lecture_3

# lecture_3 - Simultaneous Events L v E2 c L c v Tr Tf T L D...

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1 Simultaneous Events L v c c v E 2 c v E 1 L L T r T f T cT r = L 2 - vT r cT f = L 2 + vT f T = T f - T r cT = v ( T f + T r ) D D = c ( T r + T f ) T = Dv c 2

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2 If events E 1 and E 2 are simultaneous in one frame of reference, then in a second frame that moves with speed v in the direction pointing from E 1 to E 2 , the event E 2 happens at a time Dv/c 2 earlier than event E 1 , where D is the distance between the events in the second frame.
3 If two clocks are synchronized and separated by a distance D in their proper frame, then in a frame in which the clocks move along the line joining them with speed v , the reading of the clock in front is behind the reading of the clock in the rear by Dv/c 2 .

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4 0 0 v 0 T B v v 0 0 0 0 T B T B T A -T A L A L B L B D B D B D A Train Frame (Alice’s) Track Frame (Bob’s) T A = L A v c 2 T B = D B v c 2 "slowing-down factor": T A T B = 1 - v 2 c 2 "shrinking factor": L B L A = D A D B = 1 - v 2 c 2
5 L A = D A T A T B = D A D B = L B L A = s L B = sL A D B = L B + vT B = L B + v 2 D B c 2 L B = s 2 D B s = 1 - v 2 c 2 T A = L A v c 2 T B = D B v c 2 "slowing-down factor": T A T B = 1 - v 2 c 2 "shrinking factor": L B L A = D A D B = 1 - v 2 c 2

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6 A stick and a clock, in relative motion 0 0 T T L L Stick Frame Clock Frame sL sL v v v v
7 The proper lifetime of a certain particle is 100.0 ns. a) How long does it live in the laboratory if it moves at v =0.96c? b) How far does it travel in the laboratory during that time? c) How far does it travel in its own frame of reference?

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8 2.7: Experimental Verification Time Dilation and Muon Decay Figure 2.18: The number of muons detected with speeds near 0.98 c is much different (a) on top of a mountain than (b) at sea level, because of the muon’s decay. The experimental result agrees with our time dilation equation.
9 Newtonian Principle of Relativity If Newton’s laws are valid in one reference frame, then they are also valid in another reference frame moving at a uniform velocity relative to the first system. This is referred to as the Newtonian principle of relativity or Galilean invariance.

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10 K is at rest and K’ is moving with velocity Axes are parallel K and K’ are said to be INERTIAL COORDINATE SYSTEMS Inertial Frames K and K’
11 The Galilean Transformation For a point P In system K: P = ( x , y , z , t ) In system K’: P = ( x ’, y ’, z ’, t ’) x K P K’ x’-axis x-axis r V P ' = r V P - r v

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lecture_3 - Simultaneous Events L v E2 c L c v Tr Tf T L D...

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