QUESTION #674

# Vacuum is a dielectric. Where does the impedance to charge flow come from?

Asked by: Vijayakrishnan

### Answer

A dielectric's impedance is a representation of the speed limit of light. Asking where that comes from is asking a much deeper question about the fundamentals of the physical world and has no concrete answer as of yet. However, it's not difficult to see that all things must have a top speed, including light. It simply must take some finite amount of time for some fundamental unit of information to move from one place to another. When sitting in traffic, if you somehow knew exactly when every car in front of you was going to move, you could move instantaneously when the first car moved and there would be no delay in the traffic pattern. However, this still requires some sort of instantaneous method of information transfer. Even if you coordinated over radio, there still is a finite amount of time light is going to take to get from the first vehicle to your vehicle. The universe needs time to be able to get the light from one spot to another. And that lag is represented as an impedance. More specifically, it's modeled as a storage mechanism affecting the phase of the signal. Space can be thought of as a combination of capacitive and inductive storage elements filling one at a time and dumping their energy to the next once full -- somewhat like a slinky moving down stairs. The inductive storage element is represented by the permeability of free space. This is a sort of magnetic speed limit. The capacitive storage element is represented by the permittivity of free space. This is sort of an electric speed limit. The inverse square root of the product of these two gives the speed of light, and the square root of the ratio of the permeability to the permittivity gives the impedance of free space (or vacuum). If you're not comfortable with that, just think about how a capacitor works. As current is pumped into it, the voltage starts to change. Steady current is related to a rate of change of voltage. More current means more charge carriers are filling the plates of the capacitor and eventually once enough of them line up on the plates, they increase the voltage across a capacitor. You can increase the capacitance of a capacitor by making the plates larger. This means that the charges have to spread over a larger area before they start piling up on each other thus increasing the voltage from plate to plate. If these plates were infinitely large, no current will ever change the voltage across the capacitor. It's also possible to change the capacitance by adding a material between the plates that further slows light down. You can analyze the effect of this material using lots of different models down to the material level, but that's the most important difference is that it is a material through which light travels slower. This also means that communication about the influence of new charges also travels slower. Again, this can be modeled in lots of different ways classically or quantum mechanically. This slow down is what allows for more charge to build up on the plates. This is much like juggling. The longer a ball stays in the air, the more balls you can juggle with ease. If the dielectric is fast, it's like juggling in high gravity -- the balls move from one hand to the other almost instantaneously. If the dielectric is slow, it's like being able to toss 10 or 11 balls into the air before catching the first one. You have INCREASED THE *CAPACITANCE* OF THE AIR with lower gravity. Likewise, you increase the capacitance of the capacitor with slower dielectric. And so capacitance really is very much related to the "speed" of light through a material. Because vacuum has a finite speed, it must also have a finite capacitance. It turns out this is also true for inductance. Together, the two make up the impedance of a vacuum. It is the TIME storage aspects (i.e. phase change aspects) of the vacuum that prevent light from moving from one point to another instantaneously.
Answered by: Ted Pavlic, B.S., Electrical Engineer, The Ohio State University

In order to answer this question, first let's consider the two main mechanisms of charge transport in materials. In a metal, the valence electrons exist in a delocalized state-- that is, an electron has a high probability of being found anywhere inside the metal. This gives a high conductivity because the electrons are essentially free to move when acted on by an electric field. Next, in a semiconductor or conducting polymer, the electrons are not in delocalized states. They are restricted to orbit given atoms, and they can only move from one to the other by quantum tunneling. This takes advantage of the fact that, even though you may start with an electron around one atom, there is some probability that at some time later, the electron may be found orbiting another atom. Electrons still have some probability of moving under the influence of an electric field, but it is much less than that of the electrons in a metal. So, semiconductors and conducting polymers have much lower conductivity than metals. Now, ask yourself-- what is the mechanism of charge transport through vacuum? Assuming that your electrodes are separated by some reasonable distance, no electrons will be delocalized between the two electrodes, so they won't be able to flow directly from one to the other. The only possible mechanism, therefore is by tunneling. If you have electrodes separated by distances much larger than, say, the diameter of a typical atom, the probability for one electron to tunnel from one electrode to the other is incredibly small, unless you have a very large applied electric field. And, saying you have a small probability of tunneling is the same as saying you have a small current for some applied electric field, which is the same as saying you have a high resistance to charge flow.
Answered by: Mike Groves, M.S., Physics Grad Student, University of Washington