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Dificulty with Einstein's derivation of TAO

  1. Dec 4, 2009 #1
    Hi,

    I'm trying to work my way through Einstein's 1905 paper On the electrodynamics of moving bodies.

    I'm having problems with section § 3. I follow until he says

    "If we place x'=x-vt, it is clear that a point at rest in the system k must have a system of values x', y, z, independent of time."

    I understand this as follows:

    Because the point is at rest in system k it's position is independent of time as measured by an observer also at rest in system k. However, the position of this point would not be independent of time when measured by an observer at rest in system K.

    Why use x' instead of [tex]\xi[/tex]? Is he using a third refernce frame?

    I'm confused here. I've searched for explanations of this and in the few I have found the author doesn't seem to understand it either.
     
  2. jcsd
  3. Dec 4, 2009 #2

    JesseM

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    Science Advisor

    Here was my attempt to follow Einstein's 1905 derivation and explain conceptually what was going on with some of the steps:
    Also, in the paragraph above that starts "Then he goes from this to the equation 1/2(1/(c-v) + 1/(c+v))*(dtau/dt') = dtau/dx' + (1/c-v)*(dtau/dt'), which also confused me for a little while because I didn't know what calculus rule he was using to go from the last equation to this one", I used an argument about what a smooth function looks like when you zoom in on an infinitesimal region, but in that step you can also just use the chain rule for partial derivatives, as explained in post #6 of this thread.
     
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