An Introduction to String Theory

Slide 9 of 37
Small "Extra" Dimensions
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One new question that arises is "Why do we live in a world with three dimensions of space and one of time?" Some of the earliest work on this idea was due to Kaluza and Klein in the 1920s, just a few years after Einstein came up with the General Relativity on which their work was based. (We'll focus on extra dimensions of space; as far as we know, extra dimensions of time would always lead to bizarre effects that are clearly ruled out in the real world.)

Now, how could we possibly not notice a whole other direction to move in? It turns out that if that direction were to "wrap in on itself" in a very small circle (or other "closed" shape), we could be totally oblivious to it. I like the tightrope analogy here as an explanation of how that could be.

It turns out that being "very small" isn't the only way that we might not notice extra dimensions. Believe it or not, given our current experimental tests, it is even possible that there is an extra dimension almost a milimeter around!

In general, extra dimensions must be "finite" (or in mathematical language, "compact"), or we could see them. (There are a few other ideas out there, too, but I won't discuss them here.) If there were several extra dimensions, they could all be circles (a torus), or they might combine into more complex shapes (like a sphere). Extra dimensions with boundaries (like the two ends of a line segment) get complicated, but they can be very interesting, too.

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