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One interesting thing to come out of theoretical physics in the last 30+ years, but only formulated in the last 10 or so is something called the "holographic principle". There are several alternative (and vague) formulations. It is not known which one, if any, will be ultimately correct ["ultimately" meaning: correct in a hypothetical theory of quantum gravity].
One of the forms of the principle is that the entire quantum state space of a region of space maps to the quantum state space of its boundary. This is suggested by Hawking's blackhole radiation theory and the identification of thermodynamical entropy with the area of the event horizon. Area would be a measure of the size of the state space of the boundary (and of the unobserved interior). Identifying thermodynamic entropy with information entropy one arrives at an identification of geometric area with information entropy. Geometry is information!
This is very similar to the classical (not quantum) Euler-Lagrange variational principle works. One specifies an "action" functional which is supposed to be extremal given boundary conditions. In this case the space of bulk solutions can be identified with the space of (valid) boundary conditions. The duality between the two corresponds to Lagrangian vs. Hamiltonian mechanics. The connection with Quantum mechanics comes from Dirac's insight (formulated rigorously by Feynman) that the minimum action principle is the saddle-point approximation of the phase of the quantum amplitude in the path integral formulation. But the holographic principle is not the same thing as the Euler-Lagrange principle, or at least nobody has been able to get anything useful out of the idea that they are the same.
Another bold idea that the universe can be arbitrarily divided into two parts by a boundary, and that the holographic states on the boundary describe the two parts of the universe on either side, and their interactions. The boldness comes from imagining that somehow combining this with the holographic principle and the identification of area with information entropy will result in a theory of quantum gravity.
This is all very exciting but it is not physics. It's physicists thrashing about in confusion because of the lack of experimental guidance.
Finally, since you talk about spacetime emerging, I'll quote a comment I wrote a week ago:
quantum mechanics presupposes the existence of Newtonian time. Quantum field theory pressupposes the existence of Einsteinian spacetime. You can get away with quantum field theory on stationary spacetimes because there you have a proxy for "Newtonian time". String theory is not very different in the way it appears to require a highly symmetric "background". But things like Hawking radiation are like the "old" quantum mechanics of Bohr and Sommerfeld. There needs to be a better theory. One in which somehow spacetime emerges.
Quantum field theory pressupposes the existence of Einsteinian spacetime. You can get away with quantum field theory on stationary spacetimes because there you have a proxy for "Newtonian time". String theory is not very different in the way it appears to require a highly symmetric "background".
But things like Hawking radiation are like the "old" quantum mechanics of Bohr and Sommerfeld. There needs to be a better theory. One in which somehow spacetime emerges.
We are not only looking at application. There is within a great, spontaneous pull towards this huge mystery, which we are in, which we are. And this inquiry cannot be brought to a conclusion via thought constructs which neccessarily fragment, inhabit a secondary subject-object divide and which can only lead to infinite regressions.
There is a curiosity to see what reality really is... we are reality after all, can we not look to ourselves for that which is also the same reality elsewhere? It seems to me that we can do that. Whatever thought construct or word salad that got us to taking this step would've been the way to here. And if that way had been peaceful then that would be the most auspicious of lives or times.
Space-Time as phenomena, not nouminon was intuited a long time ago in many different parts of the world. Emergent space-time begs the question "from where or what?" And then, this something which is the matrix of space-time would also be analaysed and the same question of its emergence would remain. This is an infinite regression.
So, I am not really sure there is a possibility of an infinite regression within science. Refinement and extension of the models dealing with specific physical situations, maybe. But if you manage to produce a mathematical model of quantum emergent spacetime, I am not sure any of the underlying model elements will be observable in principle, and the theory will deal with which are and which are not, again alone or in combination.
We still haven't come to terms with the epistemological implications of Quantum physics, but then again we haven't really come to terms with the epistemological implications of Kant, either. We have met the enemy, and he is us — Pogo
Reason is the tool of science, so it is the limits of reason that I am addressing. This is a more precise formulation of what I am trying to talk about. So, I take the question to be whether or not reason is limited in some way. We are concerned here with the inquiry of how did the universe come to be, or an inquiry about causality in ultimate terms. I don't think this can be concluded to the satisfaction of the intellect by trying to construct a chain of cause-effect. Are you suggesting that it perhaps could be, that there could be some answer of the thought-reason-language type that would conclude the question of the ultimate origin of the universe?
"But if you manage to produce a mathematical model of quantum emergent spacetime, I am not sure any of the underlying model elements will be observable in principle..."
I think this situation will be unsatisfactory to the intellect and it will try to somehow model the unobervables. Each stage of the inquiry and model building can only lead to further questions... ad infinitum.
As I have said before I believe that science/reason is immensely valuable, its just that as a tool or mode of knowledge I believe it has definite limitations, which if not spotted could cause confusion and madness. Some inquiries are just not amenable to reason, but there are other ways too.
I believe there are hints of this in current work in theoretical high energy physics, which by focusing on quantum cosmology, the big bang, and quantum gravity has ever more tenuous links with experiment. At some point it becomes "metatheoretical" physics, in which one develops theories not to explain phenomena, but to explain theories of phenomena. This may be a satisfying intellectual pursuit to some, but Physics it may not be any more. We have met the enemy, and he is us — Pogo
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