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Derivation of Lorentz Transformation for Acceleration

  1. Jan 28, 2014 #1
    1. The problem statement, all variables and given/known data
    Starting with the Lorentz transformation for the components of the velocity, derive the transformation for the components of acceleration.


    2. Relevant equations
    Lorentz Transformation for position and time :
    ##x'={\gamma}(x - vt)##
    ##t'={\gamma}(t - {\frac{vx}{c^2}})##
    Resulting transformation by taking ##{\frac{dx'}{dt'}}##
    ##u'_x={\frac{u_x-v}{1-{\frac{vu_x}{c^2}}}}##

    3. The attempt at a solution
    Before I go through the trouble of typing out my attempt in LaTex (I'm on my phone), let me make sure I'm going at this right because I think I'm over thinking this and now its all twisted in my head.
    Based on what they did to get the velocity transformation, I should be able to just take ##du'_x## and divide by the same ##dt'## used in the velocity transformation? Because it should be CHANGE of velocity over change in time. So ##{\frac{du'_x}{dt'}}## should give me what I want right?


    EDIT: I've refined my confusion.

    Its about how they are getting dx' and dt'.
    They are given as:
    ##dx'= {\gamma}(dx - vdt)##
    ##dt'={\gamma}(dt - {\frac{vdx}{c^2}})##

    I'm not sure what they are differentiating with respect to so I don't know how to treat ##u'_x## as far as differentiation goes. I'm assuming(hoping) that my confusion is a result of the my notions of classical mechanics not being consistent here and not a result of losing my grip on Cal 1 stuff.
     
    Last edited: Jan 28, 2014
  2. jcsd
  3. Jan 29, 2014 #2
    It does seem that you are losing your grip on calculus. ##x'## and ##t'## are functions of ##x## and ##t##, so their total differentials will be linear forms of total differentials ##dx## and ##dt##.
     
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