Exploring Manifolds Beyond Spacetime: Unification Programs in Quantum Gravity

[jlcd]

Any papers about manifolds beyond spacetime? It's because the quantum objects may not be embedded in spacetime at all (which is where our current quantum gravity programmes work).. but other kind of manifolds where Einsteinian spacetime and quantum objects are emergent from them? What are the unification programmes along this line?

 

[Chronos]

You need to define 'beyond spacetime' before it can be addressed

 

[spacejunkie]

Take a look at Ed Anderson's "The Space of Spaces". http://arxiv.org/abs/1412.0239

 

[jlcd]

You need to define 'beyond spacetime' before it can be addressed

Beyond spacetime -> Non-manifolds based. I think I read the Perimeter Institute has mentioned this in one of the papers but forgot which is. Without manifolds.. how do you translate spacetime to another mathematical structure that can take the Bell Correlations even light years apart too? Remember that even if in default or ambient mode, no signal can be sent faster than light.. there is something faster than light correlations going on in the background. Who knows.. it may be the default or ambient mode.. meaning if you use the non-manifolds structure that give rise to quantum mechanics and relativity as emergent.. you can bypass the limitation of c in Spacetime... Most important.. what model can offer all this possibility? What research programme has looked into this?

 

[torsten]

One possible research program is the Causal set theory of Rafael Sorkin and co-workers. But it seems you look for another representation of quantum theory?
In that case check out the approaches using model (or topos) theory especially forcing.
Interesting for you is maybe also my own approach using exotic smootness where I identified wild embeddings (wild knots, Alexanders horned sphere etc.) with the quantum states. This approiach uses smooth manifolds but got naturally very wild mathematical objects (like foliations leading to factor III von Neumann algebras).
Here is a link: http://arxiv.org/abs/1601.06436
Smooth quantum gravity: Exotic smoothness and Quantum gravity