Our Universe is massive...or is it really small?
As was stated in the introduction, the total energy of the string results in the fundamental particles that make up matter. This energy consists of the Winding Energy & Vibrational Energy. Remember the Calabi-Yau manifolds- just a fancy name for the curled up 6-dimensions we canŐt see? Well, this figure consists of multi-dimensional holes around which strings can wrap (we see a two-dimensional analogy in Figure 7.) The wrapping around of these dimensions by the string gives the string what we call Winding Energy. This energy is proportional to the size of the radius of this dimension. To understand how the Vibrational Energy relates to the radius of the dimension we have to understand a fundamental aspect of quantum theory previously unmentioned. Like a person confined in a small room for too long, a particle gets "stir-crazy." The smaller we try to confine a particle, the greater its vibrational energy becomes. To truly understand why or how this comes about, you have to throw logic to the wind...which is exactly what Quantum Theory usually does. Thus if we make the circular dimension smaller, we confine the string, and thus increase its vibrational energy. Let us assume the radius of the circular dimension is R times the size of the Planck constant. By making certain calculations we find an amazing result. If we analyze what happens when a string wraps around a circular dimension of radius 1/R we find that the Winding energy of the original string becomes the Vibrational energy of the new string and vice versa. Since these two strings just swap their two types of energy, their total energy remains the same, and thus their physical properties remain the same. What this all means- the physical properties of the universe are the same in these two different geometric representations.
How Can a Universe Immeasurably Small be the same as a Universe Extremely Large? Robert Brandenberger, a physics professor at Brown University, along with a Harvard colleague helps explain this paradox. Brandenberger discovered that a circular dimension has two notions of distance. One distance is measured with the use of unwound string, and the other is with the help of wound strings. Conveniently enough, the wound string distance in Universe A is exactly the same as the unwound string distance in Universe B, and vice versa. Why is it that we know only one distance? Just as physicists do, we use light (photons) as our distance indicators. The light we receive in our eyes helps us measure distances, just as we can use fancy machinery to time how long it takes light to bounce off an object, and then determine the objects distance. Well, there is another way to measure time, or so we thinkÉ..its just that no one has ever come across it before. Assuming that the three extended dimensions we are living in are circular, then it is possible that there are strings that wrap around the dimensions & thus our universe. According to these strings, the universe is very small. How small? Small enough for them to wrap around.