by David Colarusso - March 25th, 2007

Einstein may have believed God doesn’t play dice, but God need not conform to Einstein’s beliefs. This piece explores the phenomenon of quantum mechanical tunneling whose explanation requires us to accept the reality of quantum mechanics. It’s not a trick; it’s reality.

Update: People have been asking for the math. So here it is. The Sun’s core temp is ~13.6 MK. For hydrogen nuclei the Coulomb barrier is roughly 0.1 MeV. This corresponds to a temperature in excess of 1 GK! Luckily, tunneling and the distribution of speeds among nuclei lower the actual temperature required. So without tunneling even the Sun’s core isn’t hot enough for fusion. To see most of this worked through, check out this link:

http://burro.cwru.edu/Academics/Astr221/StarPhys/coulomb.html

for a less mathematical explanation, try:

http://en.wikipedia.org/wiki/Nuclear_fusion#Requirements

Transcript:

The Tabletop Explainer

Episode Six (6)

What is quantum tunneling?

Some of us were taught in high school that the electron orbits around the nucleus like a planet around the sun. However, this description has been understood as a gross mis-representation for the better part of the last century. As it turns out, there is a characteristic uncertainty related to the very small. No one can tell exactly where something is; the best one can do is figure out where something is most likely to be. We can visualize this with something called a probability cloud. Here we see the probability cloud of a proton at the center of a hydrogen atom. The denser regions are where the proton is more likely to be found. However, this uncertainty is not due to an inability of ours to measure the small in an exact manner; it is a fundamental aspect of the world in which we live, and its implications are extraordinary.

Let us take for example the phenomenon of tunneling. If we can’t tell exactly where something is then it follows that we can’t tell exactly where it’s been or where it will be. The best we can hope for is where it most probably will be. So there’s a small chance that a racket ball thrown repeatedly at a barrier could just tunnel through the barrier, appearing almost magically on the other side. We don’t see this often because a racket ball’s pretty big and its uncertainty pretty small. But if we deal with matter on the subatomic scale it becomes much more likely. Here our projectile approaches the barrier, we see here its probability cloud, although it’s most likely near the center of the cloud we can see that there is a small chance of it being on the other side of the barrier, and so sometimes it is. Tunneling isn’t a mathematical trick or an assumption, it’s an observable fact. It’s made use of commonly in modern electronics and in a real way allows for life on earth. To see why, let us trace the creation of a photon in the sun. The light from the sun that we see reflected off the moon, the light which drives the earth’s weather, that provides the energy for life all originates from the process of nuclear fusion in the sun. Two light atomic nuclei collide, forming a new element, and in the process light is released. But these nuclei are both positively charged and so repel each other. Only if they have enough energy can they overcome this potential barrier and fuse. But if you do the math, the nuclei in the sun don’t have enough energy. The sun’s just not hot enough, non the less, the sun shines, and it does so because of tunneling. Just like our physical barrier, there’s a chance that our particle could be on the other side, and so the sun shines.

[roll credits]

What do you think?



This piece was designed to get you thinking. So find a physicist and get talking, or post a comment and get a discussion going. The main point is that quantum mechanics is real because it properly describes nature. Einstein may have believed that God doesn’t play dice, but God need not conform to Einstein’s beliefs.

Entry Filed under: Quantum Mechanics