with an invariant interval and without measures such as speed or pace that require combining dimensions.

The invariant interval with coordinates in 3D space (*r*) and 3D time (*t*) between two events 1 and 2 (second subscript) is:

*c²* (*t _{11 }– t_{12}*)² +

*c²*(

*t*)² +

_{21 }– t_{22 }*c²*(

*t*)² – (

_{31 }– t_{32 }*r*)² – (

_{11 }– r_{12}*r*)² – (

_{21 }– r_{22 }*r*)²,

_{31 }– r_{32 }which can be plus or minus depending on the sign convention. Here *c*² is a conversion constant that does not favor spatial over temporal coordinates.

The invariance of the interval under linear coordinate transformations between inertial frames follows from the invariance of

*c² t _{11}² + c² t_{21}² + c² t_{31}² – r_{11}² – r_{21}² – t_{31}²*

for any point event. This quadratic form can be used to define a bilinear form

*u · v* = *c²* *t _{11}² t_{12}*² +

*c²*

*t*² +

_{21}² t_{22}*c²*

*t*² –

_{31}² t_{32}*r*² –

_{11}² r_{12}*r*² –

_{21}² r_{22}*r*²,

_{31}² r_{32}which is often written in matrix form. The signature is then (+ + + – – –).