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We use renormalization arguments (and experiments) to change the couplings of a theory and suppress the higher energy physics (saying things like “whatever the fundamental theory, this will be true of the low energy theory.”). And we then get some set of fields, correlation functions, etc. My question is just about the possibility of, say, a theory of quantum gravity that compromises the renormalization arguments we’d been using to determine the sensitivity of EFTs to the space of possible high energy theories. So, perhaps the actual theory wasn’t included in the high energy theory space?

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    $\begingroup$ For one, we know EFTs are useful because we have experimental data to compare its predictions with (and dispel any serious doubts about its usefulness). Theory must explain data, not the other way round. $\endgroup$ – Avantgarde Oct 16 '18 at 20:33
  • $\begingroup$ @Avantgarde Interesting! I wonder if someone might respond by asking “how do you know that you’ve found the right theory, when other theories might explain the data just as well?” And what the response to them would be. $\endgroup$ – Hanguk Oct 16 '18 at 20:39
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    $\begingroup$ There is no 'right' theory when one talks about EFTs. The Schrödinger equation is not predictive for $p<m$ while the Dirac equation is (because it is relativistic). But it doesn't mean that one is right and the other is wrong; they are both useful, in their own regimes of validity. $\endgroup$ – Avantgarde Oct 16 '18 at 21:04
  • $\begingroup$ I might be misinterpreting you here, but I meant to include the regimes of validity in that question. So, we have a low energy theory of quantum gravity valid at scales below the Planck scale. And then someone poses the question I first asked and the one I asked in response to you. $\endgroup$ – Hanguk Oct 16 '18 at 21:19
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Physics theories model experimental data. Starting from the very successful Maxwell equations solutions, which model macroscopic electromagnetic behavior, the the solutions of Schrodinger's equation which clarified the spectra of atoms, to the good fit of the present standard model of particle physics to almost all data accumulated from the 1960s, physical theories are an encapsulation of a great lot of measurements, if the are successful. They are successful if they can predict new measurements correctly. If they are not falsified, they are considered validated and standard.

Thus , if a possible higher energy theory for quantum gravity does not embed the lower energy effective field theories, it might be a competing theory for gravity, but not for a theory of everything, in effect it will be a different effective theory.

A theory of everything headed by quantum gravity should embed all the validated by data effective field theories, otherwise it is falsified as a theory of everything.

The data trumps mathematics. Of course it might mean that nature has not given us a theory of everything

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  • $\begingroup$ Thanks for the response, @anna v! Going along with your answer, I guess I'm trying to ask whether anything specific to the high energy theory could compromise the claims our EFTs make at the scales/energies they're defined at. So, the low energy theory of quantum gravity, or quantized GR, makes some claims about dynamics at low energy. If someone tells us that "the high energy theory might not even be a quantum field theory, and so you can't use the RG flow to say how sensitive your theory is to the high energy theory," are they justified? Or do we just invoke the empirical data agreement? $\endgroup$ – Hanguk Oct 18 '18 at 1:08
  • $\begingroup$ In general, we are in the stage of reseach where mathematics has to be used to model nature, not words, as in older times, as with mathematics we can look to consistency with data. A chariot pulling the sun is a nice fairy tale in our age, it was considered a working proposition three thousand years ago. So "...and so you can't use the RG flow to say how sensitive your theory is to the high energy theory," is equivalent to a chariot in the sky. Only if the statement has hard mathematics that model data will be even considered. (just searched what RG flow is btw, too many abbreviations ). $\endgroup$ – anna v Oct 18 '18 at 4:32

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