>>414
改訂
相対性理論の間隔dsから
(cdτ)^2=(cdt)^2-(dx)^2
=(cdt)^2(1-(dx)^2/(cdt)^2)
τ^2=t^2(1-(v/c)^2)

(cdｔ)^2=(cdτ)^2+(dx)^2
=(cdτ)^2(1+(dx)^2/(cdτ)^2)
t^2=τ^2(1+(dx/cdτ)^2)

(cdt)^2=(cdτ)^2/(1-(dx)^2/(cdt)^2)
t^2=τ^2/(1-(v/c)^2)

t'=tγ
t=t'γ'
t=t'/γ

γ=√(1-(v/c)^2)
γ'=1/γ=1/√(1-(v/c)^2)=√(1+(dx)^2/(cdτ)^2)
γ'^2=1/(1-(v/c)^2)=(1+(dx)^2/(cdτ)^2)
γ'^2-1=(dx)^2/(cdτ)^2=1/(1-(v/c)^2)-1
v'=c√(1/(1-(v/c)^2)-1)=c√(1/γ^2-1)=c√(γ'^2-1)
γ'=√(1+(v'/c)^2)=√(1+(c√(γ'^2-1)/c)^2)=γ'
=√(1+(c√(1/γ^2-1)/c)^2)=1/γ

t'=tγ
t=t'/γ=t
t=t'γ'=tγ/γ=t

だと思うんだけど