1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Explaining time dilation

  1. Mar 12, 2009 #1
    1. The problem statement, all variables and given/known data

    Two planets A and B are at rest with respect to each other and are L apart in this frame. They have synchronised clocks. A spaceship flies at speed v with respect to planet A and synchronises its clock with A-B.

    We know that when the spaceship reaches B, B's clock reads L/v and the ship's clock reads L/γv. How would someone account for the fact that B's clock reads L/v, which is more than its own L/γv, considering that the spaceship sees B's clock as running slow.

    2. Relevant equations

    I'm not sure if I got the correct solution, please help me to check if the reasoning is correct.

    Let the frame A-B measure (x,y,z,t).
    Let the ship measure coordinates (x',y',z',t').

    Using the Lorentz transformation for time,

    [tex]t' = \gamma (t - vL/c^2)[/tex]

    When A-B resets its clock at zero (t=0), t' registers [tex] - vL\gamma / c^2[/tex]. Relative to the time of A-B, the ship's clock runs at vLγ/(c*c) slower.

    When the ship passes B, time at AB is t = L/v. Then,

    [tex]\gamma (\frac{L}{v} - \frac{Lv}{c^2}) = \frac{L}{\gamma v}[/tex].

    My solution:

    When I reset my clock at A, this event is not simultaneous with the time reset at the two planets. In fact, the planets have a "head start" of vLγ/c^2. In the planet's time it takes L/v for me to reach there. In my time, to adjust for the head start, the time to reach B is L/γv.

    The resolution of the paradox (that my clock is slower on my ship than the planet's, although due to time dilation, I should read the planet's clock as slower) lies in the assumption that the time reset of the A-B system and the reset of the ship are simultaneous, but they are not.
  2. jcsd
  3. Mar 12, 2009 #2


    User Avatar
    Science Advisor
    Homework Helper

    Hi bigevil! :smile:

    this is all very confusing :redface:

    what's all this about "resetting"? :confused:

    i can't see whether you've got it or not …

    the important question is whether times on A and B which are simultaneous for A (or B) are also simultaneous for the spaceship :wink:
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: Explaining time dilation