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Key Equations

Time dilation Δt=Δτ1v2c2=γτΔt=Δτ1v2c2=γτ
Lorentz factor γ=11v2c2γ=11v2c2
Length contraction L=L01v2c2=L0γL=L01v2c2=L0γ
Galilean transformation x=x+vt,y=y,z=z,t=tx=x+vt,y=y,z=z,t=t
Lorentz transformation t=t+vx/c21v2/c2t=t+vx/c21v2/c2
Inverse Lorentz transformation t=tvx/c21v2/c2t=tvx/c21v2/c2
Space-time invariants (Δs)2=(Δx)2+(Δy)2+(Δz)2c2(Δt)2(Δs)2=(Δx)2+(Δy)2+(Δz)2c2(Δt)2
Relativistic velocity addition ux=(ux+v1+vux/c2),uy=(uy/γ1+vux/c2),uz=(uz/γ1+vux/c2)ux=(ux+v1+vux/c2),uy=(uy/γ1+vux/c2),uz=(uz/γ1+vux/c2)
Relativistic Doppler effect for wavelength λobs=λs1+vc1vcλobs=λs1+vc1vc
Relativistic Doppler effect for frequency fobs=fs1vc1+vcfobs=fs1vc1+vc
Relativistic momentum p=γmu=mu1u2c2p=γmu=mu1u2c2
Relativistic total energy E=γmc2,whereγ=11u2c2E=γmc2,whereγ=11u2c2
Relativistic kinetic energy Krel=(γ1)mc2,whereγ=11u2c2Krel=(γ1)mc2,whereγ=11u2c2
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