Basic Science Saturday on the QT

WooHOO! Basic Science Saturday. Be warned! This is a very simplified description and illustration of a very important concept: Quantum Tunneling. It's a curious thing but I think it’s fairly easy to understand qualitatively. As long as we avoid the usual bad analogies and the math which can be more than a bit dicey.

I’m going to forgo the usual bad analogies because I think they add more confusion than they’re worth because of the orders of magnitude that separate us from the quantum world. What works for a single particle is one thing, but what works for an object made up of a trillion trillion particles is something else.

Just how removed the world of one subatomic particle from our macro world is something I hope to illustrate below. How big is a proton? It’s roughly 10-13 cm in diameter, although the diameter of a proton is sort of a misnomer to begin with since it’s not like a little rubber ball with discrete boundaries. It’s hard to contextualize that small of an object. We need a frame of reference. So let’s, for once find a use for Charlie Brown to illustrate the size issues.

Take Charlie Brown (Somebody please take him! How much longer must we endure recycled comics that weren’t funny to begin with. But I digress)

But let’s imagine mister whinny, boring not with his usual round head which I have arbitrarily estimated at 38 cm (It’s a big fat head. Not really a blockhead but more of a big fat ball of self loathing) but with a head the size of our sun. Assuming we preserve the relative proportions of the sun to CB’s usual blockhead, how big would a proton be?


Would you believe it would be about 3.7 microns?! Even if whimpering simp Charlie Brown’s head were the size of the orbit of Neptune, the proton would still only be a hair shy of an inch in diameter. So we are talking teensy here. So far removed is this world from our macro one, that we should never expect bodies with our mass and numbers of particles to behave in the manner we’re about to describe. Statistically, it’s essentially impossible.

But down deep at the level of the proton or electron, things are strange. Turns out that’s a really good thing for us.

A proton isn't a discrete particle. It is something that is explained as having particle - wave duality. We have a wave function to describe a proton, and there is the possibility of a discrete solution to the equation at a specific time and place - that’s the particle part. For better or worse I tend to think of subatomic particles as a specific observed instance of a wave function. This actually helps me to mentally accept the duality. Unless we are seeing a specific instance, the proton or electron behaves as a wave function and therefore even a single electron or proton can appear to be many places at once - just like a wave. On those occasions when a specific instance is being observed, we see more discrete particle behavior. But generally it works to think of it as a fuzzy cloud like the diagram below. Remember this is just a means to illustrate this.


The fuzzy cloud is the wave function which tells us the likelihood of finding the particle solution or a specific instance of the thing at a particular location in space. The denser areas of the cloud correspond to areas where the particle is most commonly found. But it can be found anywhere in this cloud at some times and if we don’t insist on measuring its precise location, it acts as if it’s everywhere in this cloud at once.

The next two diagrams illustrates that second to last point. The particle can be located anywhere in the cloud of the defined wave function though the probability changes with respect to a particular region. Because the little bugger is so tiny, we can never know both its precise location and its velocity. This concept sometimes gives people fits but it really is fairly simple to grasp. Imagine you are in a pitch black room with a superball bouncing around and you have a strobe light to get a picture of it. (Ok, I have succumbed to the siren's call of bad macro metaphors as well. Someone should have lashed me to the mast.) With the lights out you can hear the thing bouncing around seemingly everywhere but hit the strobe and you can snap a picture of exactly where it is at that instant. Of course there is a problem when you look at the photo you took with the strobe. You see the superball in all its glory but you can't tell where it's headed or how fast. It's just a picture of a ball in the air. You can't tell where it's headed, what it may hit, or how hard. Now as to why this is a bad metaphor goes back to the issues of scale we mentioned earlier. Light from a strobe hitting the superball imparts negligible force on the velocity of the ball. At the level of a proton, however, the energy of a single photon used to detect its whereabouts imparts tremendous force upon the proton altering its momentum and path. Measuring its position always influences its path. That's the uncertainty principle.


Now let’s imagine this very tiny wave function approaching some kind of energy barrier (an electric field for example)


If the barrier is great enough, the particle represented by the wave function will bounce off as we’d expect. The behavior here is very similar to what would be described by classical mechanics. No surprises yet.


But what if the barrier (field) is not so great in size? This next proton approaches a barrier as before. But notice that the region defined by the wave function actually extends beyond the width of the barrier. In other words, in this situation there is some probability that if we collapsed the wave function, the particle would be on the other side of the barrier. It might bounce off as before - then again it might not.


Keeping in mind that this is just an illustration, if the width of the energy barrier is small enough with respect to the wave function of the particle in question, something pretty strange can occur.

The result? The particle may appear to have tunneled through the barrier appearing on the other side with the exact same energy it started with. It’s not magic, it’s just math - really really hard math...


This isn’t just theoretical. It is observable in the behavior of prisms and in an advanced form of microscopy. It has relevance to superconductors, radioactive decay, processor design limits, and even to fusion reactions in the core of our beloved sun to name a few.

The sun you say! Turns out, if quantum tunneling wasn’t real, we wouldn’t exist. The sun requires it to be a fact for it to generate light and heat as it does. One of the problems scientists and engineers are facing here on earth when trying to develop a working fusion reactor is that they have to raise the temperature and pressures to levels far higher than exist in the sun’s core. That’s because the normal conditions within the sun’s core are insufficient to overcome the repulsion of like charges when trying to bring two hydrogen nuclei together long enough to fuse. That seems like a potential problem (badda boom!). The like charges create an ‘energy barrier’ (see where this is going?) that prevents this from happening. But because our dear sun is so very very huge (channeling Michael Palin), nuclei can fuse because a certain percentage ‘tunnel’ through the barrier of like charges and fuse. Science doesn’t get any better than that.

Due to the scale involved and the numbers of particles in question, it should also be apparent that this doesn’t mean we can walk through walls from time to time. We’ll just have to be content with the fact that we get to live because of it and stick to the doors.