The
Special Theory of Relativity encourages one to think of space and time as being different labels for
coordinates in a single entity called
spacetime. As such, instead of using
x (three dimensional) and t (one dimensional) in equations, treat the two together as a single object x
μ=(t,
x)
T (four dimensional): this is called a
four-
vector.
Four vectors extend to covering other things besides space and time: they can represent any quantity which transforms in the correct way between different frames of referrence (ie. by
Lorentz Transformations: x'
μ=Λ
μνx
ν). Such possible quantities arise from pairs of
(three) vectorial and
scalar quantities, eg:
Four-vectors and their associated higher order
tensors are conventionally written down using the
abstract index notation.