String Theory in Three Minutes

A cross-section of a quintic Calabi–Yau manifold. A Calabi–Yau manifold is a special space that is typically taken to be six-dimensional in applications to string theory. It is named after mathematicians Eugenio Calabi and Shing-Tung Yau

20th-century physics says everything is made up of point particles with a bunch of different properties. But where do these properties come from and where does gravity fit in?

Particle physics is a bit of a misnomer — modern understanding suggests these particles are excitations in quantum fields. So, really, field physics is more appropriate — this is incomplete too since we fail to explain gravity. Turns out, we can get a self-consistent explanation of all particles and gravity if we concede that they’re tiny little strings. The way these strings vibrate determines their properties and ultimately, the particle. Instead of points tracing out lines (as in Feynman diagrams), these strings trace out two-dimensional surfaces as they move through space and time. This is how we describe interactions between them.

Worldlines of point-like particles or a worldsheet swept up by closed strings in string theory. Image by Author.

As for the nature of these strings, it turns out they can be both open and closed loops and their vibrational mode defines their characteristics. Now, the unification of particle physics and gravity is certainly a victory so what’s wrong with string theory? Well, for the theory to even begin working, you’d need upwards of 11 dimensions, and then some exotic ideas follow through. Bosonic string theory is 26-dimensional, M-theory is 11 while superstring theory only requires 10.

We only experience three spatial dimensions and one temporal dimension. So, we have to think of ways these other dimensions are hiding. Compactification is one way of modifying the number of dimensions in a physical theory. We assume some of the extra dimensions are “closed up” on themselves to form circles. A standard analogy for this is to consider a multidimensional object such as a garden hose. If the hose is viewed from a sufficient distance, it appears to have only one dimension, its length. However, on approaching the hose, you’d discover that it contains a second dimension, its circumference. So, an ant crawling on the surface of the hose would move in two dimensions while we’d only perceive one.

Source: xkcd

And finally, to make matters worse, It doesn’t help that we’ve had no experimental triumphs vindicating this theory because strings are theorized to be in the domain of Planck lengths; the smallest theoretical length.

As always, thank you for reading and have a great day (or night)!