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Are relative velocities in std config equal in value?

  1. Apr 12, 2015 #1
    In the wikipedia page of Lorentz Transformation (http://en.wikipedia.org/wiki/Lorent...ormation_for_frames_in_standard_configuration) it's said that

    The problem I'm having here is that while taking Lorentz Transformation as true, I failed to verify the statement above, i.e. I can't get "O′ measures O to move at velocity −v along the coincident xx′ axes". Here's my calculation:

    Is there something wrong with the calculation? Or did I just have a misunderstanding of the statement in wikipedia?

    Any help will be appreciated!
     
    Last edited: Apr 12, 2015
  2. jcsd
  3. Apr 12, 2015 #2

    Orodruin

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    Yes, you assumed that the t' you got from the world line of Q was the same as that you should use for the world line of P. This is not the case, you need to take relativity of simultaneity into account.

    Edit: I suggest you instead attempt to compute the world line of P solely by Lorentz transforming how it looks in the unprimed system. You will get an expression for t' as well as xP', which you can relate to the velocity.
     
  4. Apr 12, 2015 #3
    Thank @Orodruin for the quick reply :)

    Did you mean that

    if so I have

    Hope I get the numbers right this time.
     
  5. Apr 12, 2015 #4

    Orodruin

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    Correct, in order to see how P moves in the primed systems, you need to take dxP'/dtP' as you did now. There really is not much more to it.
     
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