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8.022pset6 - Massachusetts Institute of Technology...

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Massachusetts Institute of Technology Department of Physics 8.022 Spring 2004 Assignment 6: Special relativity; Magnetic fields Post date: Thursday, March 18th Due date: Thursday, April 1st Be sure to write your name and section number on your pset Please staple multiple pages together 1. Invariant interval (8 pts): A quantity that is left unchanged by Lorentz transformations is a called a “Lorentz invariant”. Consider two events described in the laboratory frame by ( t 1 , x 1 , y 1 , z 1 ) and ( t 2 , x 2 , y 2 , z 2 ). Show that Δ s 2 ≡ - ( c Δ t ) 2 + (Δ x ) 2 + (Δ y ) 2 + (Δ z ) 2 is a Lorentz invariant. 2. Galilean tranformations (10 pts): Prior to special relativity, people related coordinates between different frames with the “Galilean transformation” — clocks in different ref- erence frame tick at the same rate, spatial positions are shifted by a term that depends on the relative velocity just as you would expect. For example, for frames that are moving with respect to each other in the x direction, we would have t 0 = t x 0 = x - vt .
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