The idea of extra spatial dimensions goes back at least to the 1920s, with the now-
famous work of Theodor Kaluza and Oskar Klein. More recently, in the context of
string theory, the concept of extra dimensions underwent a phase transition. It is
no longer categorized as an intriguing speculation, but instead it has evolved into
a persuasive theoretical construct. String theory requires for its consistency the
existence of six or seven extra spatial dimensions, depending on which formulation
is used.
But no one has seen any sign of these extra dimensions, and indeed the 1/r2
character of both gravity and electrostatics appears to be a clear signal that space
is three-dimensional. For n space dimensions, the spreading of flux lines would
produce a force proportional to l/r™_1. If there are extra dimensions, they must
be very effectively hidden from view.
For many years the only theoretical idea for hiding these dimensions was com-
pactification: the extra dimensions were assumed to be curled up into a microscopic
structure, with a size scale set by the Planck length, ^JflG/c3 ~ 10-35 m. This
assumption kept the extra dimensions impeccably sheltered from experimental
challenge. The idea may of course be correct, but there is an obvious motivation to
explore more potentially observable alternatives.