> I would go even further: Natalie Wolchover only interviewed string theorists and quantum field theorists. They all assume that gravity in some way or another will just be yet another quantum field theory.
I didn't want to push that point too much. I am personally uncomfortable with the lack of emphasis on empirical evidence. However, that's not to say there can be fruitful results.
In terms of re-thinking geometric approaches, I quite liked (what I understood of) Nima Arkani-Hamed's suggestion for avoiding issues with localization. Similarly for Penrose's twistor theory.
The idea is to focus on the amplitude of scattering interactions from the momentum-space twistor perspective, rather than perturbations about a point in space-time.
For background: Nima made a name for himself by greatly simplifying complex particle interactions, from tens of pages of Feynman diagrams to around a page. I think of the above as an extension of that project. However, I don't recall all the details, as it's been six years since I went to his talk on this.
Oh yes, I've heard a bit about the Amplituhedron. Unfortunately, it only serves to simplify the perturbative calculations in Yang-Mills theories order by order, i.e. the Feynman diagrams. It doesn't describe the full (non-perturbative) theory, so it's not really a candidate for a replacement of "classic" local QFT.
Thank you for pointing this out; this accords with my recollection, but you clearly stated a fundamental issue with the approach in its current state.
I thought of the idea as more a sketch of how things might be looked at with a perspective change, rather than a full-blown theory (at least in the form I saw it in 2014). I guess I was holding out for the (highly unlikely) possibility of an asymptotic limit or something similar. It just seemed to be rooted more in reality than most of string theory/LQG. Of course, that could be my bias towards novelty!
> I guess I was holding out for the (highly unlikely) possibility of an asymptotic limit or something similar. It just seemed to be rooted more in reality than most of string theory/LQG. Of course, that could be my bias towards novelty!
I totally understand! I was quite excited about the Amplituhedron, too, when I first read about it!
I didn't want to push that point too much. I am personally uncomfortable with the lack of emphasis on empirical evidence. However, that's not to say there can be fruitful results.
In terms of re-thinking geometric approaches, I quite liked (what I understood of) Nima Arkani-Hamed's suggestion for avoiding issues with localization. Similarly for Penrose's twistor theory.