Ever have a day when everything went wrong? Say you predicted you would have a normal day. But your alarm clock didn’t ring. Already running late, you couldn’t find your backpack (or whatever you use). Finally you stagger out the door, but your car won’t start. Later, you find out you missed a surprise quiz (or whatever). It’s not you, it’s the whole prediction game…

#1 – observer effect; #2 – the Heisenberg Uncertainty Principle (last time); #3 – quantum tunneling (this time); #4 – butterfly effect (next time); #5 – external perturbations; #6 – why care? Existentialism; #7 -Why care? Time value of money

————————————————-

#3: Quantum Tunneling

According to quantum theory, objects are not as localized in space as we intuitively think. Instead, they have wave-like characteristics and are actually “smeared” over a space within which they may be said to exist with some probability at each point within that space. A tiny object like a subatomic particle, if near enough to a thin barrier, thus has a certain probability of being on the other side of the barrier. If it is, it has thus “tunneled” through the barrier without making a hole in it. This is quantum tunneling.

Video: http://www.youtube.com/watch?v=6LKjJT7gh9s&NR=1&feature=fvwp

Actually, the term quantum tunneling is applied to the ability of objects to “tunnel” through other kinds of barriers than a solid one. For example, consider the somewhat notorious example of an idealized pencil balanced on its tip.

Source: http://2.bp.blogspot.com/_cldxKGOzgeM/Sb-pzadDENI/AAAAAAAACF.....ncil+on+it%27s+tip.JPG

If the tip sharp, except for a tiny flat spot (say, a couple of atom wide) it might be difficult to balance, but one might think that with sufficient care it could be done. Well not exactly. Because the pencil is actually “smeared” a little bit, it has a certain, rather small probability of being tipped enough to lose balance and fall. Since the smearing is symmetric, it could in fact fall in any direction. The probability of being tipped enough to lose balance is small enough that a single such pencil would be unlikely to fall for a long time (Easton, 2007, p. 1103). But get enough pencils together and one will fall soon enough. For example, balance an array of 1000 x 1000 pencils and one will fall, knocking over other pencils and leading to a general domino-like conflagration with an average (but unpredictable) delay of around a month. What pencil will start the general crash and in what direction the pencils fall is impossible to predict.

But maybe the system we’re interested in predicting the future of is not so finely tuned. Maybe we can handle the Observer Effect, the Uncertainty Principle, and now quantum tunneling adequately for our system. Our troubles are still not over. Tune in next time for Spoil Sport #4: the Butterfly Effect.

Reference

D. Easton, The quantum mechanical tipping pencil – a caution for physics teachers, European Journal of Physics, vol. 28 (2007), pp. 1097-1104.