I agree that the CS might be the most physically relevant thing, but at the end of the day the integration over LIPS volume is essentially classical physics (including SR). All the quantum stuff is in the matrix elements.
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The RG seems special to me in science writ large. Given the information the couplings encode, we can roughly characterize how sensitive our theory is to the unknown (underlying theory space) and thus hedge our bets against theory change—the great challenge to realism.
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One of the first things we want an element in our ontology to satisfy is “survival,” and since we can run the couplings to retrieve the dynamics at any scale over which our theory is defined, we seem to have something of an advantage wrt. the rest of science
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