Midterm Question 3

Imaginary time is this mathematical model that Hawking introduces to explain the shape of time and space. These imaginary numbers in the model are supposed to be at right angles to the regular real numbers. Imaginary time is just an idea to help us understand the different directions of the universe. In real time, as time (or the history of the observer) increases, space also increases. In imaginary time, as time increases, space can either decrease or increase. Einstein’s theory of relativity combines real time and three other dimensions of space that together make up a four-dimensional spacetime. In this spacetime, even though time increases in the direction of real time as described earlier, the other three dimensions of Einstein’s theory could cause an increase or decrease in the direction of space, similar to that of imaginary time. Then, as time is increasing, space could be going in the other direction.
This brane theory is a part of the M-theory, in that it can have a variety of spatial dimensions. A brane (p-brane) is one of many objects that can be extended in more than one direction. A brane has a length in p directions and can have a variety of spatial dimensions. So a brane with length p = 1, would be equivalent to a string. A brane with p = 2 would be a surface. A brane with p = 3, would be equivalent to a four-dimensional (3 space, 1 time) surface. According to the equations of the supergravity theories, the p-branes could be found to be 10 or 11 dimensions. Most of these (like 6 or 7) dimensions are so small we don’t really notice them. The remaining four dimensions are big enough for us to see and feel their effects. The brane theory then has four (the others are too small) dimensions – three space dimensions and one time - which are just like the model from Einstein's theory. Spacetime then, can move in any direction.