Quantum Gravity

Here is one of two methods that help explain. The next post will follow tomorrow if I have time. The complexity of the pictures involved is linked down below in Fig 15-17. This will give some generalizations that I had been looking too, to comprehend the model of strings and its geometrical discriptions.

Continuity



Topology is the branch of mathematics concerned with the ramifications of continuity. Topologist emphasize the properties of shapes that remain unchanged no matter how much the shapes are bent twisted or otherwise manipulated.

Such transformations of ideally elastic objects are subject only to the condition that, for surfaces, nearby points remain close together in the transforming process. This condition effectively outlaws transformations that involve cutting and gluing. For instance a doughnut and a coffee cup are topologically equivalent. One can be transformed continuously into the other. The hole in the doughnut will be preserved as the hole in the handle of the coffee cup.










Topology becomes an important tool in superstring when it is treated as quantum mechanical object. This branch of mathematics is concerned with smooth, gradual, continuous change of geometric shape. For example, a square can be continuously deformed into a circle by pushing in the corners and rounding the sides. The essential rule is that no new hole can be created in the new form by tearing. Some topological equivalent objects are shown in Figure 15-17.

Unfortunately I lost the link to this quote and if someone could remember seeing this, I hope you will let me know.

We expect that the divergences of quantum gravity would similarly be resolved by introducing the correct short-distance description that captures the new physics. Although years of effort have been devoted to finding such a description, only one candidate has emerged to describe the new short-distance physics: superstrings. Vibrational modes

This theory requires radically new thinking. In superstring theory, the graviton (the carrier of the force of gravity) and all other elementary particles are vibrational modes of a string (figure 1). The typical string size is the Planck length, which means that, at the length scales probed by current experiments, the string appears point-like.

The jump from conventional field theories of point-like objects to a theory of one-dimensional objects has striking implications. The vibration spectrum of the string contains a massless spin-2 particle: the graviton. Its long wavelength interactions are described by Einstein's theory of General Relativity. Thus General Relativity may be viewed as a prediction of string theory!

This highlighted print tells us a lot, about the higher dimensional values assigned to spacetime as being a result. If we were to entertain the holographical consideration of these higher spaces manifesting into the spacetime curvature, that we have come to know and love, then we have indeed not only used Klein to travel to the fifth dimension but have come back home, to what GR represents for us a sa tangible?