Chapter1_11 - c ′ ∆ − ′ ∆ = ∆ − ∆ The...

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PHY3063 R. D. Field Department of Physics Chapter1_11.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 t=t B -t A , x=x B -x A , y=y B -y A , z=z B -z A . These space-time intervals also transform according to the Lorentz transformations. A B Frame O x ct c t=c(t B -t A ) x=x B -x A Light Cone 45 o A B Frame O' x' ct' c t'=c(t' B -t' A ) x'=x' B -x' A 45 o z z y y t c x x x t c t c = = + = + = ) ( ) ( β γ β γ z z y y t c x x x t c t c = = = = ) ( ) ( β γ β γ The following are Lorentz 4-vectors: = z y x t c r ~ = 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 ( S) 2 : 2 2 2 ) ~ ( ) ~ ( ) ( r r S = = 2 2 2 2 )
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Unformatted text preview: c ′ ∆ − ′ ∆ = ∆ − ∆ The quantity ( ∆ S) 2 is a Lorentz invariant ( same in all inertial frames ). If ( ∆ S) 2 > 0 the two events A and B are said to be “time-like” and there exists an inertial frame where the two events occur at the same spatial point ( i.e. ∆ x'=0). If ( ∆ S) 2 < 0 the two events A and B are said to be “space-like” and there exists an inertial frame where the two events occur simultaneously ( i.e. ∆ t'=0). If ( ∆ S) 2 = 0 the two events A and B are said to be “light-like” they can only be connected by light (traveling at speed c). differentials...
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