Lecture 32 - Recap of last lecture Consequences of the...

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Recap of last lecture Consequences of the postulates of special relativity : 1. Speed of light is a constant 2. Simultaneity of events is frame dependent 3. Time intervals are frame dependent 4. spatial intervals (length) is frame dependent 5. Space-time interval is frame independent. (Space-time interval) 2 = (c*time-interval) 2 - (space-interval) 2
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Time Dilation Space-time interval is frame independent If the light receiver is placed at the origin of the moving frame and receives the light at time t’ Space time coordinate is (x’,t’) = (0,t’) For the observer at rest the same event occurs at (x,t) = (ut,t) Since (∆s’) 2 = (∆s) 2 therefore c 2 t’ 2 = c 2 t 2 – u 2 t 2 Or t’ = t(1-u 2 /c 2 ) 1/2 or t = g t’ also written as t = g t 0
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Time Dilation t = g t’; g = 1/(1 – u 2 /c 2 ) 1/2
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Length Contraction ∆t 0 = 2l 0 /c
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Length Contraction Space-time interval is frame independent ∆t =∆t 1 + ∆t 2 = 2l/c(1 – u 2 /c 2 ) or l = l 0 / g d = l + u ∆t 1 = c∆t 1 or ∆t 1 = l/(c-u) ; ∆t 2 = l/(c+u)
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Proper Time/Length t = g t 0 ; l = l 0 / g g = 1/(1 – u 2 /c 2 ) 1/2 Time and Length measured in the frame at rest with respect to the event or object being measured is called the proper time t 0 and proper length l 0
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This note was uploaded on 01/27/2012 for the course PH 2233 taught by Professor Dipinkardutta during the Spring '11 term at Mississippi State.

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Lecture 32 - Recap of last lecture Consequences of the...

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