Chapter 20 - Relativity - Davidson Physics

Announcements Review The Twin Paradox Length Contraction Final QuestionsYet another gedanken experimentYou and a friend both decide to measure the length of an objectThe object is at rest in your frame of reference; your friend is seated on a train moving with a constantspeed vWhat happens?In your frame of reference:The object is not movingYou measure the length of the object to be L 0 = v∆t, where v is the speed of your friendThis time interval ∆t is not a proper time interval because the two events that define it (yourfriend passes the back of the object and your friend passes the front of the object) occur at twodifferent places so you must use two synchronized clocks to measure the time interval ∆tIn your friends’s inertial frame of reference:The object is moving with a speed vTo your friend, the two events that you measured occur at the same place so the time interval ∆t 0she measures is a proper timeTo her, the length L of the object is L = v∆t 0Since you and your friend are moving relative to one another, the time that she measures isdifferent than the time that you measure (time dilation)Length contractionL = v∆t 0 = v∆tγ = L √0γ = L 0 1 − v 2 /c 2Relativity