| Firstly, I note your > as a Physicist So, while I could let your "basic forms" do some heavy lifting in your second sentence, I would like to draw your attention to: > entirely different languages First, let's start with the Hamiltonian formulation : https://en.wikipedia.org/wiki/Initial_value_formulation_(gen... which leads us to https://en.wikipedia.org/wiki/Canonical_quantum_gravity cf. https://en.wikipedia.org/wiki/Second_quantization or if you're not looking deep into compact objects (astrophysically) or concerned with theoretical UV divergence problems, Perturbative quantum gravity (quick lecture) https://webspace.science.uu.nl/~hooft101/lectures/erice02.pd... vs https://en.wikipedia.org/wiki/Perturbation_theory_(quantum_m... Numerical methods can be even more similar: there's several approaches to gravitation on the lattice, for instance, that would be familiar to lattice QCD people. Programmes to make use of objects used by HEP (Lie algebras, configuration/phase/state spaces) for strong gravity are not accidental. > You can do quantum field theory in a curved spacetime Birrell & Davies likes to stress "Curved Space" (as in the textbook's title).
It's not a band-aid at all, it's a first approximation, up to the so-called one-loop level. There are higher-order approximations. It's not the 1960s any more, and especially after the 1982 Nobel (the same year as Birrell & Davies was published), I think it's not super-controversial to argue that every good physical theory is an effective theory, even if the characteristic scale has not been determined. > why are the electromagnetic, weak, and strong interactions described by a totally different formalism to gravity? > certainly seem disparate Teaching tradition! Also fossilized successes of https://en.wikipedia.org/wiki/Abductive_reasoning But to me a variational approach on the Ricci curvature tensor (following Pirani https://journals.aps.org/pr/abstract/10.1103/PhysRev.105.108... ) and on the Faraday electromagnetic tensor (Bondi & Pirani started this in http://www.theory.physics.ubc.ca/530-19/planewave-bondi.pdf ) are very similar, not very disparate. Indeed, you can see how one arrives at the spin-2 gauge boson for the former (symmetric rank-2 tensor) in the same way one arrived at the spin-1 gauge boson for the (totally antisymmetric rank-2) Faraday tensor. But this is certainly not a successful approach to a "full theory of all four of the interactions", however it led to "just" an effective field theory that is good to shorter lengths than we likely will be able to probe any time soon. |