Indistinguishable particles

Imagine you have two red balls that look exactly the same. Now imagine you have two blue balls that also look exactly the same. You put all four balls in a box, but you don't remember which red ball went in first or which blue ball went in first.

Now let's say you want to take out one red ball and one blue ball. You reach into the box and take out a red ball and a blue ball. But how do you know which red ball you picked? How do you know which blue ball you picked?

In the world of physics, this is a problem when dealing with particles that are exactly the same, such as electrons or protons. These particles are called indistinguishable particles because they are impossible to tell apart.

So how do physicists deal with this problem? They use a fancy math called quantum mechanics to describe the behavior of these particles. According to quantum mechanics, the state of a group of indistinguishable particles is described by a wave function. This wave function tells you the probability of finding an individual particle in a certain place at a certain time.

In other words, when dealing with indistinguishable particles, physicists don't worry about which particle they're dealing with. They just focus on the overall behavior of the group. It's kind of like if you had four balls in the box, but you didn't care which one you picked out. You just knew you were going to get one red ball and one blue ball.