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Speed paradox

  1. Aug 6, 2010 #1
    A particle traveling at 0.5c for 1 second covers 1.3E8m (speed=.5*3E8 and gamma=.866) and not 1.5E8. The average speed was then 1.3E8 m/s = .43c and not .5c. What is going on here? Was it travelilng at 0.5c or at .43c?
    Last edited: Aug 6, 2010
  2. jcsd
  3. Aug 6, 2010 #2
    This is relativity.

    The particle, from its perspective, travels .5*3e^8m in 1 sec. From your perspective, the particle travels the distance in more time (a lower average speed). Both the particle and the observer agree that it reached a point in space, and disagree on the time it took to get there.

    The Lorentz factor (your gamma) tells you the degree of the relativistic effect.
  4. Aug 6, 2010 #3


    Staff: Mentor

    By definition the particle's speed in the particle' frame of reference is 0. And yes, it is 0 in one frame and 0.5 c in another and 0.999 c in yet another. There is even a frame where it's speed is 0.43 c, but that is not the particle's frame.
  5. Aug 7, 2010 #4
    Suppose you are observing the particles motion over a road And you are stationary above the road. For you the particle covers 1.5E8m on the road in one second. But in the particles perspective, the road moves past a distance of 1.5E8 * 0.866 = 1.3E8m in a time of 1 * 0.866 = 0.866 seconds. So, the particle concludes, the road is moving at 0.5c.

    So, Neither the particle nor the road sees any velocity at 0.43c.

    BTW 0.866 is 1/gamma. From what I remember, gamma is always greater than 1.
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