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Good questions indeed. If its any comfort I am also looking for(working on) such models. But they are not ripe yet.What is the difference between observer in quantum mechanics and observer in relativity? Are they not equal? Should they be made equivalent by some kind of transformation? does this already exist in our physics?

And when you say observer.. do you mean a human or a machine observer?

Also I'm looking for the model where these degrees of freedom that precede spacetime can form some kind of structure that can hold the observer.. do you know of any models that explore this?

But Scrutinizing what an observer is, and what observation is, in the existing theories is a very good starting point.

I would say that an observer, is something(a physical system) that infers information about something else(called the system under study) by means of "observation". Roughly this "observation" must be some kind of physical interaction, where the observer extracts/gains information about the system.

*( Note: Nowhere (classical or quantum) does observer ever mean "human". This is a persistent confusion that cant be washed away. Certainly Niels Bohr wasn't talking talking about humans. Any later claims are IMO from people who simply misunderstood all this deeplyy. )*

First are two distinctions to make, or "passive"/classical vs "active"/quantum measurements.

- In classical mechanics - both special and general relativity - the physical process of observation, is assumed to be possible to make arbitrary small so that you can extract the desired information without distorting it.
- In quantum world, this is not possible becauase the process of acquiring information, changes the system. And not just at the classical way (which can be arbitrary small), but in a fundamental logical way. Ie. in quantum world you can not "copy" information without disturbing it.

I will not ramble too much but i claim that thi difference has deep confusing consequences if you later, elevate the state of law on par with state of the system (like i think we must do)!

But beyond this, there are essentialy one overall key constructing principle for physical law

- The laws of physics must be same for all interacting observers, meaning they should be able to communicate their observations and agree.

Note that one does not need for SR, to explain or "declare" in detail what an observer is, all that matters is how they are RELATED. And that is poincare transformations. Of course its presumed the existence of 3Dspace and time (this is certainly questioned if you take this to another level and attempt to model an observer and explain exactly HOW this "structure" can encode notions such as spacetime; but that is far beyond what Einsteins did)

One can then argue that the class of observers are larger, looking at those related by 4D diffeomorphisms, and argue towards General relativity. But also here, no attempt is made to explain what and observer is.

I would say thats related to the fact that its not necessary eactly because the observers observational interations are "passive".

In quantum mechanics OTOH, an observer is a classical measurement devices that is interacting with the system during "observation" in a way that can never be reduced to a passive observation. This is a big step forward vs classical mechanics. But combining this instrumental observer with the constructing principles of classical laws, become extremely complicated, becauase so far even in quantum theory the notion of "PHYSICAL LAW" is a classical concept.

This is something I've been given a lot of thought and there is a key conflict here. And different research programs have different stances to this. But those programs that take a deep stance and try to suggest a constructing principle for the structure of the observer; and put it into the above context seems to be absent. So what to you do? This has lead me to the insight of evolving law. It is actually not too alien from the evolution of the geometry leading to Einsteins equations, but there is a much deeper twist which is that the observer can not be passive, the observer is unavoidable encoded int this mess, in a way that noone yet seems to have understood well enough to describe it mathematically.

So if you dont find what you are looking for i have the answer for you - it means you have to create it yourself ;-) If you succeed come back and enlight the rest of us.

/Fredrik