Logic of E-H action, ricci scalar, cosmological constant?

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SUMMARY

This discussion centers on the logic of Einstein's equations, particularly the Einstein-Hilbert (E-H) action, the Ricci scalar, and the cosmological constant. The E-H action is expressed as S_{EH} = k ∫ R dV - 2k ∫ Λ dV, where the cosmological constant is expected to be almost zero. Participants explore the implications of statistical reasoning on the Ricci scalar as a "density of information divergence" and the cosmological constant's association with discrete information. The conversation emphasizes the need for a deeper conceptual understanding of General Relativity (GR) and its foundations in quantum gravity.

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  • Knowledge of the Ricci scalar and its significance in GR
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Physicists, mathematicians, and researchers interested in the foundations of General Relativity, quantum gravity, and the interplay between information theory and physics.

  • #61


Fra said:
It's a bit like Zurek's sentiment that "What the observer knows is inseparable from what the observer is".

This means that in my representation, an observer is technically a system of related microstructures, and this system is the observer. So the information is the identifier of the observer. And information is evolving, and identification of observers are a result of spontaneous structure stable formations which are relations to it's environment.

An implication of this, is that there is not much sense in the notion that "two different observers has the same information" if we by this also also means that the information has the same confidence levels etc. Because if two observers really have the same information, then the two observers conincide.

The distinction between observers, is measured by their disagreement, which in turn is measured by their interaction. And with observer, I also include any subsystems of the universe. And my idea is to extract from the process of disagreeing (a process of communicating opinions) the structure of interacations.

So my picture is that the laws of physics and the physical interactions, are the laws of information processing and communication. And to incorporate the "observer" in these "interactions" is to include the information processors or transcievers in the communication.

This is to me a generalisation of Einsteins Gravity, in that spacetime itself "responds" to the the dynamics in spacetime. IE. the observers "respond" to the communication that is relative to them. The result are evolving observers. And the observer-observer interactions, analysed starting from the simlpest possible observers and scaling up the complexity, should chart out the structure of all interactions. Classifications will emerge here.

/Fredrik
 
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  • #62


Fra said:
This is to me a generalisation of Einsteins Gravity, in that spacetime itself "responds" to the the dynamics in spacetime. IE. the observers "respond" to the communication that is relative to them. The result are evolving observers.

This also shows the problem. Given the original association the geometry of spactime responds to what's going on relative to it, the missing step was still, exactly how does this relation look like. Einsteins equation is a solution to this in GR.

In this case, the question is, exactly HOW does the interaction "the observer" participates in provides a selection for it's evolution. This is the problem I am trying to solve in my way. At first there is the simple idea of random walking towards some optimum, as per some ME principle, but the interesting part is that the space the walk takes place in is also dynamical, and the optimum is moving. So there is no global optimum, just some strange kind of relational optimum. This is a bit unpredictable and I don't know for sure what will come out of this, but I've already convinced myself that a local speed limit in line with lorentz stuff will be emergent, but this is deformed as everything evolves. I also think a universal attraction of structures will emerge, and I think this can explain gravity. And the supposed "explanation of this attraction" lies in the connection that causes an evolution in the observer, given interactions it participates in.

That is a lineout. But the details are in progress of course. Unfortunately I have not found that awfully many existing papers that is doing just this, although many approaches share elements of tihs.

/Fredrik
 

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