# Is this a reasonable analogy for quantum tunnelling?

1. Sep 4, 2011

### Turtle492

Hi, I wanted to explain quantum tunnelling to people with no scientific background - I've come up with the following analogy, but I'm only a physics undergrad and I'm not sure if it's a good enough analogy. I can do the maths behind tunnelling but it's just the concept I'm trying to get across. I don't want to have to try to explain potential wells or the not-at-all-like-a-billiard-ball nature of tiny particles like electrons.

The analogy I've come up with is this:
Imagine you're throwing a tennis ball at a thick window. The tennis ball doesn't have enough kinetic energy to break the glass, so it bounces off. But if you do it enough times, if you close your eyes and throw the ball at the window, when you open them there's a chance that the ball will be on the other side of the glass.

The only thing is I'm not sure if the glass should be intact or broken. As I understand it, it's not that the ball (or electron, say) borrows enough energy from the universe to break through the barrier, just that there's a finite chance of it being found on the other side when you look, so I was intending to say that the window won't be broken, but I wanted to check that that was accurate. Obviously any classical analogy for a quantum effect won't be completely accurate, but like I said I'm just trying to get the concept across.

I appreciate any advice, just don't make it too technical!

2. Sep 4, 2011

### ZapperZ

Staff Emeritus
Your analogy is more confusing than the phenomenon it is trying to "analogize". You are leaving the impression that (i) we don't know what's going on during the tunneling process (ii) all we care about is that it is on one side at one time, and then appears at the other side later, without caring what happened in the middle.

Zz.

3. Sep 4, 2011

### fleem

The glass wouldn't be broken. The more general analogy is that conservation of energy can be disobeyed while the system is isolated from the rest of the universe, as long as it is obeyed when we observe (interact with) it. This also provides a classical analogy for why a single particle can take multiple paths that would otherwise be (classically) mutually exclusive--its like energy was created out of nothing when the particle split into two. Of course, as you say we should always include the caveat that a given classical analogy is really not correct, but only good for getting our minds around things early on. In this analogy, the glass wouldn't be broken because if it were, we could end up with more energy than we had when we started (unless the particle broke the glass in some way that the final system had the same energy it had at the beginning). On a side note, this really isn't an analogy as you put it. There really is a chance the ball would end up on the other side without breaking the glass.

@Zzapper, I thought the jury was still out about what happened in the middle! If not only because so many scientists still assume there even is a classical analogy. (FWIW, I'm certain there isn't one)

Last edited: Sep 4, 2011
4. Sep 4, 2011

### ZapperZ

Staff Emeritus
Which jury is this?

I can affect a lot of things regarding tunneling by introducing stuff in the tunnel barrier. In superconducting tunnel junctions, I can introduce magnetic impurities in the barrier that will cause the tunneling spectroscopy to be different.

So what is it that is a mystery here?

Zz.

5. Sep 4, 2011

### xts

Make an easy experiment: take two prisms (45°, like used in binoculars). Combine them face-to-face, putting a hair between them. And give it to your pupils, to see how much light comes through them - if the gap is wide, the whole light is reflected with total internal reflection.
Then ask them to calculate that in terms of waveoptics. QM tunneling is pretty much the same - actually - QM calculations for photon tunneling would lead to the same results, as waveoptics.

6. Sep 4, 2011

### Ken G

It is not surprising that changes in the barrier (such as removing it altogether) will affect what shows up on the other side. It's also true that if you look for the ball inside the glass, you might find it there, in a place where it isn't supposed to be, classically. I think the point of "closing your eyes" in the analogy, and the associated mystery, is that if you look at the ball when it is in the glass, the energy to break the glass will come from your looking at it (in the tunneling scenario-- obviously in real life we don't have this, the probability is absurdly small if it makes any sense in the first place). So it can't tunnel through the glass without breaking the glass if you watch it the whole way, and that's why you have to close your eyes if you want it to happen (lots of luck, of course!). Personally, I think the analogy is as good as any classical analog-- and I think a search for classical analogs is a fine thing to do, it's true you can't take them too literally but who said you could take the quantum mechanical description literally either? No physics theory should be taken literally, that's not what physics is for (it is for predicting outcomes).

Perhaps your point is, you object to the way "quantum weirdness" is cast as something we totally can't understand, when in fact our theory works great. I think what should be said is that it seems weird when we think along classical lines, and that paradoxical character can only be exposed by a classical analogy. So instead of framing it, "here's an analogy to help you understand what is happening," we can say "here's an analogy to help you understand why this behavior is regarded as so surprising." For the latter purpose, I'd say the analogy performs adequately.

Last edited: Sep 4, 2011
7. Sep 4, 2011