4.2 Quantum Geometry

summary

Is there an absolute notion of fundamental particles?

- The main aspect of string theory is to understand quantum geometry—to unify general relativity with quantum mechanics. This is the biggest achievement of string theory.
- What have we learned about the quantum geometric aspects of string theory?
- The first thing we want to understand is if the notion of fundamentality is invariant. If we see an electron, or a photon, are those fundamental particles? Does everyone agree? Is this idea duality frame invariant?

What is the difference between an elementary and composite particle?

- In particle physics, we divide particles into two types: elementary and composite. We can imagine a nucleus of an atom being made of different constituents. Each one of those constituents could be elementary. Perhaps they, too, would have something that comprises them, but at some point you would expect to have a fundamental object.
- But it turns out in the context of string theory that even this idea is not duality frame invariant.
- One example is the idea of magnetic monopoles. Although they have never been found in nature, we can theorize about their existence, and it turns out they would have to be extremely massive. So we could imagine them as composite configurations of gluons and electrically charged fields, which behave as though they have a magnetic charge.
- We can change our parameters so that these configurations shrink down in size to a point. As this happens, the electrically charged object becomes larger and larger—meaning the object itself could in turn be thought of as consisting of many of these point-like monopoles!
- As the monopole shrinks to a point, it behaves like an elementary particle, and the electron in turn becomes larger and larger and no longer looks like an elementary particle anymore. There is no exact distinguishing point at which this happens. Therefore the
**notion of what is fundamental is not fundamental itself.**

What can we say about the notion of quantum effects?

- In physics we are used to the situation where we begin with a classical system and quantize it. Quantum effects make the system “fuzzy,” or uncertain.
- The amount of uncertainty is governed by Planck’s constant, h. We can dial the quantum effect by varying parameters, making the quantum effect bigger or smaller.
- But if we continue to increase the quantum effects, an extremely “fuzzy” system can appear like a new classical system. Meaning we can travel from one classical system to an entirely different one by dialing the quantum effects. Which one is more fundamental, we cannot say.
- The pillars of physics are falling down, one by one. String theory is overturning many ideas we believed to be fundamental.