# 15 time is rela1ve by pythagoras theorem a2 b2 c2

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Unformatted text preview: s the wave from event Red earlier. 11 (d) Sally detects the wave from event Blue later. “Light” Clock hDp://www.youtube.com/watch?v=V7vpw4AH8QQ 12 “Light” Clock: Time Dila1on Distance travelled = speed of light x &me taken Light travels with the same speed in both cases: “Sta1onary ­mirror” case: Light travels shorter distance, Tick ­tock dura1on is shorter. “Moving ­mirror” case: Light travels longer distance, Tick ­tock dura1on is longer. Time is dilated! A moving clock runs slower! 13 14 Scan from: TIME, DECEMBER 31, 1999, ALBERT EINSTEIN, PERSON OF THE CENTURY / KENNETH AUCHINCLOSS Time is Rela1ve (a)  Sally, on the train, measures the &me interval Δt0 between events 1 and 2 using a single clock C on the train. (b)  Sam, watching from the lawn, requires two synchronized clocks, C1 at event 1 and C2 at event 2, to measure the &me interval between the two events; his measured 1me interval is Δt. 15 Time is Rela1ve By Pythagoras’ Theorem (a2 + b2 = c2): ≥ Δt0 Proper &me Δt0: Time interval between two events that occur at the same point in the reference frame in which the clock is at rest. 16 The Twin Paradox hDp://www.youtube.com/watch?v=oOL2d ­5 ­pJ8 Albert Einstein didn’t have a twin brother – but he had some funny ideas of what you could do with one. He imagined two iden1cal twins – let’s call them Al and Bert. Now, Al is a couch potato, but Bert likes to travel, so he hops into a spaceship and zooms oﬀ at close to the speed of light. That’s when Einstein’s special theory of rela&vity kicks in. It says that the faster you travel through space, the slower you move through &me. So from Al’s point of view Bert’s 1me would be moving slower than his own. To put it another way, 1me might ﬂy when you’re having fun – but when clocks ﬂy, they run more slowly in rela1vity. Ager a while Bert decides to head back, s1ll at close to the speed of light, and returns to his brother with his holiday snaps. But when Bert arrives home, Al will now be older than his twin. Which makes their double dates a lot more awkward. Although it seems implausible, Einstein just followed his theory to its logical conclusion and it turns out he was right. 17 This concept of ‘&me dila&on’ provides the basis for our Global Posi&oning System – which is how your Sat Nav knows you need to ‘turn leg in two hundred yards.’ Evidence of Time Dila1on: Muon Decay 18 Evide...
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## This document was uploaded on 03/22/2014.

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