Jean DAVID wrote:
imagine a very long string (as long as the distance from Earth to the Sun)
that is continously unwound by traction at a certain speed in a middle of an
empty space (no gravity). the string is supposed to be thin, unbreakable and
inextensible. I decide to stop the unreeling at one end at time t.
Does the other end continue to go on by the time the information from the
blocking end arrives (that is 8 minutes later at t+8mn)
or does it block instantaneously (at time t) because of the fact that the
string is not extensible ?

If you truly had an inextensible string, the speed of sound in that
string (the speed of propagation of disturbances) would be
infinite. Such materials are physically impossible according
to relativity.

There are many such thought experiments you can do, all
arriving at the same conclusion: you can violate relativity if
you can create perfectly rigid materials. "Perfectly rigid rods"
are another common theme.

- Randy