Question

4. Determine the timelike, spacelike or lightlike character of the 4-vectors: y" = (0,-1, 1,1) z" = (3,417,100) , ; in Minkowski spacetime in Cartesian coordinates 5. Show that if is a unit timelike vector, it is always possible to find a Lorentz transformation such thawill have components (0,0,0,1). Show that if k" is a null vector, i is always possible to find a Lorentz transformation such that k" has components (1,0,0,1). Hence show that if UV,-0, and U"is timelike, then V"is spacelike, while if U and V are both null vectors, they are proportional to each other. 6. Show that any spacelike 4-vector can be expressed as the difference of two isochronous null 4-vectors. Note: Two 4-vectors A",B" are isochronous if AB0 7. Show that for any second rank covariant tensor X, that XapXoHowever for third rank covariant tensor-exam) + r吶1.

Answer 1

A genende 4-en the comfonents are usuaith Call ed (z ) The invanient gength ofHte、 Y-vec-fore is given by train e , inerti al -vec-tr· Y-confonents cn an hal Li

乙"-(3,4,1 , loo) . SRO; İ.e. time liKe Necton. Please Post individlual uton mention Perci cuton one