vanhees71 said:
Since it's not clear, what "beables" are in a precise physical sense, it's hard to say.
Let's assume that we by "beables" of a particular observer, we mean the retained information of all it's past interactions(inferences). At any point of time(any NOW), all this just
IS. This set can even be taken as the label for the observer itself. You define the obsever/agent, from what is "knows".
An observable on the other hand is not something that IS, it's rather a potential linear operator. At best the beables are a reasult of a sequence of local measurements by an observer. But the general agent-measurement is likely not described by just a linear operator projection.
In this view, the structure of be beables can not just be made up from nowhere, they are expected to be a result of evolution, following the results of inference/observation and evolution. So the observables and the beables should bear some relation. (It is an open problem still to use this to arrive at constraints on the beable structures - which would of course in the end some how be related to the constraints on the structure of matter, as the physical basis of the beables must be matter, or "confined energy" to be more general)
vanhees71 said:
It is simply a mathematical feature of gauge theories that only gauge-independent quantities have well-defined physical meaning, i.e., they describe observable phenomena, while gauge-dependent ones cannot, because they are not uniquely defined by the physical situation to be described.
This is similar to that the inference from a single observer/agent, can not uniqely define the situation. Because one perspective is not exhaustive. Similar to that in quantum tomography one needs a lot of measurements to determine a quantum state. What you mean by "physical situation" needs to be described by the joint information from all possible observers. And the observers has to be able to communicate and form a consensus. But this presumes an evolved communication channel and communication protocol. Spacetime and the fields of interactions are what must encode these communication channel and protocol. So the subjective choices(gauges) needs fields to counter for the distorted communication, this the creates an agreement as per speficic symmetries.
This actually works as long as all the possible obsevers are only related by poincared transforms withing the classical environment, and that the system we study complexitywise is SMALL and shortlived relative to the classical context.
But if we want to understand why spacetime is 4D, and why all the fields look like they done, and how the forces are related as one changes energy and observational scales, I think thinking of this as just "consistency" conditions is not helpful. It's not "wrong", it's just not helpful, and it lacks a deeper level of understanding. This is why the questions I posed, seems silly in the context of the domains where standard QT shines. But the questions become more meaningful when you try to increase explanatory value, or entertain more general measurement situations.
I am trying to translate the procedure used in the lab, down to an individual agent/observer level. As we humans are clever enough to control the whole classical environemnt, what is the "observer" in the conventional they is not the single physicists, it is, at least for localised experiments, the whole classical environment and laboratory with all the detectors. I think this is also how Bohr thought of it. But as you consider the information capacity that exists in the classical laboratory, related to an atom. Alot of things can not be traslated to the sitation where you consider instead that the atom, is observing it's environment.
The problem with QT, is that the observer is not allowed to be arbitrary, it must be dominant and classical, and inside observers, which you have in the cosmological perspective does not satisfy the necessary premises to implement the standard procedure of how to perfom experiments in a particle lab. I think this perspective is the missing link to merge with gravity and unify things.
/Fredrik