Physics 305
Problem set 10
Due: Mon, Apr 23
[1] Griffiths problem 11.14 (page 464).
[2] Griffiths problem 11.25 (page 475).
[3] Consider two consecutive Lorentz transformations, by velocities u and then v, both in the x
direction. The corresponding transformation can be expressed as the matrix product of the two
corresponding individual transformation matrices.
(a) Find the transformation matrix corresponding to this series of velocity boosts, by directly
carrying out the product of the two matrices.
(b) Show that this matrix is the same as one would obtain from a single velocity boost, using the
velocity obtained from the addition relation shown on page 498 of the text.
[4] Griffiths problem 12.16 (page 499).
[5] Two events occur at the same position, at an interval of 4 seconds, as measured in the rest
frame where these events occur.
(a) By what distance will these events be separated in a moving frame in which the events are 5
seconds apart? Also what is the relative speed of this frame as compared to the original frame?
(b) Calculate explicitly the Lorentz invariant interval (the square of the displacement 4-vector),
showing that it is the same in each frame.
(c) Is is possible to find a frame in which the two events are simultaneous? Why or why not?