Particle physics of quantum field physics and gravity of general relativity are incomplete, that is a given. My usual reflections when I read something like this is instead to ask for examples of why these theories are “staring each other in the face without talking” and “whether gravity was quantized” given that there is a perfectly consistent quantum field theory for everyday physics, which Wilczek calls Core Theory.
“It’s a good equation, representing the Feynman path-integral formulation of an amplitude for going from one field configuration to another one, in the effective field theory consisting of Einstein’s general theory of relativity plus the Standard Model of particle physics.”
“… if you only want a theory that makes sense when gravity is weak, like here on Earth, there’s no problem at all. The little notation k < Λ at the bottom of the integral indicates that we only integrate over low-frequency (long-wavelength, low-energy) vibrations in the relevant fields. (That’s what gives away that this is an “effective” theory.) In that case there’s no trouble including gravity.The fact that gravity is readily included in the EFT of everyday life has long been emphasized by Frank Wilczek. As discussed in his latest book, A Beautiful Question, he therefore advocates lumping GR together with the Standard Model and calling it The Core Theory.”
Distler describes how Core Theory is a perfectly useful theory. “It’s often said that it is difficult to reconcile quantum mechanics (quantum field theory) and general relativity. That is wrong. We have what is, for many purposes, a perfectly good effective field theory description of quantum gravity.” “Nonetheless, at low energies, i.e., for
we have a controllable expansion in powers of ε. To any finite order in that expansion, only a finite number of couplings contribute to the amplitude for some physical process. We have a finite number of experiments to do, to measure the values of those couplings. After that, everything else is a prediction.
In other words, as an effective field theory, gravity is no worse, nor better, than any other of the effective field theories we know and love.
The trouble is that all hell breaks loose for ε∼1. Then all of these infinite number of coupling become equally important, and we lose control, both computationally and conceptually.”
Given a low energy flat background at this time by way of cosmology, we should be fine with an effective quantized field theory that is incomplete, but where all our basic theories talks with each other and that has gravity included on an equal footing.
Or at least that is what this layman glean from some of our proficient theoretical scientists. I really don’t understand why popular science descriptions then routinely and without ever giving references inserts incompatibilities where there seem to be none.