One of the most disturbing aspects of General Relativity is the 'Marble versus Wood' duality of the theory: Matter creates curvature, and curvature doesn't create curvature (at least not directly)
The holographic principle suggests a reason for this division: matter fields and gravity are paired to structures that exist in different dimensions: so 4D gravity (if taken over a finite region $\Omega$ of spacetime) should be paired with some (abstract or actual) 3D (2 spatial+1 time?) boundary $\partial \Omega$ where a QFT of some sort exists, but the curvature in this 4D spacetime is dictated by 4D distributed matter fields, which themselves might be related to some 5D gravity (possibly actual, but maybe unobservable) that has the 4D spacetime as part of its boundary.
Arguably one could extend this idea to lower and higher dimensional mappings. Besides the pragmatic but inherently hard question about what could be gained by such insight, I'm asking if
Has anyone tried to formulate physical theory in terms of a hierarchy
of such mappings?
It seems that such formulation would have to deal somehow with the fact that the boundary operator is nilpotent ($\partial \partial \Omega = 0$) when defining the hierarchy
So, if the set $HM(D)$ gives all the possible meaningful holographic mappings between compact manifolds of dimension $D$ and their boundaries, then one can imagine that a full description of physics could be achieved by experimentally finding the elements $hm_0, hm_1...hm_X$ with $hm_i \in HM(i)$ and $X$ some maximum dimension above which all different mappings become completely unobservable at 4D
This post imported from StackExchange Physics at 2014-06-03 17:01 (UCT), posted by SE-user lurscher