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Brian Greene and other string theory proponents envision the first three "extra" space dimensions (beyond the three space dimensions we know well) as akin to a tiny sphere affixed to each locus of our normal three dimensions. These tiny spheres, with their additional three dimensions, are not as yet detected b/c they are so tiny. At our scale, and even at the scale of the most powerful microscopes we have today, the additional dimensions are undetectable because they are "folded" back on themselves, contrary to the "unfolded" dimensions we normally experience. Thus space seems smoothly three-dimensional for us. Even Greene admits imagination fails him in trying to describe what it really means to have additional dimensions beyond these six space dimensions.

I believe that physical theories should ultimately attempt to describe physical reality: what is really real? Accordingly, what on earth does it mean to have ten space dimensions? It seems likely that such postulates are merely mathematical artifacts not indicative of physical reality.

For example, envision an electron (or whatever particle you prefer) at location x, y, z. With seven additional space dimensions, it's full physical location would be described as x, y, z, a, b, c, d, e, f, g. And t for time. This means that for every particle we can pinpoint at a given locus x, y, z, there are actually seven possible "real" locations for that particle. In other words, every particle we locate in 3-space has seven versions. What forms the boundaries between the location of these particles? If there are indeed distinct dimensions beyond the three we know of, how do particles in these additional dimensions interact? I know Greene's imaginary spheres are just that - imaginary - but they are meant to suggest some physical reality of the extra dimensions. It seems to me that mathematical physics has gotten ahead of the need for empirical realism.

This is one reason why I think people like Lee Smolin and John Moffat are probably correct in generally rejected the validity of string theory.