Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Linearity of Lorentz transformations from Homogeneity

  1. Sep 17, 2014 #1
    In this paper: http://www.jstor.org/stable/25170907?seq=1 the authors claim to show that linearity of the lorentz transformaiton follows from homogeneity of space and time. They consider two reference systems K and K' with coordinates (x,t) and (x',t') and write down the transformation laws as
    $$f(x',x,t) = 0; h(t',x,t) = 0.$$
    They then say that homogeneity of space implies
    $$f(x' + \epsilon, x + \epsilon,t) = 0; h(t', x+ \epsilon, t) = 0$$
    which they say represent a translation of the origin, or equivalently the translation of the place at which an event occurs, and where ##\epsilon## is an arbitrary parameter of dimension length.

    Now, is not this transformation assuming that if the event, according to K, originally placed at ##x## away from the origin, is moved to ##x + \epsilon##, then that same event, according to K', will be moved to ##x' + \epsilon##?

    If so would not that contradict the fact that K and K' does not agree on lengths? It seems that if an event is moved by ##\epsilon## in K, then it should be moved by ##\epsilon'## in K' with (in general) ##\epsilon \neq \epsilon'##.

    So are the authors making an erroneous assumption? Or where does my reasoning go wrong?
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted

Similar Threads - Linearity Lorentz transformations Date
A Multipole expansion of linearized field equations May 16, 2017
B Linear momentum Jan 23, 2017
Linearity of Lorentz transformations Dec 1, 2010
Question on linearity of Lorentz transformations Jul 12, 2009
Why must the Lorentz Transformations Be Linear? Sep 7, 2006