PeterDonis said:
What does this mean? Where are you getting it from?
To give a mathematical theory of the "inside observer" and it's interactions, is of course an open issue, i have no answer.
But conceptually en external observer is external to the system of study, where it can without principal limits prepare, control and monitor the system of study and make repeats to get statistics. The systems back-reaction onto the observing context, is limited to updating counters or state revisions. No need to worry about the observer beeing saturated with information, or dominated by the system. This is like the normal observer in QM, where essentially the whole classical environment is the observer.
An internal observer is one that is rather existing "inside" the system. So the internal observer essentially observes all of it's own environment. So the usual "preparations" and acquisiton of confident statistics etc isnt possible the same way. In this case hte backreaction from the system onto the observing context cant be ignored. But there is not quantum theory for this, but this doesn't mean one can entertain it's conceptually.
It's like an extension of the tradition of gedanken observers of Einstein, where he essential pondered about what observer in various states of motion would observer, taking it further seems unavoidable when pondering about howto unify QM with gravity, as the inside observer is the natural thing.
Especially in a computational perspective, the difference between external and internal observers become important as an inside observer is conceptually constantly overflowed with information, and has to simplifly, compress and decide what to discard. An external observer, such as a big lab, studying atoms, don't have the same problem, here only time limits the inferences.
Towards Physics of Internal Observers: Exploring the Roles of External and Internal Observers
"Following Einstein's thought experiments, one could ask: What would it look like to sit inside a photon or to be a photon? And what type of observer could represent this more global perspective of the photon's interior? To address these questions, we introduce the concepts of internal and external observers with a focus on their relationship in quantum theory and relativity theory"
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https://arxiv.org/abs/2304.01677
The concept of inside or intrinsic observers in different context are older than Einstein though, even Riemann was seeking the "intrinsic measures" of geometry by considering what can be measured by inside observers. But the concept can be generalized to the inferred theories. As we know, Einstein mainly worried about states of motion, but if one considers also the encoded information, we get the well known weird information paradoxes and other things. How can one understand the invariance of the laws of physics during these transformations? And the point of my post was really that, perhaps transient violation of some observer equivalence relations are unavoidable in order to understand this. Ie. to what extent CAN we understanda "equivalence" between two observers can simply can't hold comparable amounts of information? Exemplified by the extreme of the external and inside observer?
/Fredrik