How Uncertainty is the Root of All Certainty

If you roll a pair of dice, you never know what you will get. You might get anything from snake eyes to twelve. But what happens when you roll a trillion pairs of dice all at once? Strangely enough, you get seven-trillion or a number very close to that figure when you add up all those dice. The uncertainty has become a certainty.

When you calculate the average dice throw, the number you always get is seven. Seven is the mean number, and two and twelve are the extreme numbers. Even if you were to eliminate all the numbers between two and twelve, you would still have an average of seven.

(2 + 12)/2=7

There is an old theorem in quantum mechanics (Ehrenfest theorem) that says that all our laws of physics that give us certain results are rooted in uncertainty. The “certain result” is called the expectation value. You calculate the expectation value by simply adding up and taking the average of all the uncertain results.

At small scales, matter behaves in very strange and unexpected ways, but at large scales, matter behaves as we expect: it follows the laws of Newtonian physics. It behaves much like a pair of dice on the quantum scale, and behaves like a trillion pairs of dice on our old, familiar scale.