In 1905, Albert Einstein showed in his Special Theory of Relativity that space is intimately connected to time via the cosmic speed limit of light and so, strictly speaking, we live in a Universe with four dimensions of space-time. For everyday purposes however, we think of the Universe in three dimensions of space (north-south, east-west, up-down) and one dimension of time (past-future). In that case, a fifth dimension would be an extra dimension of space.

Such a dimension was proposed independently by physicists
Oskar Klein and Theodor Kaluza in the 1920s. They were inspired by Einstein’s
theory of gravity, which showed that mass warped four-dimensional space-time.

Since we’re unable to perceive these four dimensions, we
attribute motion in the presence of a massive body, such as a planet, not to
this curvature but to a ‘force’ of gravity. Could the other force known at the
time (the electromagnetic force) be explained by the curvature of an extra
dimension of space?

Kaluza and Klein found it could. But since the
electromagnetic force was 1,040 times stronger than gravity, the curvature of
the extra dimension had to be so great that it was rolled up much smaller than
an atom and would be impossible to notice. When a particle such as an electron
travelled through space, invisible to us, it would be going round and round the
fifth dimension, like a hamster in a wheel.

Kaluza and Klein’s five-dimensional theory was dealt a
serious blow by the discovery of two more fundamental forces that operated in
the realm of the atomic nucleus: the strong and weak nuclear forces.

But the idea that extra dimensions explain forces was
revived half a century later by proponents of ‘string theory’, which views the
fundamental building blocks of the Universe not as particles, but tiny
‘strings’ of mass-energy. To mimic all four forces, the strings vibrate in
10-dimensional space-time, with six space dimensions rolled up far smaller than
an atom.

String theory gave rise to the idea that our Universe might
be a three-dimensional island, or ‘brane’, floating in 10-dimensional
space-time. This raised the intriguing possibility of explaining why gravity is
so extraordinarily weak compared with the other three fundamental forces. While
the forces are pinned to the brane, goes the idea, gravity leaks out into the
six extra space dimensions, enormously diluting its strength on the brane.

There is a way to have a bigger fifth dimension, which is
curved in such a way that we don’t see it, and this was suggested by the
physicists Lisa Randall and Raman Sundrum in 1999. An extra space dimension
might even explain one of the great cosmic mysteries: the identity of ‘dark
matter’, the invisible stuff that appears to outweigh the visible stars and
galaxies by a factor of six.

In 2021, a group of physicists from Johannes Gutenberg
University in Mainz, Germany, proposed that the gravity of hitherto unknown
particles propagating in a hidden fifth dimension could manifest itself in our
four-dimensional Universe as the extra gravity we currently attribute to dark
matter.

Though an exciting possibility, it’s worth pointing out that
there’s no shortage of possible candidates for dark matter, including subatomic
particles known as axions, black holes and reverse-time matter from the future!