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Basic question about relativity

  1. Oct 27, 2009 #1
    So if I hop into a spaceship and leave at a very fast velocity, why is it that, upon returning, I will have aged less than my twin who stayed on earth?

    I've seen the triangle diagrams for this, but I just cannot understand why it seems to be that there is some *absolute* frame of reference here. It seems that we're saying that my velocity was absolutely higher than that of my twin's. If I am leaving the planet at a velocity v, then he's leaving me at the same velocity. If I accelerate away from him at acceleration a, then he's doing the same from my frame of reference. What is it that I'm not seeing?
     
  2. jcsd
  3. Oct 27, 2009 #2
    One who feels acceleration is the one who ages slower towards his brother. There are a bunch of threads about this, just type tween paradox in topic search
     
  4. Oct 27, 2009 #3

    JesseM

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    There is no suggestion of absolute velocity here, but you have to remember that the time dilation equation only works in inertial frames of reference, if you accelerate you are changing velocity in every inertial frame (acceleration is objective--when you accelerate, you know you've done so because you'll feel G-forces which you can measure with an accelerometer). So for example, you're free to pick an inertial frame where, during the outbound leg of the trip before you turn around, it is your ship that is at rest while the planet is moving away at speed v, and in this frame it is the twin on the planet who's aging slower during the outbound leg; but then in this frame, after you turn around and begin the inbound leg of the trip, you'll have to be moving at a speed even greater than v in order to catch up with the planet, since it will still be moving at the same velocity of v, and thus in this frame you'll be the one aging slower on the inbound leg. It always works out that although different inertial frames can disagree about who was aging slower during some particular phase of the trip, they all agree in their predictions the respective ages of the twins when they unite at a single location (as they must, since otherwise it would be easy to check whose prediction was right and whose was wrong, establishing a preferred frame of reference), and they always agree that the one who accelerated at some point in the trip has aged less than the one who moved at constant velocity throughout. The fact that an inertial path between two points in spacetime always involves more aging than a path between the same points that includes accelerations is closely analogous to how, in 2D geometry, a straight-line path between two points (a path with constant slope in any cartesian coordinate system, although depending on how the coordinate axes are oriented the value of the slope can be different in different cartesian coordinate systems) always has a shorter distance than a path between the same points that isn't straight (which has a change in slope somewhere along it). See this post for more on this analogy.
     
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