Hi Ian,
On a final note and then I let you go. First of all thanks for your interest and your reply in my blog. Time is just the hardest thing to understand. So I think it is better to leave time as external parameter until some ideas have been clarified. This does not hinder the argument.
In a static picture one can apply the ideas of semantically closed theories on quantum reference frames. If we have a quantum reference frame, where for physical reasons, there are only finite degrees of freedom, then only limited information on the objects can be accessed. For instance if only finite SU(2) representation are possible, than such a reference frame is not able to uniquely distinguish an up and down spin in the direction of the reference frame. This is called degradation of a reference frame. It leads to a probabilistic description even for a spin collinear with the reference frame. The probability is due to an epistemic limitation on the exact (classical) distinguishability of all the 'directions' (elements of SU(2)) and the back reaction of the object on the reference frame. So it is assumed that the real symmetry is the full SU(2) but the limited resources leads to a statistical description, like statistical mechanics.
If we demand the theory to be semantically close and the limitation is a physical one, like the finite size of the universe or the system would collapse in a black hole, then the epistemic limitation has to be taken seriously and has ontic consequences. To close the theory, I suppose the group has to be replaced by another one, that does not pretend, that there are infinite resources. I would not know, how to do that. But I can imagine that some additional quantum effect could result from this.
In a way, when Heisenberg went to Einstein, telling him, that only observable elements should enter the theory and Einstein replied, that it is the other way round: the theory tells, what is observable. This is true for naive realistic theory. Semantically closed theories would do Heisenberg's intuition justice, that theoretical terms should be physically realizable.
One could play a kid's game: Kid: what do you mean by spin? Me: a finite (2 dimensional) representation of the 'rotation group'. K: What is that? M: A description, that if you measure any direction, you know how probable you find an up or down result relative to that direction. K: What you mean by 'direction'? M: This is where a gyroscope points. But one needs a infinite sized gyroscope in order to distinguish all directions and having no back reaction. K: But this is absurd. The gyroscope would collapse into a black hole. Are you explaining a concept with something that cannot exist physically.
Thanks for the conversation
Luca