 So let's have Newton's third law, and Newton's third law basically says that the force on particle 2 due to particle 1 equals negative the force on particle 1 due to particle 2. I have the Sun, I have a planet. The Sun, it's a gravitational force on the planet, the planet equally has a gravitational force equal in opposite direction. But this, well again, it's a law of nature within the realms of classical mechanics in which Newton's first law, in other words this law of equilibrium, there is this inertial reference frame that exists. In the inertial reference frame there is something called equilibrium. Equilibrium says in the absence of a cause there will be no effect. In other words, stationary motion, constant velocity. So within the realms of this classical mechanics, there's certainly never been an experiment to show that the deviation from that, so we take it as a law of nature. But it gives us a beautiful opportunity to delve a bit deeper. There's something beautiful that comes out of here. We say force equals m dv dt, first derivative of velocity. This is a scalar. I can put it in there. In other words, force equals v mv dt. We know what mass times velocity is. Mass times velocity is linear momentum. So force is the relative change of linear momentum. Now let's have this as the momentum of particle one, of particle two and of particle one. In other words, we're going to have that the dv t of the momentum of particle one is going to be negative the dv t of g two. I can bring that to the other side. And remember if I have the dv x of f plus the dv x of g above the functions of that, I can write the dv x of f plus g. So if I bring this to this side, I have the dv t, the dv t of p one plus p two. This is going to equal zero. So what does that tell us about p one and p two? Well, p one plus p two. These two momentums have got to equal a constant because the derivative only of a constant will give you zero. And what does this tell me? There is something in here. There's something that's conserved there. There's a conserved quantity. I say that linear momentum is conserved. Linear momentum is conserved. So despite doing, going from the law of nature, doing a bit of simple calculus, I have discovered a conserved quantity. There is conservation of linear momentum. Now you can likely ask yourself which came first, the chicken or the egg. Is it because there is a law of nature that there is conservation of linear momentum? Is it because there is a third law of nature that there is conservation of linear momentum? Or does nature conserve linear momentum? And from that, because I can work in reverse, does that give me a law of nature? Is there something inherent within nature that conserves certain things? Certain things in nature are conserved and from that follows the law of nature. Or is it this way around? And certainly before relativity came along, physicists believed things in this direction. Then can any nerther, proven later by Wigner, but sitting after the time of Einstein, we think as physicists we think in reverse now, there is conserved quantities in nature and from that we can derive the laws of nature. So we now have laws. We now have the concept of conserved properties and as always, nature will always let this happen. It is a property of nature to have certain conserved quantities. But there is something that goes beyond this and that is something that we will discuss. This conservation of linear momentum comes from a symmetry principle. Now what is symmetry? Now once again, school, university, I shoot a cannonball up. The cannonball has this parabola motion. I only have to work out half of it because the side is symmetric from today. Not what symmetry is about. There isn't a simple definition I can give you of symmetry. Once you have seen enough examples of symmetry principles, it will become part of you, you will understand symmetry principles. You can come up with a lot of symmetry principles. From a symmetry principle, it has been well shown wherever there is a symmetry principle, there is a conserved quantity. From a symmetry principle, which you set yourself, if you find one or if you set one by thought experiment, if you can find a symmetry principle from that, a conserved quantity exists. From that conserved quantity, I can work out, I can derive a law of nature. It goes in this direction. Only as a physicist once you can start talking in terms of symmetry principles. Later on in advanced physics, the breaking of symmetry is the bedrock of most of what we understand from a symmetry principle. We will do some examples so you can start understanding what a symmetry principle is. You are going to get a conserved quantity and once you have a conserved quantity, you can find a law of nature. That is beautiful. That is how you think as a physicist, not from starting from the side.