relativity_4 - PHY2061 R D Field PHY2060 Review Space-Time...

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PHY2061 R. D. Field Department of Physics relativity_4.doc University of Florida Space-Time Intervals Consider two events A=(t A ,x A ,y A ,z A ) and B=(t B ,x B ,y B ,z B ) and define Δ t=t B -t A , Δ x=x B -x A , Δ y=y B -y A , Δ z=z B -z A . These space-time intervals also transform according to the Lorentz transformations. A B Frame O x ct c Δ t=c(t B -t A ) Δ x=x B -x A Light Cone 45 o A B Frame O' x' ct' c Δ t'=c(t' B -t' A ) Δ x'=x' B -x' A 45 o z z y y t c x x x t c t c Δ = Δ Δ = Δ Δ + Δ = Δ Δ + Δ = Δ ) ( ) ( β γ β γ z z y y t c x x x t c t c Δ = Δ Δ = Δ Δ Δ = Δ Δ Δ = Δ ) ( ) ( β γ β γ The following are Lorentz 4-vectors: Δ Δ Δ Δ = Δ z y x t c r ~ Δ Δ Δ Δ = Δ z y x t c r ~ and = dz dy dx cdt r d ~ = z d y d x d t cd r d ~ Space-time Separation ( Δ S) 2 : 2 2 2 ) ~ ( ) ~ ( ) ( r r S Δ = Δ = Δ 2 2 2 2 ) ( ) ( ) ( ) ( x t c x t c Δ
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