In a rare, insightful moment, Peter Woit offers his suggestions on where a deeper understanding of space-time and quantum gravity should be headed. I tend to agree with him.

The big problem with the supposedly now conventional view that spacetime needs to be replaced by something more fundamental that is completely different is of course: “replaced with what?”. A lot of attention is given to two general ideas. One is “holography”, the other Arkani-Hamed’s amplitudes program. But these are now very old ideas that show no signs of working as hoped. . . .

One lesson of the development of our best fundamental theory is that the new ideas that went into it were much the same ideas that mathematicians had been discovering as they worked at things from an independent direction.Our currently fundamental classical notion of spacetime is based on Riemannian geometry, which mathematicians first discovered decades before physicists found out the significance for physics of this geometry.If the new idea is that the concept of a “space” needs to be replaced by something deeper, mathematicians have by now a long history of investigating more and more sophisticated ways of thinking about what a “space” is. That theorists are on the road to a better replacement for “space” would be more plausible if they were going down one of the directions mathematicians have found fruitful, but I don’t see that happening at all.To get more specific,the basic mathematical constructions that go into the Standard Model (connections, curvature, spinors, the Dirac operator, quantization) involve some of the deepest and most powerful concepts in modern mathematics. Progress should more likely come from a deeper understanding of these than from throwing them all out and starting with crude arguments about holograms, tensor networks, or some such.

To get very specific,we should be looking not at the geometry of arbitrary dimensions, but at the four dimensions that have worked so well, thinking of them in terms of the spinor geometry which is both more fundamental mathematically, and at the center of our successful theory of the world (all matter particles are described by spinors). One should take the success of the formalism of connections and curvature on principal bundles at describing fundamental forces as indicating that this is the right set of fundamental variables for describing the gravitational force. Taking spin into account, the right language for describing four-dimensional geometry is the principal bundle of spin-frames with its spin-connection and vierbein dynamical variables (one should probably think of vectors as the tensor product of more fundamental spinor variables).What I’m suggesting here isn’t a new point of view, it has motivated a lot of work in the past (e.g. Ashtekar variables). I’m hoping that some new ideas I’m looking into about the relation between the theory in Euclidean and Minkowski signature will help overcome previous roadblocks. Whether this will work as I hope is to be seen, but I think it’s a much more plausible vision than that of any of the doomers.

From Peter Woit's blog "Not Even Wrong" on recent articles discussing the somewhat fringe notion getting attention of Space-Time unraveling.

## 2 comments:

(connections, curvature, spinors, the Dirac operator, quantization) What I’m suggesting here isn’t a new point of view, it has motivated a lot of work in the past (e.g. Ashtekar variables).

So what are your views on Ashtekar variables and LQG? What about spinors, and the octonion program promoted by many researchers including John Baez and N Fuery et al?

personally I'd like to see a theory that puts space and time on the same footing, that time is a kind of space. I've also wondered about complex spacetime, specifically Kaluza Klein theory with the extra dimensions describing additional dimensions in terms of imaginary numbers

Mitchell Porter

"in terms of the spinor geometry which is both more fundamental mathematically, and at the center of our successful theory of the world (all matter particles are described by spinors). One should take the success of the formalism of connections and curvature on principal bundles at describing fundamental forces as indicating that this is the right set of fundamental variables for describing the gravitational force. Taking spin into account, the right language for describing four-dimensional geometry is the principal bundle of spin-frames with its spin-connection and vierbein dynamical variables (one should probably think of vectors as the tensor product of more fundamental spinor variables).

What I’m suggesting here isn’t a new point of view, it has motivated a lot of work in the past (e.g. Ashtekar variables)."

what do you think of this ?

specifically

"(all matter particles are described by spinors)"

John Baez and N Fuery et al combine the spinors with octonions

" One should take the success of the formalism of connections and curvature on principal bundles at describing fundamental forces as indicating that this is the right set of fundamental variables for describing the gravitational force."

if successful would imply Ashtekar variables or something like it is fundamental

if you don't like LQG

could you create a new way to describe gravity in the formalism of connections and curvature on principal bundles perhaps with spinors and octonions and spectral triples besides Ashtekar variables

or even gravity isn't quantum mechanical but still describe gravity in the formalism of connections and curvature on principal bundles

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