lec22 - The Relativity of Time *Relative motion change...

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11/13/11 1 Δ t = Δ t o v c 2 β = v c and γ = 1 − β 2 Δ t = γΔ t o The Relativity of Time *Relative motion change change the rate at which time passes. *The amount by which a measured time interval is greater than Δ t o , the proper time, is called time dilation .
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11/13/11 2 Example Your starship passes Earth at t = 0 with a relative speed of 0.9990c. After traveling 10.0 y (your time), you stop, turn, and travel back to Earth with the same relative speed. The trip takes another 10.0 y (your time). How long does the round trip take according to measurements made on Earth? (Neglect effects of accelerations involved in turning, stopping and getting back up to speed) Key Ideas: 1. Measurements from two inertial reference frames 2. Outward trip involved two events 3. Proper time 4. Time dilaton
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11/13/11 3 Twin Paradox 8.6 light-years Alice calculates: Ted calculates:
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11/13/11 4 The Relativity of Velocity v OA = v OT + v TA v OA = v OT + v TA 1 + v OT v TA c 2 Classical Relativistic
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11/13/11 5 The Relativity of Velocity v OA = v
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lec22 - The Relativity of Time *Relative motion change...

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