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. It’s not you, it’s the whole prediction game…

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

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#2: The Heisenberg Uncertainty Principle

This physics principle holds that you cannot simulate a system to reliably predict its future because you cannot know both the position and the momentum of any object in it exactly. The more accurately you know one, the less accurately the universe says you can know the other. A quick, 3-minute video introducing the Heisenberg Uncertainty principle is at http://www.youtube.com/watch?v=iFwRAvpWDB8. Note that it applies in theory to all objects, not just electrons. For example, it applies to photons (light) too: http://www.youtube.com/watch?v=KT7xJ0tjB4A&NR=1. You can do the experiment in that video at home. Got a laser pointer and an opaque sheet of something you can cut a narrow V-shaped notch in? I used a black vinyl notebook cover with a narrow V a few inches long and an inch wide at the widest point, cut with an ordinary sharp scissors. Shine the laser beam through the V at a wall. Move the beam close enough to the point of the V and the spot on the wall will smear – the Heisenberg uncertainty principle in action (like in the video).

The Uncertainty Principle connects uncertainty about position and momentum as follows. The uncertainty in position, delta x, time the uncertainty in momentum, delta m, equals h/4*pi where h is Planck’s constant, a rather tiny number. Since momentum is velocity*mass, we have uncertainty about velocity too (as well as mass, for that matter). So there is uncertainty about place, velocity, and mass of any object. Out of tradition, let’s focus on position and velocity.

To fully describe a system, such as the universe, or some part of the universe smaller than the whole thing, we need simply list the position and velocity of everything in it. How many numbers are needed to describe the position? Three, a side-to-side location, a front-to-back location, and a height (usually known as x, y, and z coordinates). How many numbers are needed to describe the velocity, where velocity consists of a speed and a direction? Three – a side-to-side speed, a forward backward speed, and an up-down speed. This concept is easiest to visualize in a 2-D simplified example.

In the figure, an object is shown with a location of about 3 feet in front your nose, and shifted about 4 feet to its right. (We ignore the up-to-down dimension here.) It is moving in the direction shown by the arrow in the interior of the graph. The length of the arrow symbolizes its speed – it is receding at about 3 feet/sec. , while moving to the right at about 2 feet/sec. rightward.

Returning to 3 dimensions, we need six numbers for every object to fully describe the system of objects (actually seven, since each object has a mass as well). Unfortunately those six numbers are in principle impossible to get with full accuracy, because they include both velocity and position values. The Uncertainty Principle tells us that more accurate knowledge for one demands less accurate knowledge about the other.

In short, if the observer effect doesn’t stop our prediction ambitions, the Uncertainty Principle will. But what if we could control both, enough at least to predict futures with confidence? Alas, we’re not out of the woods, because of the esoteric physics phenomenon called “quantum tunneling.”

Tune in next time for part #3 of this series, “Spoil Sports of the Prediction Game.”