How String Theory Actually Accomplishes Grand Unification

Many introductory explanations of string theory tend to feel mysteriously unsatisfying. The focus is usually on its implication of extra dimensions or the now popularized metaphor of the strings in the theory being akin to the strings on a violin, with the different vibrations of the infinitesimal strings producing different elementary particles just as the vibrations of a violin string produce musical notes.  Yet, digesting this information alone fails to connect it to the claim that has brought string theory its popular glory, that it is a potential “Theory of Everything” capable of uniting the previously irreconcilable pillars of modern physics. This part is usually glossed over with the simple assertion that this is just what it does.  In the midst of trying to grasp string theory’s profound and novel view of the universe it’s easy to lose sight of this issue of foremost importance: how exactly does it purport to seam together quantum mechanics and general relativity? Here, we will try to understand first, what the rift between QM and GR actually is, and second, how string theory resolves it.

Let’s first take a brief look at the main theoretical rift between the two theories, which will frame our subsequent discussion of the correlate physical rift. In essence, general relativity describes how the geometry of the spatial fabric transmits the force of gravity. Gravity is one of four fundamental forces, the others being the electromagnetic force, the strong force and the weak force. The three nongravitational forces have all been mathematically incorporated into quantum mechanics respectively in the theories of quantum electrodynamics, quantum chromodynamics and quantum electroweak theory, which all introduce a “messenger particle” that transmits the force (e.g. photons transmit the electromagnetic force). Physicists have failed to formulate a corresponding quantum theory of the gravitational force with the methods used for the other forces (which, as we will come to understand, involve a “particle” interpretation). Since the gravitational force is described by general relativity, and quantum mechanics cannot incorporate gravity, we see that this is the main theoretical rift between QM and GR. String theory, with its “string” interpretation, successfully incorporates a quantum theory of gravity with a messenger particle called a graviton.

Explanation of the physical rift should add a more clear and concrete understanding of why GR and QM don’t mesh. A central principle of GR is that space is smooth, like the surface of a bowling ball. QM, however, dictates that on ultramicroscopic scales, space is actually a violent torrent of irregularity, like the back of a porcupine, referred to as the “quantum foam”. The quantum foam originates from the fact that empty space really isn’t empty, as Heisenberg’s uncertainty principle informs us. In reality, “empty space” is really full of virtual particles instantaneously popping into being and annihilating each other. Clearly, the smooth space described by GR is at odds with the bubbling foam described by QM.

The key to string theory’s strategy for a solution is to replace the traditional interpretation of the fundamental constituents of the universe - zero dimensional point particles - with 1 dimensional strings. String theory’s claim is that the elementary particles that we see as points, if observed at a finer scale of resolution, are actually strings that have spatial extent but are simply too small to make out with current technology. If the string interpretation is indeed correct, this puts a fundamental limit on how small space can be – a limit that the point particle interpretation does not impose – because the fundamental constituents of the universe would then have a tiny amount of spatial extent. How does this address the problem of the quantum foam? Well, the effects of the quantum foam only become prominent at extremely small scales of space, below that of the “Planck length”, a millionth of a billionth of a billionth of a billionth of a centimeter. The minimum size limit introduced by strings turns out to be above the size where the quantum foam would take effect. In this way, string theory resolves the physical conflict between QM and GR because it essentially removes quantum foam from existence. Even though it is still a mathematical possibility, string theory says that the foam does not materialize because, at least in our universe, space does not get small enough.

Currently, there is still no experimental proof of strings, but string theorists note that this is because technology does not yet have the ability to probe the miniscule scales necessary to observe them. It would be quite astounding if it turns out that we have been deceived into imagining protons, neutrons and the like as round, circular points when they are really tiny filaments of string.