This year we give thanks for one of the bedrock principles of classical mechanics: conservation of momentum. (We've previously given thanks for the Standard Model Lagrangian, Hubble's Law, and the Spin-Statistics Theorem.) There are analogous notions once we include relativity or quantum mechanics, but for our present purposes the version that Galileo and Newton would have recognized is good enough: in any interaction between bodies, the total momentum (mass times velocity of each body, added together vectorially) remains conserved. Now, you might feel somewhat disappointed, thinking that conservation of momentum is important, sure, but not really cool and interesting enough to merit its own Thanksgiving post. How wrong you are! First, conservation of momentum isn't just an important physical principle, it played a crucial role in the development of the idea of reductionism, which has dominated physics ever since. Aristotle would have told us that to keep an object moving, you have to keep pushing it. That sounds wrong to anyone who has taken a physics course, but the thing is -- it's completely true! At least, in our real everyday world, where Aristotle and many other people choose to live. Push a cup of coffee across the table, and you'll notice that when you stop pushing the cup comes to a stop. Galileo comes along and says sure, but we can go further if we instead imagine doing the same experiment in an ideal environment that is completely free of friction and air resistance -- and in that case, the cup would keep moving along a straight line. This has the virtue of also being true, but the drawback of not relating directly to the world we experience. But that drawback is worth accepting, because this backward step opens an amazing vista of progress. If we start our thinking in an ideal world without friction, we can assemble all the rules of Newtonian mechanics, and then put the effects of air resistance back in later. That's the birth of modern physics -- appreciating that by simplifying our problems to ideal circumstances, and understanding the rules obeyed by individual components under these circumstances, we can work our way up to the glorious messiness of the world we actually see.
The second cool thing about conservation of momentum is that it was not Galileo who came up with the idea. As with many grand concepts, it's hard to pin down who really deserves credit, but in the case of momentum the best candidate is Persian philosopher Ibn Sina (often Latinized as Avicenna). Ibn Sina lived at the turn of the last millenium, and was one of those annoying polymaths who was good at everything -- he's most famous for his contributions to medicine, astronomy, and philosophy, but also dabbled in physics, chemistry, poetry, mathematics, and psychology. Along the way he introduced the idea of "inclination" or "impetus." Now, Ibn Sina (like anyone else in the year 1000) had some wrong ideas about mechanics and motion, and historians of science argue over whether his notion of inclination really matches our contemporary idea of momentum. But he defined it as "weight times velocity," and -- most importantly -- understood that it would be conserved in the absence of air resistance. Sounds like momentum to me. Finally, conservation of momentum is important because it has sweeping implications for the way the world works at a deep level, implications that many people still have trouble accepting. Back in Aristotle's time, the natural state of a coffee cup, like anything else, was to be at rest. But we look around us and see all sorts of things moving around. So clearly these motions require an explanation of some sort -- something that keeps them moving. Despite the later triumphs of Newtonian mechanics, that way of thinking still seems very natural to us, and leads us to a certain outlook on the ideas of "cause and effect." Things don't just happen (this way of thinking goes), they happen for some reason. And we can take this line of reasoning all the way back to a purported First Cause or Prime Mover. But the lesson of conservation of momentum -- and indeed, of all of modern physics -- is exactly the opposite. Things don't move because something is pushing them; they move because they just are, and can continue to do so forever. The fundamental relation between different events is not one of cause and effect; it's one of inviolable patterns, in which no particular events are distinguished as "causes" or "effects." And this viewpoint, as well, can be traced all the way back to grand questions of the universe -- why is there something rather than nothing? There doesn't need to be an answer to this question of the form "Because X made it so" -- the answer can simply be "Because that's the way it is." So thanks, conservation of momentum. The next time I find myself on a perfectly frictionless surface in the absence of any air resistance, I'll be thinking of you.