14_special_rel

6c 125 so fast meter stick will measure 08 m to

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Unformatted text preview: .8 m to stationary observer standing on a platform, you see a shorter train slip past, though the occupants see their train as normal length UCSD Physics 10 Why don't we see relativity every day? We're soooo slow (relative to c), that length contraction and time dilation don't amount to much 30 m/s freeway speed has v/c = 10-7 = 1.000000000000005 30,000 m/s earth around sun has v/c = 10-4 = 1.000000005 but precise measurements see this clearly UCSD Physics 10 Velocity Addition Also falling out of the requirement that the speed of light is constant for all observers is a new rule for adding velocities Galilean addition had that someone traveling at v1 throwing a ball forward at v2 would make the ball go at v1+v2 In relativity, reduces to Galilean addition for small velocities can never get more than c if v1 and v2 are both c if either v1 OR v2 is c, then vrel = c: light always goes at c UCSD Physics 10 Classic Paradoxes The twin paradox: one twin (age 30) sets off in rocket at high speed, returns to earth after long trip if v = 0.6c, 30 years will pass on earth while only 24 will pass in high speed rocket twin returns at age 54 to find sibling at 60 years old why not the other way around? Pole-vaulter into barn high-speed runner with 12 meter pole runs into 10 meter barn; barn door closes, and encompasses length-contracted 9.6 m pole (at 0.6c) but runner sees barn shrunken to 8 m, and is holding 12 m pole! can the barn door close before the pole crashes through the back? resolution in lack of simultaneity: "before" is nuanced UCSD Physics 10 If I'm in a car, traveling at the speed of light... If I turn on my headlights, do they work? Answer: of course--to you, all is normal you are in an un-accelerated (inertial) frame of reference all things operate normally in your frame To the "stationary" outsider, your lights look weird but then again, so do you (because you're going so fast) in fact, at the speed of light, all forward signals you send arrive at the same time you do And the outside, "stationary" world looks weird to you But I must inquire: how did you manage to get all the way up to the speed of light?! UCSD Physics 10 What would I experience at light speed? It is impos...
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