Homework Set #1 - Due
January 22
1. a) Show that Eq.(11.2) in Jackson is invariant under a
Galilean transformation.
b) Show that Eq.(11.4) in Jackson is not
invariant under a Galilean transformation.
2. Show that Eq.(11.23) in Jackson is correct, i.e.,
that for any 4-vector (A0, A1,A2,A3)
=(A0,A) , the
form
A0A0-A.A
is
a relativistic invariant.
3. Section 11.3 in Jackson shows a derivation of the Lorentz
transformations. If in Eq.(11.15) you replace the actual
values of the
two sides of the equation using (11.14) and
(11.14') , Eq.(11.15) becomes : 0=lambda^2 x0. Comment on this. Is the
derivation correct
or not? Why? What happens if you
use a plane wave moving in the positive x direction flashed at the
origin at t=t'=0 rather than an spherical
wave? Does the derivation still work?
Why?
4. Explain which of the following paths in Minkowsky space
are possible or not (click here to see figures):