An Introduction to String Theory

Slide 10 of 37
<<   [Outline]   >>

When I say that momentum along an extra dimension is "invisible", I mean that we simply can't detect it directly. It's as if we can see that there's the black speck of an ant down on the tightrope, but we can't make out whether it's sitting still or walking around the rope, much less how quickly it's walking around. (It may help to imagine a transparent tightrope...)

That separation of momentum into "normal" p and "extra dimensional" p shouldn't come as too much of a surprise. In a way, it just comes from the Pythagorean theorem. For example, in two dimensions, p² = p_x² +  p_y². Think of the "extra" dimension as just another direction, like y.

In Quantum Mechanics, it turns out that only specific p_extra values are allowed. That leads to a discrete "tower" of observed masses for every fundamental particle! (If the extra dimension is very small, we will see that these "internal momentum" states are very heavy, which would explain why we have not yet observed them in particle accelerators.)

As it turned out, using extra dimensions to unify gravity with electromagnetism directly didn't match experimental observations, so the idea was more or less dropped for 50 years or so. In the meantime, physicists explored Quantum Mechanics.