Re: How to draw a spactime diagram for the T and U paradox.

You can relax.  There will be no explosion.  The first postulate of Special
Relativity says that if the two don't explode at rest, they will not
explode in any Lorentz system.  I will try to describe in words what a
space-time diagram would look like in the rest frame of the T.
That is the system in which an equal time measurement of the length of the
moving U would give U/2, leading to the mistaken conclusion in 
ID: 1000024454.Ph.
Take T for the rest length of the T, and U for the rest length of the U,
with U>T.  After the U stops moving, the T and U will be at rest, each with
vertical world lines given by:
For U, x=U and x=0.
For T, x=U and x=U-T>0.
Before that, T will be at rest with the same world lines.
The world lines of U will be diagonally upward to the right, with x and t
both negative at first.  The x distance between the ends of U, at equal
time, will be U/2 (for gamma=2).  When the left end of U reaches t=0, x=0,
its x motion must cease, because the left end can't go past the vertical
world line at x=0 for any t>0.  Thus, the world line for the left end of U
will then follow the vertical line x=0.  The world line of the right end of
U will keep following the same diagonal line, now for positive x and t,
until it reaches x=U.  Then it will follow the verical world line x=U.
Since the left end of U cannot go past x=0, it will never strike the left
end of the T at x=U-T.  The motion of U may look strange to an
unsophiscated observer, but not to me.  At the same time that a measurement
of the left end of U shows a constant x, a measurement of x for the right
end will indicate that it is moving.  The key words in the preceding
sentence are "measurement" and "At the same time".
The physical length of U never changes.  It is this type of measurement of
U that shows strange behavior.  Before relativity, it made sense that
measuring the two ends of a moving object at the same time gave its length,
and this length was the same when it was at rest.  This conclusion follows
from the Galilean transforation equations, which assumed a universal time.
 But in relativity, with time and space both changing in a Lorentz
trasformation, this method of measuring length is no longer appropriate 
for the length of the stick.  It is wrong.  "At the same time" means
different things in different systems.  In any other system, the
measurements would be seen to be made at different times for each end.
A moving stick does not get shorter.  It is only a faulty measurement that
gives a shorter result.  The actual length of a stick moving at constant
velocity can be found by Lorentz transforming to its rest system.