String Theory

But wait... I thought this was Mathematics, not Physics!

Before I begin with the topic of String Theory, I want to touch on one of the prevalent ideas of the course: what is mathematics? Although I still haven't quite pinned down an exact definition for myself so far this semester, I would say that if we look to the past, one of the defining characteristics thus far of many mathematicians' work was an attempt at describing the world around them. String theory is another one of these attempts, and therefore rest easy knowing that I'm not terribly off topic with this brief introduction of String theory (link to "Making sense of String theory", a presentation by Brian Greene).  

Newton, Einstein, and Kaluza walk into a bar...

There are several advancements in describing the world around us which led to the development of String theory in the first place. Beginning back in the time of Newton, the idea of gravity was developed, and a mathematical model was made to describe the effect that it had on celestial bodies, as well as anything else that you cared to apply it to (as long as we stay away from the edge cases!). The one thing that Newton noted, however, was that while he could model the effect that gravity was having on the world around him, he could not think of a way in which the force of gravity could act across such large distances through the vacuum of space.  

Next up, several hundred years later, Einstein took a stab at this gravity thing. His theory says that space is like a lattice, and that matter warps space such that there is a "well" in the vicinity. This "well" drew in objects, and this is the "force" that Newton was modeling yet unable to describe.  

Shortly thereafter, Kaluza heard about how Einstein came up with his theory, and decided to try to follow the same idea to describe electromagnetism. Unfortunately, Newton had already used up all of the old, boring dimensions, so Kaluza had to be a hipster and come up with his own, new dimension; a fourth dimension. After some finagling, Kaluza showed that if we set up four dimensions mathematically such that Einstein's equations hold true, out pops the equations describing electromagnetism which had previously only been found experimentally!... Unfortunately, when this theory was looked at in more detail, and worked on by other great minds at the time, it was shown to not fit the physics of our universe. Although this theory itself didn't quite work out, this idea of there being more than three dimensions of space wound up being very useful further down the line in the development of...

String Theory

The overarching idea of String theory can be determined in much the same way that Calculus was developed in the 1600s (see how I went full circle?); if you take a physical object and look at it closer and closer and closer and closer, what happens? In calculus, we can look as close as we want at a curve, and therefore we can describe the curve's slope at any instantaneous point. In string theory however, we hit an elementary particle - a string - which makes up all other particles that we've heard of up until now (protons, electrons, neutrons, quarks, etc). The idea is that these elementary strings vibrate in different ways just like the strings of a guitar vibrate a different frequencies. When a guitar string changes the frequency that it vibrates at, the note that is produced changes. When the vibration of these elementary strings changes, different particles are formed. Instead of getting an A# or a Bb, we get protons or electrons.  

The ideas of this theory were fleshed out into the language of mathematics, and further play with the mathematics led to the idea that there are actually 11 dimensions; 10 dimensions of space, and one dimension of time. This might explain why Kaluza's theory didn't quite pan out.  

This all seems well and good, but how could we go about proving that this theory is true? After all, if you are willing to accept a few wild claims such as magic is real, and that wizards and witches are particularly good at hiding themselves from mere muggles, then the realm of Harry Potter could be true. One way that we are currently trying to show this theory may be plausible is through showing that these other dimensions of space do exist. At CERN, the LHC (Large Hadron Collider) is ramming particles into each other in the hopes that the collision will produce gravitons. This would result in less energy than the particles originally started with, suggesting that perhaps they traveled across the different, currently unobservable dimensions.  

In conclusion

String theory is a way in which we attempt to develop a unified theory of our universe. It happens to be based on mathematics. An intriguing question that I am currently trying to tackle in another venture of mine is why does mathematics even relate to the physical world in the first place? Why does this abstract concept of 7 + 5 = 12 relate to how many apples Sally has? The answers to this are difficult, but one thing is for certain; Newton would appreciate it if Sally would hold onto her apples better - gravity is hard enough to figure without MORE apples hitting his head.