Tensors and Relativity: Assignment 1
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- (1) In
, 
. Use the chain rule and the Lorentz transformations to compute the first and second partial derivatives of 
wrt 
, 
and 
. Use these results to compute the wave equation in the coordinate system of . - (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.