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Time dilation

  1. Sep 9, 2007 #1
    It's my firt time reading special relativity and this question bug's me . It is said that times runs slower at greater velocities .
    Let's say I leave home in a space craft and fly for some time at 99% the speed of light measured from earth. It is said that when i come home i will be older than my twin brother .
    Now let's transfer ourselves in the space craft . The earth now will move with 99% the speed of light from me . So when my brother comes back to me (he remained back on earth ) he should be younger than me .

    So which one is it ?
  2. jcsd
  3. Sep 9, 2007 #2
    When the journey is completed, the brother that traveled will be younger. This follows from the transforms of SR which relate space and time in relatively moving inertial frames
  4. Sep 9, 2007 #3
    Can you be more explicit please .
    How can you say which is moving and which isn't ? Acording to the space craft the earth is moving .
  5. Sep 9, 2007 #4


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    This is the question posed by the classic twin paradox--read the linked website for an in-depth answer, but the short answer is that the standard time dilation equation of special relativity only works in inertial (non-accelerating) frames, while your brother has to accelerate and change velocities in order to return to Earth, so he can't apply the time dilation equation in the same way to predict how much you'll age based on your velocity relative to him throughout the trip (and there can be no doubt about which one of you accelerates and which doesn't, because the one who accelerates will feel G-forces during the acceleration). But you are free to pick any inertial frame to predict how much both of you age, it doesn't have to be the Earth's--you could pick the frame where your brother was at rest during the outbound phase of his trip while the Earth was moving at a significant fraction of the speed of light, and in this frame you do age less than your brother during the outbound phase, but then when your brother turns around to catch up with the Earth he must move even faster than the the Earth in this frame, so he ages slower than you during the inbound phase and the net result is that this frame makes exactly the same prediction about your relative ages when you reunite (as will every other inertial frame).
  6. Sep 9, 2007 #5
    One more questions .
    Let's say we have to space crafts moving towards each other . We know nothing of their movement before . We also have no still point to determine which has which velocity . All we know is their relative velocity .
    Can we say know if the time runs slower in the second craft compared to the first , or is it the other way around ? Or it's a complete mistery ?
  7. Sep 9, 2007 #6
    With no initial conditions given - two spaceships that pass each other have no way to know which is moving - if they make measurments using clocks and rulers as they pass each other, each will see the clock on the other spaceship running slow, and they will measure the other spaceship to be contracted. In other words nothing can be concluded because the situation is symmetrical

    On the other hand, if there is an initial synchronization of clocks on two separated spaceships at rest in the same frame, and one is accelerated so that it is now moving toward the other, Einstein predicted that when the two ships meet, the clock on the spaceship that was put in motion will show less time when the two clocks are brought together and compared in the same frame
    Last edited: Sep 9, 2007
  8. Sep 9, 2007 #7


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    In relativity it's not that it's a mystery, it's just that the notion of "rate of aging" is intrinsically coordinate-dependent, much like "velocity" (would you say it's a mystery which craft has a larger velocity, or would you say there is no single objective answer to this question?) This is related to the fact that "simultaneity" is also dependent on your choice of reference frame in relativity--different frames disagree about whether two events at different locations (like the event of an observer on Earth celebrating his 40th birthday and the event of a traveler on a ship celebrating her 35th) happened at the same moment or at different times, and frames which say they happened at different times can disagree on which happened first. Philosophically you may choose to adopt the notion that there is such a thing as an absolute present and thus an absolute truth about which frame's definition of simultaneity is correct--this philosophical position is known as presentism--but if relativity is correct you have to accept that there is no experimental way to distinguish which frame this is, so it may be more natural to adopt an alternative philosophical view known as four dimensionalism or eternalism which treats time as a dimension in a four-dimensional spacetime where all events are equally "real", and the choice of how to slice up this 4-dimensional object into a series of 3-dimensional spatial "moments" is an arbitrary one with no correct answer (in this view, asking what the 'true' answer is to the question 'did these events happen at the same time?' is just as meaningless as asking about the true answer to the question 'did these events happen at the same x-coordinate?')
  9. Sep 9, 2007 #8


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    But Einstein would also say there's no "objective" sense in which the two clocks were "synchronized" before the acceleration, they were only showing the same time in their rest frame but not in other frames.
  10. Sep 9, 2007 #9

    Of course - there is no universal time in SR
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