1 - Introduction

Summary

Imagine you could shrink into the atomic world. On this small scale, motion is violent and chaotic. Atoms shake and dance wildly, and each carries an electron cloud that is a blur of motion. By contrast, the behavior of a very large number of atoms, such as a baseball or planet, is quite sedate. Their positions, motions, and properties change continuously yet predictably. How can the behavior of macroscopic systems be so predictable if their microscopic constituents are so unruly? Shouldn't there be some connection between the two?

Indeed, the behaviors of the individual microscopic elements are reflected in the properties of the system as a whole. In this course, we will learn how to make the translation, either way, between microscopic behaviors and macroscopic properties.

The translation between microscopic and macroscopic behavior

The statistical tools

If you guess whether a flipped coin will land heads or tails, you have a 50% chance of being wrong. But for a very large number of flipped coins, you may safely assume that nearly half will land heads. Even though the individual elements are unruly, the behavior of a large system is predictable (Figure 1.1).

Your prediction could go the other way, too. From the behavior of the entire system, you might predict probabilities for the individual elements.