 In classical physics so far, you're familiar with this idea of Newtonian momentum. So if an object has mass m and it's moving with velocity v, we say it has momentum p equals mv. Now this is useful because momentum is conserved by interactions, and so we can use this to solve all sorts of physical problems. For example, by setting momentum before equals momentum afterwards and then solving for the velocity. Now let's see how this formula holds up in a relativistic setting. So here we have Bob looking at two balls, a green and a pink one, flying towards each other with exactly the same velocity. So we can break this up into horizontal and vertical components. So for the green ball, these are v and w, where they're measured in Bob's frame. And for the pink ball, the components are s and r, also measured in Bob's frame. Now because these balls have the same velocity, we have vb equals rb and wb equals sp. So after the collision, the balls bounce off each other. Now because the initial situation was symmetric, both of these balls are moving with exactly the same speed, after the collision they'll still be moving with the same speed, because there's no reason for any one ball to have picked up more speed than the other. Let's look at Newtonian momentum conservation in the y direction. So before the collision, the green ball is coming downwards with speed wb, and the pink ball is coming upwards with speed sp. After the collision, the green ball is going upwards with speed wb, and the pink ball is going downwards with speed sp. Now because the balls have the same velocity, we have vb equals rb and wb equals sp. And so the momentum before the collision is the same as the momentum after the collision. So momentum is conserved.