Compactifying dimensions

Note: while I previously accepted this idea, I recently was confused as to the details behind how exactly the 5th dimension in KK theory is actually “wrapped up”, from an infinite dimension to finite “cylinder” of sorts (or the commonly used analogy of a loop available at each position in spacetime). This is all mostly explained away by the notion of compactification, whereby an infinite dimension is “wrapped up” and is then traversed periodically. This is different from the previous examples I’ve seen with mathematical compactification, whereby the real line is projected onto the unit circle. This probably needs a little more expansion; perhaps both could be possible explaining the “wrapping up” of the extra dimension.

Sources

• KK theory seminar report