Introduction
These new theories that have been presented involve more than the typical four dimensions. Ten and even eleven dimensions have emerged. So, what are these extra dimensions and in what form do they exist?
Current Four Dimensions
Sensory experiences give us information about a 3-dimensional world that includes width, height, and length (or depth). We all can comprehend these three dimensions simply by moving in our 3-d world. Einstein claimed that there was also a fourth dimension: time. Much like we can move in a 3-dimensional world, we also move through time (forwards and backwards). These four dimensions present a world with three space dimensions and one time dimension.
Six Dimensions
The notion of any extra dimension to the four known dimensions was conceived by the Polish mathematician Theodor Kaluza in 1919. Kaluza thought that extra spatial dimensions would allow for the integration between general relativity and James Clerk Maxwell’s electromagnetic theory. Suported by Swedish mathematician Oskar Klein in the 1920s, these extra dimensions were actually minute, curled-up dimensions that could not be detected due to their extremely small size. These two mathematicians said that within the common three extended dimensions (that we are familiar with) are additional dimensions in tightly curled structures. One possible structure that could envelop six extra dimensions is the Calabi-Yau shape, which was created by Eugenio Calabi and Shing-Tung Yau.
One More Dimension
Are there infinite dimensions simply curled up into smaller and smaller structures?
M-theory, which attempts to unify the five theories, requires one more spatial dimension than the five individual string theories. This new dimension was actually overlooked in past work because the calculations done were only estimations; this mathematical error blinded physicists from seeing this extra dimension. As new dimensions have been found, it begs the question as to whether there are only eleven dimensions? Are there infinite dimensions simply curled up into smaller and smaller structures?
Branes
The word “brane“ is derived from “membrane“, a 2-dimensional surface on which objects can move. Branes are essentially the same because the either one or both of the endings of an open string are moving on them. The image below shows the configuration called a Dirichlet-Boundary-Condition.
But in contrast to a traditional membrane, branes can have between negative one and ten dimensions. To distinguish between the number of dimensions involved, branes are written as ‘Dp-brane,’ where p is an integer that represents the number of dimensions. Some of these dimensions even have special qualities. Maybe you were wondering about a brane that contains a negative one dimension. This is a brane that is fixed in both time and space and is called a “d -instanton.: If p equals zero, then all spatial coordinates are fixed; thus, this structure is called a “D-particle.” A D1-brane is then consequently called a “d-string.” A D9-brane is not spatially fixed (neither in time nor in space) because it fills the spatial dimensions completely. For this reason, a string bound to a D9-brane can move around freely in space. This condition is called a Neumann boundary condition.
Sources and Links
- “D-branes.” Viewed: August 2004. < http://www.sukidog.com/jpierre/strings/dbranes.htm >.
- Greene, Brian. “The Elegant Universe.” Vintage Books, New York: 2003.
- “Imagining Other Dimensions. “ NOVA: the Elegant Universe. Viewed: August 2004.