The "length" of the vector is a Lorentz scalar and is given by x μ μ x μ μ = η η μ μ ν ν x μ μ x ν ν = ( c t ) 2 − − x ⋅ ⋅ x = d e f ( c τ τ ) 2 where τ τ is the proper time as measured by a clock in the rest frame of the particle and the Minkowski metric is given by η η μ μ ν ν = η η μ μ ν ν = ( 1 0 0 0 0 − − 1 0 0 0 0 − − 1 0 0 0 0 − − 1 ) . This is a time-like metric.