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Transcribed Image Text: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.
-
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