Post by Luigi Fortunati
[[Mod. note --
To put it another way, can you explain why you think it's paradoxical
that observer B1 observes something different from observer A?
I do not consider it paradoxical that observer B1 observes something
different from observer A.
I think it is paradoxical that observers B1 and A see different things
both real: if one thing is real the other must be apparent and vice
This is why I speak of reality and appearance.
A simple and clear example is the following.
If observer B1 stands on the carousel, he sees the earth rotate a full
360 degrees in 5 seconds and sees the carousel stationary.
Instead, observer A on the ground sees the carousel rotate 360 degrees
in 5 seconds and sees dry land.
One sees one thing, the other sees another: can both be real? Obviously
If what observer A sees is real, what observer B1 sees can only be
In fact, if the Earth really rotated at that angular velocity, it would
[[Mod. note -- What do you mean when say that something is or isn't
"real"? In special relativity we don't really have such a concept.
Rather, we have the concept of what some specified (inertial) observer
ALSO, note that B1, B2, B3, ... observing the body X to be Lorentz-
-contracted does *not* imply any special internal stresses in X.
There are several two different ways of obtaining ("proving") the
statement in my previous sentence. For example:
(a) We can introduce the concept of "stress tensor", note (show)
that it is in fact a tensor, note that Lorentz transformations
can be viewed as tensor transformations of coordinates, and make
use of the elementary tensor calculus result that a tensor that's
zero in one coordinate system (basis) is zero in any other coordinate
system (basis), so that the stress tensor vanishing in A's inertial
reference frame implies it must also vanish in any other inertial
(b) More generally, to reason about internal stresses in objects, we
need a theory of (relativistic) continuum mechanics, and we can
use this to work out the internal stresses in the body X, computed
in A's intertial reference frame, B1's inertial reference frame,
B2's intertial reference frame, etc etc.
(c) At a microscopic level, the size of an object is determined by the
lengths of the chemical bonds between the object's constituent atoms.
These lengths are in turn determined by the Schroedinger equation
for the atoms' valence electrons. So, we could work out how
solutions of the Schroedinger equation change under Lorentz
(a), (b), and (c) should all give the same answer, namely, the usual
Lorentz contraction does *not* imply any special internal stresses in