Chapter1_14 - In the O-frame(Rocket frame 50 49 50 49 ly D...

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PHY3063 R. D. Field Department of Physics Chapter1_14.doc University of Florida According to Rick, John was born 241 years before he was! 1 ly = c×(1 year) 9.464×10 15 m Space-Time Transformations - Example A B Frame O x ct c t=50 ly x=49 ly C D Rick A C Frame O' x' ct' John B D Jim Rick Suppose Jim, John, and Rick were all born simultaneously in the Earth Frame ( O-frame ). Jim and Rick were born at the origin at t = 0 ( i.e. at A = (0;0)) and John was born on a distant planet 49 light-years from Earth ( i.e. at B = (0;49 ly)). Rick is put in a rocket ship at the moment of birth heading for John at speed V/c = β = 0.98. Rick reaches John at a time ct = 49 ly/0.98 = 50 ly. Let the O'-frame be the rocket frame ( i.e. Rick’s frame). In the O-frame (Earth frame)
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Unformatted text preview: In the O'-frame (Rocket frame) ) ; 50 ( ) 49 ; 50 ( ) 49 , ( ) ; ( ly D ly ly C ly B A = = = = ) 246 ; 251 ( ) ; 10 ( ) 246 , 241 ( ) ; ( ly ly D ly C ly ly B A − = = − = = where I used 925 . 4 025 . 5 1 / 1 98 . 2 = = − = = βγ β γ . According to Jim on the Earth at Rick’s meeting with John: Rick’s age = 50 years Jim’s age = 50 years John’s age = 50 years Rick traveled a distance of 49 ly According to Rick on the rocket at the meeting with John: Rick’s age = 10 years Jim’s age = 251 years! John’s age = 10 years + 241 years = 251 years! Rick traveled a distance of 9.75 ly! John traveled a distance of 246 ly! (ct;x) (ct';x') Round off to the nearest light-year...
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