Two days ago I bought THE ELEGANT UNIVERSE. My first question is: Mr. Greene states that a string is a one dimensionl string. 1. The nature of a string would require two dimensions, as I know it. 2. If these strings are to oscillate, needn't they be two dimensional? 3. How could it be one dimensional? Is he meaning it's literally one dimensional, or is he being a bit lax..
Recall that a line is one dimensional. You need to keep reading, he explains multi dimensionality of strings deeper in the book.
He actually means onedimensional. Why do you say that "The nature of a string would require two dimensions"? Imagine a cable, and make it extremely (infinitely) thin. In order to specify a point on it, you need only one number. By definition, it has then one dimension. In order to oscillate, the can be embedded in a higher dimensional space, but the string itself does not need to have any more dimensions.
Maybe a rookie question, but cant the inverse square law of expanding energy/matter describe our dimensia?
ahrkron - Yes I understand, but the drawings show them as a loop. And he says they're like a rubber band. He doesn't say a straight string, he says a loop, and draws a loop. A loop must be two dimensional.
Only if you are talking about the "interior" of the loop. However, the string is only the perimeter itself, which is a line. As such, any point on it can be completely specified via one number. It doesn't matter if such line is straight or not. In a similar way, the surface of a sphere is a two-dimensional space, just as a table top is; as far as the numner of dimensions goes, the apparent curvature (as seen from the 3D space in which both are embedded) does not matter. Maybe this will help: think about a point living on the string, able to travel along it. Regardless of the curves and twists the string may have, the point only needs one number to know any "address" within its world. Put in a different way, the structure of the manifold resembles that of any other line (straight lines included): a point on it has neighbors only in two directions (which you can call "forward" and "backward"). On the other hand, on a 2D space, each point has an infinity of directions to choose neighbors from, and it can characterize locally its neighborhood by using a copy of R^{2}.