Published: 11 January, 2006

In the brane world, there are 10 dimensions, not just 3

How many dimensions are there?

We can move up and down, forward and backward, and left and right. These are the 3 spatial dimensions that we can experience in our daily lives. So our common sense tells us that there are 3 dimensions. This is a basic fact of nature. Stretching your arm forward, you can rotate your arm so that it points in any direction you want (to point backwards, you may have to move your body). While you are doing this little exercise, the clock is ticking. That is, time is moving forward.

This was our understanding until a century ago, when in 1905, Albert Einstein came up with the theory of special relativity, which has been shown to be correct to a very high accuracy. In special relativity, time is treated almost like another dimension; one may perform a special type of rotation between space and time, which is called a boost. Nothing can be accelerated to move faster than light. Also, energy equals mass times the speed of light squared. In an elegant mathematical framework, time is treated as another dimension, so we may consider space-time to be 4 dimensional.

Einstein then went on to unify special relativity with gravity. Mathematical consistency led him to the theory of general relativity, where space-time is curved. Again this theory has passed many tests. In the past 100 years, it became very clear that we live in a quantum world, where atoms, molecules, and electronics obey quantum rules quite differently from our daily experience. It is natural for scientists to unify quantum mechanics and Einstein's gravity. This turns out to be a very challenging problem. Many great minds (including Einstein himself) had tried over the years. Twenty years ago, such a theory was finally discovered, namely, the superstring theory. The theory is very deep. After an intensive effort over 20 years by hundreds of physicists and mathematicians, we have some idea what the theory is telling us. To start out, the theory has 10 dimensions, 6 more spatial dimensions than our experience tells us. We believe these 6 extra dimensions are curled up into tiny sizes, much smaller than atoms, too small to be detected with the most powerful microscope.

Consider ants crawling on a tabletop. In their daily experience, they can explore only 2 dimensions, those of the table surface. They may see a bee up flying, or occasionally landing on the table top, but that 3rd dimension is something they can only see or imagine, not experience. Perhaps we are in an analogous situation. Instead of a tabletop, we live in a 3-dimensional space called 3-brane (a name generalizing 2-brane, i.e., membrane). For some reason, we (i.e., atoms, molecules, photons etc.) are stuck in this 3-brane, even though there are 6 additional dimensions out there. Gravity, like the bee, can go everywhere. We call this the brane world, a rather natural phenomenon in superstring theory. At the moment, physicists are working hard to understand this scenario better and to find ways to experimentally test this idea.