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Twin (rod) paradox

  1. May 9, 2008 #1
    Ok guys,
    Explain me this.

    In twin paradox, one of two twins, paul and peter, when paul goes for a space ride at very high speeds, and peter stays back at earth, when paul comes back, peter is older than him, and paul is still younger because of assymetric aging, also called time dilation.
    In detail, when paul starts journey, he accelerates, and his aging process (or clock) slows down. When he travels with a constant speed, his aging process slows down. when he accelerates again to reduce his speed, his aging process slows down. He starts his backword journey again in same manner and his aging slows down. And as there is no time contraction, but only time dilation, an irreversible process, at the end he has aged slowly, and thus, is younger than peter. I agree to that.

    Does this same happen with length contraction? I mean, instead of paul and peter, If there would have been two rods L1 and L2, and L1 would have been sent for a space travel, at each step its length would contract, as was the case with time dilation in the case of paul. When the rod comes back to earth, would that rod L1 measure less than road L2?

    Only conseptual explanation, no math please...
  2. jcsd
  3. May 9, 2008 #2
    Briefly, without the maths, the rods will be the same length whenever they return to the same location and at are rest with each other. Length contraction is "temporary" and is not cumulative like time dilation.
  4. May 9, 2008 #3


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    In its own reference frame L1 stays the same length at all times. It appears to contract while its moving in reference to the L2 frame. So when it comes back and stops it is the same length as it always was.
  5. May 9, 2008 #4
    hey buddy, thanks, can you tell me, why time dilation is cumulative?
  6. May 9, 2008 #5
    Hi, I am sure others on this forum will give you a much better conceptual and philosophical explanation than I can.

    This is my take on the subject. When we talk informally about time we could be talking about the clock rate (how fast it is ticking) or the cumulative total elapsed time between two events. The clock rate is instantaneous and determined by the relative velocity between the two observers and when the two clocks are at rest again with each other they both return to the same clock rate just as the measuring rods return to the same length. The cumulative length is the path that the rods followed through space and for one rod it is obvious that one has accumulated a greater path length than the other. The cumulative time is the length of the journey through time rather than through space. Classical dynamics does not have this notion of different paths through time and only considers paths through space.

    In the relativity concept of 3 space dimensions plus one time dimension, everything has a four velocity of c. An object that is stationary to the observer, is moving at maximum speed along the time dimension and accumulating time rapidly (ageing fast) but not accumulating any distance. At the opposite extreme, a photon is moving at c, purely along a spatial dimension and accumulating distance rapidly but not ageing at all.

    Hmmm..I'm rambling..I'll leave it for the experts :P
    Last edited: May 9, 2008
  7. May 9, 2008 #6
    No, I think that was good.
    Until others reply, Let me ask,

    How is time axis different than other axis, apart from being invisible?

    Is not the tick-rate of clocks for time equivalent to the length of the rod in space? Like length of the road signifies the distance between any two points in one of the three space axis (x y z), while tick-rate is the distance between any two points on the time axis. We think there are x, y and z axis in space, but it is only a concept, just like time axis is a concept. When we say somebody is moving in spacetime, it is not only the movement in x, y or z direction but also in time direction as well (with respect to somebody or some reference frame, of course).

    But if tick-rate is equivalent to length of the rod for respective axis, how come length contraction is temporary and time dilation cumulative?
  8. May 10, 2008 #7
    The length is contracted, the total distance traveled by the twin is less than the distance as measured by the twin who stayed at home.
  9. May 10, 2008 #8
    So both the time and distance were shorter for the traveling twin. After rendezvous both time and distance will be identical for both twins again. Space and time, or better formulated, distance and duration are on an equal footing in relativity.
    Last edited: May 10, 2008
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