Answer Happy

12.5. Lorentz invariance of the wave equation. Consider the Lorentz trans- formation d' = 7 (x – vt) and ť =7 (t- VC - (t-) Vi-(02/2). Recall that the wave equation in one di- We use standard notation 7 = 1 a2 1 a2 mension is written in terms of the operator The goal of this problem ar2 c2at2 is to check that the operator - 2022 is invariant under the Lorentz transformation, i.e., in the primed frame that is moving with velocity vê, it assumes the same form 22 1 22 That is to say x + x' and t +t'. Do this by writing a/ax and afat ac'2 c2 at 2 in terms of a/or' and 8/8ť from the transformation. (6 points). Show that the operator that occurs in the three-dimensional wave equation V2 (1/cm) has the same form for a Lorentz transformation along the z-axis. Hint: How do y and z transform? (2 points)