Addendum: Fearful Symmetry

In my earlier review I neglected to mention what might even be considered the punchline of the whole symmetry story. The symmetries of ordinary life are of time and space - translation and rotation. The gauge fields that underlie the strong, weak, and electromagnetic forces have a different character, associated with rotation in some mysterious internal "space." Early in the twentieth century Kaluza had a remarkable idea, further developed by Klein: suppose that in addition to ordinary space there were attached a tiny circle to each point, too small for us to notice, making a total of four space dimensions and one of time. Add gravity to this, and voila!, electromagnetism emerges. The circular symmetry of the hidden dimension produces the gauge symmetry underlying electromagnetism.

It turns out that if we add more dimensions and other symmetries we can produce other Yang-Mills gauge fields - the stuff of all the forces. There turn out to be some problems, like the electron winding up with a gazillion times too much mass.

Fast forward six decades to string theory. String theory also needs extra dimensions, and likes them to be curled up. A hasty marriage with Kaluza-Klein is arranged. God still has his little jokes though. Superstring theory can sort of fix the electron mass - it makes it zero - but string theory has its own ways of making gauge fields and doesn't need Kaluza-Klein symmetries.

TBD - or not.

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