Mean squared displacement

Have you ever played with a ball? You probably threw it and watched it bounce back. Imagine doing this many times, and as the ball moves, you keep track of its position.

Now, let's say you want to figure out how much the ball has moved over time. You can do this by measuring the distance between where the ball was thrown and where it landed each time, squaring those distances, and then taking the average of all those squared distances.

This average is called the mean squared displacement (MSD). It's a way to measure how far an object has moved over time. It tells you both how much an object has moved on average, and how spread out its movements are.

MSD is often used in science to study the movement of particles, cells or molecules. It can help researchers understand how they move in liquids or gases. For example, by studying the MSD of a virus in a liquid, scientists can learn how it spreads in the body, which can help them develop new treatments.

So, just like measuring how far a ball moves can tell you about its journey, tracking an object's MSD can tell you a lot about the way it moves from place to place.