Oand o' have parallel axes. according to o, o' is moving with velocity, v = (vi , v2, v3) = ! v! (sin a cos b, sin a sin b, cos a) what is the lorentz transform, χμ'v', between these reference frames? what is the relationship between, a.μ.v, and xv.μ? prove that the proper time, eq. (1.8), is an invariant. if o looks at a rod that formally had rest length, l, that now is aligned with the velocity vector and moving with velocity, v, what will o consider the length to be? do this problem as follows: find the rotation that takes o' to o" such that, ês, is aligned with, v. then apply the lorentz tranform this takes you to system o, where o is obtained from o by the same rotation that took o' to o". now apply the inverse rotation to get from o to o.