Complexity Explorer Santa Fe Institute


Introduction to Renormalization

Lead instructor:

6.1 From Quantum Electrodynamics to Plasma Physics » Quiz Solution

1. What is a plasma?
A. a gas where the electrons have been separated from the nuclei, leading to a fluid with positively and negatively charged particles freely moving around.
B. a very high-temperature system where the disorder is maximal.
C. a mixture of two types, or species, of gases.
D. a system with a very strong electric field.

Answer (A). Very often, plasmas are found in high-temperature situations (e.g., at the heart of a nuclear explosion), so (B) is often a good guide. But one can also have "cold" plasmas, particularly when the gas is very low density; in those cases, it's relatively easy to prevent electrons from recombining with nuclei (as they generally desire), because it takes them a long time to find one. An interesting limit case is a conductive material; we don't usually think of, say, steel as a plasma, but there is indeed a freely-moving population of electrons inside the material, and many of the stories from this section can be told there as well (the major difference is that the nuclei are fixed in place). Interestingly, (D) is very often what creates a plasma; for example, you might put an enormous amount of charge onto a capacitor. This generates a very strong electric field. If the field is high enough -- at the "breakdown voltage" -- then the electrons will separate from the material, and flow freely.


2. How is a plasma like the quantum vacuum?
A. "virtual" electron-positron pairs behave like electrons and (positively-charged) ions.
B. definitely both things that Geordi La Forge has to handle on a daily basis in Starfleet engineering.
C. in both cases, electric fields changes in the underlying system configuration, leading to distance-dependent shifts in the measured charge of an object.
D. both (B) and (C)

Answer (D). The ontological status of "virtual" particles is a difficult one to handle; we often like to talk about virtual particles as if they're just regular particles with uncertain immigration status, but this leads to all sorts of confusions. Sean Carroll will literally travel to your house and punch you in the face if you selected (A). This is why this unit is about plasma. For more on the distinctions and differences, take a look at and other writing by Sean on this question, including the arXiv preprint on "Boltzmann brains":