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sr1 - [mm m mm maxim[W m m at pom P a “ Did(AW/Wm_g4_=...

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Unformatted text preview: [mm m mm maxim [W m m at pom} P a “ Did (AW/Wm) __g4_;-._=_ £5 9 We: 45:?) __“ ><ACP>£ xgzm we ‘ :> VACPB: mmw _ __ a my“ (macho '2 gm) 35(7) 354 95:33 w): X(2<B(P>+\/£5> ‘ mm: X ( £5 + mam) _ we: b/ 2 Dflzv/mzf’é ;, (a: We e M: “Far \/<<c (Mum/ax :7 a” xgw :@>’A i . " MOI/D03 (75> Woe/<5 E3) m wfilflim M5 7% ngm) M & $47M, 052,) WEE EL é. AWPM, Length Contraction & Time Dilation Consider “observers” (Ahthur and (B)erbara riding on two railroad trains which are on parallel tracks. Suppose that the trip is veryr smooth (not elutraklj and that there are no landmarks. Arthur thinks his train is at rest and Barbara's train is moving past him in the positive x—direetion. However, Barbara. believes she’s at rest and Arthur is Ineving post her {in the negative redirection). Unless the trains accelerate or deeelerate there’s no way to resoive this disagreement; Arthur and Barbara are equally good (“inertial”) observers. Suppose they each observe two “events”, say two flashes of light. Arthur may determine that the events occurred at different locations separated by £191 and at different times separated by a time interval Arr. For the some two events Barbara finds {MB and Am}. : According to Einstein / Lorentz, the reiations between the distance and time intervals that Arthur and Barbara measure is: An,“ = “(£3.33 + 2:55.153) ; Ah 2 “(($33 + rigors/(:2). where: 7 = (1 —— 182T”? and {3 m We. Suppose that Barbara finds the light source is at rest in her system (on her train], so that A2}; = 0. Perhaps it is a clock which emits a flesh of light every second. The time interval She measures for the two flashes is At}; 5 in. Simple substitution in the above er‘iuetions shows that Arthur finds a longer time interval between flashes: fits = 7513 : Ne- J‘Lrther siso sees the flashes occur at different locations (Barbara‘s clock is moving), separated by: Arr/1 m ofitd m veto. Arthur finds a lenger time interval between flashes and concludes that Barbara‘s clock is running slow. Note that if Arthur were carrying the clock and Barbara were timing the flashes, she would also measure a time interval of fifty) and she would coneiude that Arthur’s clock is running slow. Let us now consider measurements of the length of Barbara’s train. Barbara can measure it by timing or light beam she bounces off a mirror at. the back of the train. {et en 2 m .41) when she is at the front (at .123 m 0}. Then, for Barbara, A33 m —LO. Since Barbara sees Arthur moving at Speed t} and she knows that her train is L0 in Eength, she cemeteries it will take a. time interval 33133 = Lu/U for her train to pass Arthur. Then, for Arthur: Arm a L = vAtA v2: 70053:}; + raging/(,3) = 71,00 _ £2) : Lg/“f. 30, Arthur will measure L < L0 and conclude that Barbara’s train is shorter than Barbara says it is. Once again, if Barbara measured Arthur’s train, she would find it shorter than Arthur said it was. To summarize: moving clocks run slow; moving lengths are shorter. ...
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