(Derek McKenzie) writes:

Now as we look around for more bits of stuff to analyse we get a bit
adventurous and place one of our rulers in the box just to see what
happens. Since a ruler is just another lump of stuff we argue that we
should be able to describe its properties with self-adjoint operators.
In particular, we attempt to describe the marks it makes against the
other 'fixed' rulers of our framework (i.e. we measure it's various
co-ordinates). We find that we fail miserably in the following sense:
no self-adjoint operators can be found that enable us to interpret the
ruler as a set of localised particles (corresponding to ruler marks)
which transform in a consistent way with those of our background
rulers! At least, this is what we find if we assume Lorentzian rulers.
If we use Galilean rulers, then we can describe the behaviour of a
ruler adequately, but this is unacceptable since we know our
background rulers are *actually* Lorentzian and not *approximately*
Lorentzian.

Well, in these theories we have a difference between parameters,
such as time and location, and dynamical variables. The angle of
a clock hand is a dynamical variable, as is the distance
of an object from one end of a ruler. On the other hand, the
supposed time and location of the various events are parameters,
and we consider the dynamical variables which track the putative
parameters as closely as possible. The QM no-go theorems tell us
that we can't have dynamical variables which are in perfect sync
with the parameters.

R.