8.06.2011

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.

18 comments:

Michael Lockridge said...

That was the clearest explanation of quantum tunneling I have seen. Not that I have seen a great many such explanations. My limited reading in quantum electrodynamics has been just enough to define my confusion, rather than lead to enlightenment.

Of course we all know, deep down inside, that it is all pixies. Pixies dancing with angels.

pboyfloyd said...

Pliny's atheist apology, "I am SO sorry! Don't hit me. AWWW, go head and hit me, I deserve it."

You are hilarious, you know that.

Now, back to read through to the end.

Good stuff.

pboyfloyd said...

"..very very huge (channeling Michael Palin), nuclei can fuse because a certain percentage ‘tunnel’ through the barrier ..."

Channel tunnelling! (Michael Palin would 'get it')

Groan.


Um, um..other thing. Micron? Smallest Transformer?

(Hey it's early, leave me alone.)

Seriously now, that's very interesting stuff.

Harvey said...

I had much less trouble learning microsurgery of the ear than this. Nevertheless, thank you for providing at least the minimal understanding necessary for what promises to be an interesting later teaching session.

Jared said...

Good synopsis of quantum tunneling, but I don't think I follow how this will tie into neurology...

GearHedEd said...

One of the ways it will tie into a discussion of consciousness is as an objection to the utterly simplistic complaint that theists are always trying to bludgeon materialists with: theists complain that in a materialistic universe, allof the constituent parts of our brains are reducible to particles of one sort or another, and thus are bound by physical laws as to behavior, i.e., deterministic. Then they ask, "If material brains are deterministic, then you could never have an original thought, and all explanations of mind / consciousness fail".

Of course, that's nonsense, because as Pliny's OP points out, subatomic particles aren't little Newtonian billiard balls. Further on that, it's not the 'matter' that matters; it's the energy states supported by the arrangement of the 'matter' that makes the difference.

Jared said...

Well, that line of argument stems mostly from the fairly faulty logic of "deterministic processes can't result in new ideas." This is patently false, we come up with new engineering processes all the time with computer programs. I don't think anyone would argue that computers are not deterministic, but here you have new concepts and ideas arising from purely deterministic systems.

I'm of the opinion that quantum properties don't play any role in the functioning of the brain. I may be wrong on this given some evidence, but it just smells like woo.

GearHedEd said...
This comment has been removed by the author.
GearHedEd said...

Jared,

I was mainly pointing to the faulty logic in theistic arguments. If there's some fundamental process involving quantum effects, I haven't heard of them (although that in no way shows that there aren't discussions out there; just that I haven't seen them...).

What I was hoping to express is the idea that such simplistic (and uninformed for the most part) dismissals as the ones theists give aren't satisfactory given the huge complexity in the whole "brain-as-electrochemical-organ" materialistic explanation.

Because it's not really about the 'matter'; it's about the energy patterns.

Harry C Pharisee said...

Great explanation Pliny!

My only criticism is that there is no need to eschew metaphors.

In fact your post is an example that word pictures can be just as accurate as "regular pictures." They both come up short without more context. ;)

Harry C Pharisee said...

Well, is it improbable to the point of impossible that the configuration of 'small' particles into 'big' particles would retain any quantum effects?

(Just playing Yahweh's advocate).

Jared said...

I won't say it's impossible, but we know that it is the movement of atoms responsible for neuronal firing and signal transduction, not movement of electrons (as in the case of photosynthesis, where the only evidence of quantum effects in biological systems actually exists).

Pliny-the-in-Between said...

AHA! some actual science discussion on the Internet - who knew.

Once again, I suppose I should have been more clear in some of my writing. Most of this discussion will have bearing on three areas of future discussion:

1) work on artificial 'minds' where tunneling has significant design implications
2) Discussing the history of views of people like Hofstadter and Penrose for example as to the nature of the mind

and
3) what Jared has alluded to - quantum woo, which I broadly call efforts to extrapolate particle effects several orders of magnitude removed from our macro world.


In time, this will be helpful to compare and contrast basic biochemical processes at a molecular level (still far removed from what we sense in everyday living) from what is happening at the particle level.

Pliny-the-in-Between said...

Harry going back to Jared's point, the processes we see occurring in nerve conduction (stuff from Neuro basics part 1) involve chemical receptor molecules, hormones, and ion pumps that alter the permeability of the cell membranes. The altered physiological behavior comes about because of a relatively large (and transient) shift in polarity across the membrane in a certain region that is propagated along the length of the axon.

the resting potential of the membranes stays remarkably steady unless a biochemical signal is sent.

pboyfloyd said...

I don't think that we do ever have 'original' thoughts. It is my understanding, and I may be completely wrong here, that everything is evolutionary. We have 'what we have', nothing is constant except change, so what's the next thing?

What boggles my mind is computers. I think that I could understand it if I could read a well written history of it. I've tried and tried and seem to have a giant mental block. I did 1/2 first-year course using PASCAL and aced that but I feel as if something is being kept from me, don't know what it is, but I'd know it if I read about it.

Michael, do you never get tired of being wrong, it's turtles all the way down.

Jared said...

I think this can mostly be summed up with the quote my Organic Chem (1&2--I got really lucky and had the same prof. for both!) professor used to always say: "subatomic particles are not like ping-pong balls"

Saint Brian the Godless said...

After a cursory read I agree, the clearest explanation of quantum tunneling that I've ever heard. You are already an accomplished writer, and you're apparently also a very good science educator. Y'Ever think of becoming the next Carl Sagan?

Okay, unrealistic, but how about a gripping novel where basic understanding of science saves the day?

I shall endeavor to read this article in it's fullness either tonight or more likely, tomorrow. And your previous ones that I've missed as well. When I feel that I'm actually LEARNING SOMETHING, I get interested, and so I am.

You are pretty fucking cool, pliny. Don't let it go to your head, though. Your lack of egotism is one of your best qualities.

Nicely done, sir.

Saint Brian the Godless said...

Oh, I see that I posted that last on the wrong, older post. I shall correct. Bye!