1. Consider the linear transformation with = (ct)' A(ct z = C(z - Bz) Dct) xx and y = y, = where A, B, C, and D are unknown constants. Find values for these constants by requiring that (ct)² - (2′)² = (ct)² - 2² and that the transformation reduce to a Galilean transformation in the limit that v/c<<1. t' = t z' = 2 - vt x'x and y = y, 2. Consider the wave equation (V² - 1822) = 0. Show that (a) This wave equation is not invariant under the Galilean transformation t' = t z = z- vt x'x and y' = y. (b) This wave equation is invariant under the Lorentz transformation (ct)' = (ct - Bz) z = (z - Bct) xx and y = y, = with ẞ=v/c and y = (1 − ẞ²)-1/2. -

1. Consider the linear transformation with = (ct)' A(ct z = C(z - Bz) Dct) xx and y = y, = where A, B, C, and D are unknown constants. Find values for these constants by requiring that (ct)² - (2′)² = (ct)² - 2² and that the transformation reduce to a Galilean transformation in the limit that v/c<<1. t' = t z' = 2 - vt x'x and y = y, 2. Consider the wave equation (V² - 1822) = 0. Show that (a) This wave equation is not invariant under the Galilean transformation t' = t z = z- vt x'x and y' = y. (b) This wave equation is invariant under the Lorentz transformation (ct)' = (ct - Bz) z = (z - Bct) xx and y = y, = with ẞ=v/c and y = (1 − ẞ²)-1/2. -