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Synchronized clocks in a moving frame

  1. Oct 11, 2015 #1
    1. The problem statement, all variables and given/known data
    It is not a homework question.I am trying to understand the concept in the attached diagram but I stuck.Hope someone can help

    2. Relevant equations


    3. The attempt at a solution
    Please see the lower part of the note,stating that Δt' = Δt/γ.However,imagine you are in the moving frame S'(the stationary train).Yes just a stationary train.If you shine a beam towards the head and back of the train,they should arrive at the same time(in your frame).Hence Δt' = 0,but this also implies Δt = 0.What's wrong?

    Thanks! 12140117_1220996931249452_4316478324503461840_o.jpg
     
  2. jcsd
  3. Oct 11, 2015 #2

    mfb

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    That equation does not apply to time differences that do not happen at one position (in your reference frame). If you calculate time differences for the two ends of the train, you get an additional term in the transformation.
     
  4. Oct 11, 2015 #3
    Thx for your reply...but i dont quite understand :d, could you explain a bit more?
     
  5. Oct 12, 2015 #4

    mfb

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    You try to use a formula for a system where it does not apply.
    It's like trying to use g=9.81 m/s^2 as gravitational acceleration on the Moon: it's simply not the right thing.
    There is a more general formula that works both on Earth and Moon: F=GMm/r^2. In the same way, there are the more general Lorentz transformations that can be used here.
     
  6. Oct 14, 2015 #5
    Sorry, I have just seen it. So, in my case, what does Δt' mean exactly?
     
  7. Oct 14, 2015 #6

    mfb

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    Difference in time between two events (as defined in the text) in the frame that got a prime.
     
  8. Oct 15, 2015 #7
    I find this derivation somewhat confusing.
    It says that that clock A starts before clock B and then takes tB - tA as a positive quantity.
    Also, it states that in the observer's frame the clocks in the moving frame are moving
    with speed v. Then the diagram shows the moving frame moving to the left with
    speed v.
    The hand on both clocks are always in the same (relative) position which doesn't
    help with the explanation.
     
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