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x α ′ = Λ β α x β + a α {\displaystyle {{x}^{\alpha '}}=\Lambda _{\beta }^{\alpha }{{x}^{\beta }}+{{a}^{\alpha }}}
Bewegungsrichtung sei x 1 {\displaystyle x_{1}}
x 1 ′ = γ ( x 1 + v 1 t ) , x 2 ′ = x 2 , x 3 ′ = x 3 , c t ′ = γ ( c t + β x 1 ) {\displaystyle {{x}^{1'}}=\gamma \left({{x}^{1}}+{{v}^{1}}t\right),\,{{x}^{2'}}={{x}^{2}},\,{{x}^{3'}}={{x}^{3}},\,ct'=\gamma \left(ct+\beta {{x}^{1}}\right)}
