From perspective of observer at rest
t t o t a l
x t o t a l
y t o t a l
z t o t a l
The moving frame to forward
t ′
x ′
y ′ γ
z ′ γ
The moving frame to backward
t ′ ( γ − 1 )
x ′ ( γ − 1 )
y ′ ( γ − 1 )
z ′ ( γ − 1 )
The final result
t ′ ( γ )
x ′ γ
y ′
z ′