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lecture5 - Physics 126 Lecture 5 Feb 21, 23, 2011 Suggested...

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M.Loy, H. B. Chan 1 Physics 126 Lecture 5 Feb 21, 23, 2011 Twin paradox Conservation Laws in Special Relativity Einstein’s definition of momentum E= γ mc 2 : what does it mean? Space-time and energy-momentum Useful formulae and example Suggested Reading: Chapter 1.5, 1.7 – 1.9
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H. B. Chan 2 Pole vaulter paradox L d/ γ Measured in barn’s frame, the pole contracts. L/ γ c v = 2 3 γ=2 Measured in pole vaulter’s frame, the barn contracts. D=L/2
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H. B. Chan 3 d/ γ Two events in Farmer’s frame {S} : Shut the front door: (x A , t A ) = (0, 0) Shut the back door: (x B , t B ) = (d, 0) In Pole vaulter’s frame {S’} (x’ A , t’ A ) = (0, 0) (x’ B , t’ B ) = ( γ d, - γ v d/c 2 ) d = L/2 c v = 2 3 γ = 2 (x’ B , t’ B ) = (L, - L/c) 2 3 d = L/2 0 L 0 From t’ B to t’ A , the barn travels v(t’ A -t’ B ) = ¾ L Closing of the front and back doors are not simultaneous the pole vaulter’s frame ¾ L B A
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M.LoySp2010 4 The “Twin Paradox” Two identical twins, Joe and Jack . Joe travels at high speed to a distant star and back. Joe’s time was 7 years. His stay-home twin brother Jack on earth aged 50 years. Jack says, Hey, that is not right. Relativity says that everything is relative, and so I say, YOU, Joe is at rest, and I traveled afar and back, and YOU should age 50 years and I, 7 years!
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M.Loy, H. B. Chan 5 Now, let us first understand what they (we) DO AGREE on! Both Joe and Jack agree on: Stay-home Jack stands under the TST clock Traveling Joe travels to distant paradise at near light velocity. Joe starts the trip in year 2011, he arrives there and the year there is 2036, measured by a clock synchronized with the TST clock. But he only aged 3.5 years during the trip. And Jack aged 25 years. (This is just like the muon problem. Be sure you understand why stay-home Jack ages 25 years, and why traveling Joe aged only 3.5 years .) TST Paradise 2011 2036
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M.Loy, H. B. Chan 6 And then Joe came back , to the same place as Jack And Joe aged 7 years while Jack aged 50 years. That is the fact. Why can’t Jack say that HE is the one that traveled away and back while Joe is stationary in his rocket? Because Joe and Jack are NOT equivalent . TST Paradise 2011 2036 2061
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M.LoySp2010 7 T h ere is no paradox: They are NOT equivalent. Jack was in the same inertial frame, i.e., earth, in all that 50 years. His biological clock on earth ran for 50 years. Joe went away and return to the same point and he experienced: - either force all the time (if he is going a circular path), or - single TERRIBLE jolt when he turned around. Joe and Jack are NOT equivalent. There is no contradiction.
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8 Joe is younger because he is the one who ‘came back’: Plan A: Go straight out and turn around BIG jolt when turning around! Plan B: Go around a circle
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This note was uploaded on 03/31/2011 for the course PHY 126 taught by Professor Hobunchan during the Spring '11 term at HKUST.

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lecture5 - Physics 126 Lecture 5 Feb 21, 23, 2011 Suggested...

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