Other Dualities: Geometry and Force

According to string theory, the universe is composed of the product of 4-dimensional space-time, \(\mathbb{R}^4\) , and a compact space which is 6-dimensional. Physics can be “geometrically engineered,” in the sense that the forces and particles of nature can be interpreted in terms of the geometry of this compact 6 dimensional manifold. Just as Einstein told us that gravity is a manifestation of the curvature, or geometry, of space-time, string theorists contend that much of the physics we see is dictated by the shape, or geometry, of the hidden 6-dimensional manifold found at every point in space. The theory holds that we live in \((3+1)\) space-time, and maybe 6 (or 7) hidden dimensions. Where are the hidden dimensions? Well, a telephone wire, as seen from far away, looks like 1D as in Fig. 85 , but we can see it is 2D upon closer inspection. Macroscopic space is 3D, but just as in the case of the telephone wire, there could be additional hidden dimensions that are too small for us to see.

Illustration for Other Dualities: Geometry and Force

Figure 85. Extra dimensions can appear upon closer inspection.