One of Physicists primary objectives is to find a Grand Unifying Theory (GUT). The point of this GUT is to unify all of the four fundamental forces that we observe in nature into one complete theory that can explain them all. There are many GUTs in existence but the most primarily focused upon GUT is a theory that goes by the name String Theory. Since String Theory seems to be the most promising GUT at the moment and has been for many years, I will use current literature to highlight and explore the implications, problems, and possibilities with String Theory.
In this section I will focus on some of the details of exactly what I mean by “unifying fundamental forces” and explain some of the technical details needed to understand the following points. In nature we observe four forces. These forces are the Strong, Electromagnetic, Weak, and Gravitational. The Theories that are behind them are Chromodynamics, Electrodynamics, Flavordynamics, and Geometrodynamics. Their strengths are in decreasing order. In order to give you a relative look at the difference between the strengths I will list the differences giving the Strong force a simple strength of 10. The electromagnetic force is of power 2 less than that so 10^-2. The Weak force is 10^-13 and the gravitational, the weakest of them all is exponentially weaker at 10^-42. All of these forces have mediators and I will list them in respective order. Gluon, Photon, W and Z, and the Graviton. The goal of string theory is to unify all the underlying theories. This has proved extremely difficult although we could easily see this take place in our lifetimes. Whoever finds this theory first will most certainly win a Nobel Prize, as this will be the most significant finding in physics ever.
All fundamental particles have wavelike and particle-like characteristics. The main assumption behind string theory is that every elementary particle is a string, a very tiny string that vibrates in space. Depending on how fast this string vibrates dictates what particle is represented. Sounds easy enough, right? Wrong. The hard part to cope with in string theory is trying to combine quantum mechanics and gravity and then being able to discuss string excitation that will carry the gravitational force. Intense math is needed to even work with this implication.
A primary objective in string theory is collapsing six dimensions into one. Let me explain. Currently there are 4 known dimensions in our galaxy. Those dimensions are 3 space dimensions and time. String theory requires 10! There is a name for reducing these extra dimensions, it is “compactification”. One way to compact these dimensions is to look for more. You may think of it like looking at a ball from extremely far away. It will look like a dot, which would be 1 dimension. If you get a little closer, but not too much closer it will look like a disc, now you have two dimensions. Now lets get right near the ball. You can obviously see that it is a three dimensional object. So maybe there are unseen dimensions hidden or “curled” up that we need to look for.
The question arises, why is time a dimension? The reason that time is a dimension is as follows. Einstein’s theory, General relativity, takes space and adds curvature, which we call space-time. In space-time space and time are intertwined, curved, and twisted by matter and energy that resides in this “fabric”. The two main ideas that scientists are focusing on are Kaluza Klein compactification, this is where the extra dimensions are rolled up into some kind of space of their own, and braneworlds. In braneworlds the extra dimensions are really large but they hold all of matter and forces in a 3 dimensional subspace. This subspace goes by the name “three brane”. The question at hand is, what characteristics can we look for experimentally to see if there actually are extra dimensions? The most promising thus far is called supersymmetry. The reason that supersymmetry is a feasible attribute to look for is because it could take place at a low enough energy that would be obtainable with current accelerator detectors. Bigger and better particle accelerators are indeed currently being constructed as we speak to further experimentation in this field and to explore fundamental particles and try to find attributes that could result in finding a GUT.
The energy needed to test string theory is extremely high. It would need to be in the neighborhood of 10^14 GeV. This high of an energy is impossible to even get near in any particle accelerator that exists to this day. The probability of us building a particle accelerator in the near future that could reach this energy level looks bleak. When a nuclear bomb goes off, the amount of energy released is usually in the Mega Electron Volts region. To get to the Giga Electron Volt region we would have to produce the energy of a million, million, million nuclear bombs going of at the same time. Although, we can look at the weak interaction where a neutron turns into a proton, and likewise, an electron decays into a neutrino. In this GUT something similar can take place with a proton. A small amount of beta decay can occur and it would be extremely noticeable. But the stability of the proton is why we exist. It is a pillar of stability for the world as we know it. So it doesn’t occur often, if at all. Many experiments have been set up to detect this reaction but none have seen it thus far.
Without getting too deep into the math of this example I would like to show a problem in physics which string theory explains, thus adding to the credibility of the theory. Black holes are stars that are so dense that their escape velocity is greater than the speed of light (3*10^8 m/s). It was shown that black holes can decay by quantum processes and that they have the physical properties of entropy and temperature. Physicists found that the temperature of black holes is inversely proportionate to its mass. Because of this relationship the black hole gets hotter as it decays. It was also shown that the entropy of a black hole is one fourth the area of the black holes event horizon. This implies that as the star decays the entropy gets smaller and that the event horizon becomes smaller as well. String theory helped provide a relationship between quantum microstates of a “quantum theory” and physically it can successfully explain black hole entropy.
Some subjects in math that are being studied right now that help further the study of string theory are K-theory and Noncommutative geometry (NCG). K-theory is a highly complex math that lets us examine the braneworlds and such associated with string theory. NCG, in short as well, is a geometry for the quantum world. Geometry as you and I know about, is only valid for a 3 dimensional world, the one we observe. NGC allows us to work with string theory as well. For a long time people (since the 40’s) have been trying to quantize space-time in a manner such that its coordinates were not real numbers. Over time this turned into quantum operators that obey a nontrivial quantum commutation relation. That’s where the name “noncommutative geometry” was derived from.
String Theory is an exciting topic in physics if not the most exciting. It is promising and its implications are boundless. If we came up with a valid and complete version of string theory would that be the end of physics? Would all of physics be complete? That is a question that cannot yet be answered. As we have not found a valid GUT, and maybe one does not even exist. The possibilities are endless but I think that we are looking in the right direction.
Much work, funding, and research must be focused on this theory to validate or altogether disprove it. The math involved with string theory, or any GUT for that matter is atrocious. You must have a very solid mathematical background to even approach it in a non quantative manner such as I have tried my best to do so in this review article.