PHY2061 R. D. Field Department of Physics relativity_5.doc University of Florida Moving Clocks & SimultaneityConsider two clocks in the O-framelocated a distance ∆x = L apart (simultaneous in the O-frame) and one clock at the origin of the O'-frame. Let event Abe the comparison of the O and O' clock at the origin and let the two clocks agree. Let event Bbe the comparison of the O' clock with the second O clock at ∆x = L. ABFrame Oxctc∆t=cγτγτ∆x=LABFrame O'x'ct'c∆t'=cτ∆x'=0proper time =time at restwith clock)()(tcxxxtctc′∆+′∆=∆′∆+′∆=∆βγ′∆=′∆xctcτwhere 21/1/−==cV. Thus, γβcx=∆and γτ=
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