M Theory and other versions of string theory seem to require a number of additional dimensions to work and because we do not experience life in 10, 11 or 26 dimensions it is assumed that these are compactified.
So my questions are as follows:
Are the dimensions compactified just to satisfy the cosmological principle that we do not occupy a special region of spacetime?
There are currently thought to be ~10^500 potential solutions to string theory. Would it simplify this to assume that we are in a 4 dimensional subset of a higher (10, 11 or 26) dimensional space? Or would it make matters more complicated?
Following on form the answer to the above question, other than violating the cosmological principle what is the problem with assuming we are a subset of a larger spacetime?
Also doesn’t this assumption mean that there is a potential solution to the problem of [action at a distance](http://en.wikipedia.org in that /wiki/Action_at_a_distance_%28physics%29) in that if entangled particles are 4D representations of higher dimensional objects then any instantaneous “communication” between particles takes place in the higher space and therefore can be instantaneous (to us) without violating special relativity. I hope this last part makes sense.
A couple of short answers until the pros get here.
The higher dimensions of string theory need to be hidden because we don’t see them in any of our ordinary observations. It’s not necessarily true that they must be tiny - some theories can make them just as infinite - but the world we live in has three measurable spatial dimensions plus one of time. It cannot have four spatial dimensions that are “visible” because orbits are not stable in four spatial dimensions and we would sure notice that.
You should take a look at brane theory to see how multi-dimensional structures - even universes - can have lower-dimensional subsets.
I don’t even understand most of your questions, though, and I have a hunch that’s because you don’t understand what you’re asking well enough to phrase the questions properly. However, that may very well just be me.
Thanks for the reply, I just used the 4D description because I was too lazy to write 3 spacial dimensions and 1 time.
I think I understand what I’m asking as I majored in astrophysics, but sadly my maths isn’t good enough to get to grips with Brane theory without a little outside help.
I will have a think to see if there is a way in which I can better phrase my questions.
In particular about what’s hard to understand about your questions:
Since the string model does assume that we’re in a 4 dimensional subset of a higher-dimensional space, assuming that makes things exactly as simple as the string model, no more nor less.