14_special_rel

In the case pictured the stationary observer sees the

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Unformatted text preview: pictured, the stationary observer sees the flash hit the back of the ship before the front UCSD Physics 10 One person's space is another's time If simultaneity is broken, no one can agree on a universal time that suits all the relative state of motion is important Because the speed of light is constant (and finite) for all observers, space and time are unavoidably mixed we've seen an aspect of this in that looking into the distance is the same as looking back in time Imagine a spaceship flying by with a strobe flashing once per second (as timed by the occupant) the occupant sees the strobe as stationary you see flashes in different positions, and disagree on the timing between flashes: space and time are mixed see description of light clock in text Space and time mixing promotes unified view of spacetime "events" are described by three spatial coordinates plus a time UCSD Physics 10 The Lorentz Transformation There is a prescription for transforming between observers in relative motion ct' = (ct - vx/c); x' = (x - vt); y' = y; z' = z "primed" coordinates belong to observer moving at speed v along the x direction (relative to unprimed) note mixing of x and t into x' and t' time and space being nixed up multiplying t by c to put on same footing as x now it's a distance, with units of meters the (gamma) factor is a function of velocity: UCSD Physics 10 The gamma factor Gamma ( ) is a measure of how whacked-out relativistic you are When v = 0, = 1.0 and things are normal At v = 0.6c, = 1.25 a little whacky At v = 0.8c, = 1.67 getting to be funky As vc, UCSD Physics 10 What does do? Time dilation: clocks on a moving platform appear to tick slower by the factor at 0.6c, = 1.25, so moving clock seems to tick off 48 seconds per minute standing on platform, you see the clocks on a fast-moving train tick slowly: people age more slowly, though to them, all is normal Length contraction: moving objects appear to be "compressed" along the direction of travel by the factor at 0.6c, = 1.25, so fast meter stick will measure 0...
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