Hey Rushil,
As others have pointed out -- this idea that everything is describable as higher dimensional ripples of spacetime is very pretty and has a well developed history. The first incarnation, and the broad heading under which most of these theories are classified, is Kaluza-Klein theory. The germinal Kaluza-Klein idea is that we can mathematically consider how general relativity would work in five dimensional spacetime and see that if the fifth dimension is wrapped up (compactified) into a circle of constant scale (the cylinder condition) then the equations we get out are the equations of four dimensional spacetime coupled to an electromagnetic field. Objects moving in the compact direction have an electric charge corresponding to that momentum. This works perfectly, and it gets even better when we consider symmetric spaces more complicated than circles. It turns out there is a seven dimensional symmetric space with symmetries that give all the standard model force fields: electric, weak, and strong. So, at first look, the answer to your question is n=11 -- all the forces of the standard model and gravity can be treated as the ripples of an 11 dimensional fabric, with 7 of the dimensions wrapped up small in a special way.
But there are problems. To complete the correlation with the standard model, we need to also find geometric descriptions of a scalar Higgs field and spinor (electron, quark) fields within this higher dimensional space idea. The Higgs fields can be found by getting rid of the cylinder condition -- letting the symmetric space wiggle and change scale a bit. But getting the spinor fields to pop out right from this picture is harder. (I've worked a little on that.) Things don't work correctly when we use the most obvious extension of spinors over the 7 dimensional symmetric space. This is the "chiral spinor" problem that hurt Kaluza-Klein theory in the late 80's. Also, if one does allow the symmetric space to wiggle, there are all sorts of other particles predicted that we don't see (the tower of KK modes). So, the Kaluza-Klein idea doesn't work perfectly when done the most obvious way.
But one can tweak things to try and get everything to come out right. One interesting thing to try is to add torsion -- which is a geometric field describing a twist of spacetime. Using this means giving up the equivalence principle of GR in its familiar form -- a price most aren't willing to pay. But if you do use torsion, which fits well with GR mathematically, you can get chiral spinors out, and get the standard model nicely using only a four dimensional symmetric space (called CP2). But, as I said, this takes some messing around with the original premise. And there are still problems.
String theory relies on Kaluza-Klein theory as a background in which the strings dance around. And people spend a lot of time playing with theories of surfaces and strings moving around together in various spaces. But this sort of thing requires a lot of outlandish speculation and doesn't work very well to produce the standard model or gravity -- which are the two theories solidly backed by experimental verification.
Really, quantum field theory already sort of describes things as ripples ON spacetime and works spectacularly well to describe almost all particles and interactions. (So one has to learn that first before dabbling properly in these wilder ideas.) But your idea, and Kaluza-Klein theory, is about getting fields as ripples OF spacetime.
And then there's the subject few want to touch. Our universe is fundamentally quantum. So what you'd really like to see pop out of these geometric theories of dancing higher dimensional spaces is a quantum field theory that matches up with what we know works. Almost no one works on this -- it's currently taboo. And I don't think anything will come together properly until people work on this too, in order to have a chance of seeing the whole thing at once.
Well, that's more or less a ramble on the subject... hope it's more than just confusing. And, of course, to really make sense of this, or anything in physics, you have to do the math.
that does not change when PhD is in front of your name (actually I never use this word). Second, I percieve your question in two ways: (a) can our physical theories be poored into this classical view (b) does nature satisfy this picture? (b) is the most tricky question and the matter has not been settled yet. (a) is more easy to answer : 
