An Elegy for a String: Exploring the Rise and Fall of the Theory of Everything

The first versions of string theory required 26 spatial dimensions, but after supersymmetry and discarding some dimensions, theorists reduced this number to only 10 dimensions. The universe does not have ten spatial dimensions, at least on large scales; Therefore, the number of dimensions should be small and mixed. When you shake your hands, you actually traverse these infinitesimally small dimensions, but these dimensions are so small (usually on the Planck scale) that you cannot see them.

With more dimensions, the options of string vibration to describe the whole physics are increased. On the other hand, these dimensions can take various forms during vibration and winding, which are called Kalabi Yao manifolds. If you fold a piece of paper back on itself, you have a few choices: you can connect a pair of edges together (cylinder), or you can connect two pairs of edges together (donut shape), or you can connect a pair of edges upside down (ribbon Mobius) or connect both upside down (clean bottle). This variety is obtained only in two dimensions. With six dimensions, you can reach 10 to the power of 500 to 10 to the power of 10,000 possible options.

All possible shapes are important because how the higher spatial dimensions stack up determines the possible set of vibrations of the strings. So that each shape, like different musical instruments, has a different set of string vibrations. For example, the sound of a trumpet is different from the sound of a saxophone because of how it is organized and the type of vibrations; But our universe is just an instrument (perhaps a wind instrument) with a single set of notes corresponding to forces and particles.

So which of the thousands of possible Kalabi Yao structures correspond to our reality? we don’t know Because we do not have the complete calculations of the string theory and we are only dealing with estimates. On the other hand, we do not know how the shape of the folded dimensions affect the vibration of the strings. We have no reliable device that makes its way into physics from Kalabi Yao’s manifold and appears in the world, so we cannot discover the shape of folded dimensions by performing inverse operations and using unique physical experiments.

The problem of supersymmetry

In the 1990s, string theorists developed five different versions of string theory. These changes were obtained based on the fundamental behavior of string theory. In some versions all the strings had to form closed loops while in others they were open. In some versions, the vibrations were one-way and in others two-way, and thus various changes were applied. These five theories are: type I, type IIA, type IIB, heterotic SO(32) and heterotic E8xE8.

Therefore, the number of theories increased unnecessarily. Five potential theories that all claim to be the best approximation of true string theory. It may seem strange, but in the 1990s, a physicist named Edward Witten declared everyone a winner.

Witten discovered dichotomies. Dualities are mathematical relationships between theories that allow one theory to be transformed into another. In this example, Witten transformed five string theories into a single knot. This idea has not yet been mathematically proven, but it suggests that the five string theories are actually statements of a single unified string theory, which Witten called M-theory. We still don’t know what M theory is and even what M stands for, but it must be real string theory.

This ideation can be useful because when approximations are judged to be valid, all five versions of string theory must converge on it, and the world is full of mathematics; But this happened nearly thirty years ago and we still don’t know exactly what M theory is. We have not even reached a solution for string theory.

To put it more clearly, our inability to understand string theory is not limited to experience. Even if we could set up a super collider experiment that would reach the energies necessary to decode quantum gravity, we still wouldn’t be able to test string theory because we don’t have a string theory. We also do not have a mathematical model that can make reliable predictions, and only estimates that we hope represent the actual physics in an accurate way. We can also test these estimates, but this does not help us understand the inner workings of the model.

Even if all the conditions are met, the tests we perform will not be completely useful. When supersymmetry was developed by the string theory community in the 1970s, it became a popular idea that many particle physicists tried to adopt. They attempted to develop energetic physics models beyond the Standard Model.

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