Tensors and Relativity: Assignment 1

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  • (1) In tex2html_wrap_inline318, tex2html_wrap_inline320 . Use the chain rule and the Lorentz transformations to compute the first and second partial derivatives of tex2html_wrap_inline322 wrt tex2html_wrap_inline324 , tex2html_wrap_inline326 and tex2html_wrap_inline328 . Use these results to compute the wave equation in the coordinate system of tex2html_wrap_inline318 .
  • (2) Use the inverse Lorentz transformations here.
  • (3) Use the time dilation and length contraction formulae in the notes.
  • (4) Use the velocity transformation equations.
  • (5) Use the velocity transformation equations to find a general expression for the speed of light in water moving at speed V relative to the lab. Then do an expansion for small values of V.

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