The Many Dimensions of Dimensions III

Today we return to the topic of dimensions. This time we will look at the history and physical effects of having extra dimensions in the Universe....

It seems obvious that the Universe has three dimensions. From the perspective of the reader, there is the forward/backward direction, side-to-side direction, and up-and-down direction. And most of the people reading this site already know that Einstein's theory of relativity makes time into a fourth dimensions like the others. (Actually the time dimension has a few different properties, but those are unimportant for now)

But what if there are more dimensions? Maybe they are too small to see, or maybe light doesn't penetrate them, or perhaps our minds are just not able to comprehend their existence! As strange as this idea sounds, the existence of extra dimensions has become a very hot topic of research in recent years.

HISTORY

As a serious research topic the idea of higher dimensions goes back to the era 1915-1926 with the work of Nordstrom, Kaluza, & Klein. Einstein had already formulated the general theory of relativity in which we live in a four-dimensional universe in which spacetime is distorted by the presence of energy. It reproduced Newton's theory of gravity in calculations where that theory was known to be correct, and improved on it by successfully predicting several other measurements.
Almost immediately people began to wonder what would happen if instead of a four-dimensional Universe we lived in a five-dimensional Universe. The result was amazing - the 5D GR equations reproduced the 4D GR equations, and added four new equations which were identical to Maxwell's equations of electromagnetism! By adding a single dimension, general relativity can predict the existence of electric and magnetic forces!
The only problem was that we do not observe and higher dimensions. The solution given at the time was that they could be tiny. A straight line is one-dimensional, as is a piece of rope when viewed from far away. But if you get closer to the piece of rope, you see that it also has thickness, and in fact has a two-dimensional surface. The same idea work for the Universe - we view it as four-dimensional, but perhaps if you had a very powerfull magnifying glass you would see that each point of space was in fact a very tiny ring or a ball and that there was in fact another unseen dimension. (Of course there are reasonable arguments that our minds could not comprehend these extra dimensions even if visible.)

Unfortunately that was the era in which quantum mechanics was fashionable, and no one bothered to continue with extra-dimensional physics. Then in the 1980's the idea was re-opened. Several new theories, including string theory and supergravity, were found to work only in certain numbers of dimensions (usually 10,11, or 26). Although these theories were later found to be less useful than originally thought, the idea of extra dimensions remained.
Experiments started looking for these extra dimensions and found nothing. It became clearer that if they existed they would be ridiculously small. Then another revolution hit in 1998, with suggestion of a Universe in which all known particles and all electromagnetic and nuclear forces are somehow trapped on a four-dimensional membrane that exists in a five-dimensional (or higher) universe. Until that time all the experiments had focused on searching for the effects of extra dimension on light or on particle properties. The limits on this new model allowed for extra dimensions as large as 1 mm (~1/25 inch).

To Be Continued...