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It's been argued rightfullly that a satisfactory formulation of a measurement theory that is to be consistent with gravity (I use this word intead of QM, to not confused current QM with a future understanding which may, or may not deform it) must somehow be formulated by an inside observer. Ie. an observer that is subject to the same issues as any other physical system. External or classical observers are simply an idealisation.

The same applies for "clocks".

But what does this mean? This is where my question comes in. I see two options.

If we described the clock as a part of the system we study, so as to get proper "relational" time, then what about the evolution of relations? They still evolve with respect to another kind of time - which conceptually we can think of as "cosmological time" without necessarily confusing it with the same term in the standard model.

Clearly this "cosmological time" does not in the same way correspond to a "clock time". But the question remains how to understand it their connection.

It's not enough as I see it to do like Pullin and Gambini to observe clocks part of the system, because this observation either implicitly makes use of a larger complex context, or ensembles.

This ultimately boils down to the problem of time as in getting rid of time by considering relational notions only, but one must not forget that relations also involve in the general case, and this "cosmological time" can not be reduced in the same way without assumptions of equilibrium in the state of relations. And then this assumptions needs at leat some level of argument to be acceptable?

/Fredrik