Sol2,
I'm not quite sure where we're headed here, but the main proponents of extra dimensions tend to favor compacitifacation ( ala Kaluza - Klein ) and embrace string theory where these quantities do have an pronounced effect at Newtonian and relativistic levels while all the time being by their very definition unable to be examined because they reside at at lesser then the Planck length. Magic, Science or the Emperor's new clothes? All the Maths seem to work correctly.
I agree with your assessment that T is not a dimension as we think of in the traditional sense.
going sideways.
I have kicked around both an idea of inherent charge on the universe and an extra macro dimension ( which engenders nothing but derision) The latter is the model most simple and intrinsically "Beautiful" , the former was an old idea and my interest was reignited when a correspondent mentioned that he had similar leanings. The problem with the first is that the G at square of the difference becomes the cube of the distance. That is the main critique. My objection is that we discard Newton at Q and cosmological scales, why does he reinsert himself without err in this instance. The lemma is a confrontation with hundreds of years of physics. Not an easy go. The former is elegant but requires "now" a compensation for the varying Hubble expansion.
What we are discussing here is OOT , but for 4000 Yrs. the Hindu's talk about the river of time, for ~<100 Yrs. Einstein's t, for less then~ 30 Feynman's arrow of time and Hawking's light cone. Parsing your link You seem like many ( myself included) to want find a concrete background which Einstein "disproved". Well the punch line is that Einstein's "Biggest mistake in my life" -Lambda, MMX's Aether, dark energy, may after all be correct.( which funny enough doesn't appear to be static!)
My basic belief is that there is a quasi-static background, which is neither accessible or usable to quantify the dynamical properties or our universe .One may tout brane or string theory or the many universes hypothesis but we have yet to approach accommodation of unity. The whole impact of Einstein on me has been not the maths ( which basically are unsolvable ATT ) but his words about the inherent beauty of truth.
John Baez gave a talk at GR-17 regarding QLG and spin foams, there's an adjunct theory/book by Ambjorn on simplicial gravity called "Quantum Geometry" I have not read the text, but the intersection of his view and Baez's appearers to be interesting.
Joao Magueijo at Imperial Collage has a view of VSL , which at origionally was applicable at the first inflationary stage after the BB, but has migrated to "special zones" where it remains a dynamical metric ...
My point being that even the most sacrosanct of cosmological constants such as G,t and dare I say it, c are questionable.
I'm sure Antonio may take exception at my last remark .
The more we learn , the less we know.