Many Body Physics

We really should have started with some fancy quote, spoken in the past, and reverberating into the ages to come. But we didn’t. So let’s start instead with a small experiment. Fill a cup with something. No, not coffee, we know you were thinking about it. Something clear. You need to see through it. You also need to have some little pieces of something floating homogeneously around in your cup, like chia seeds once they are really squishy, or that weird aloe drink they sell at the supermarket. The latter, in fact, proves to be the best for this experiment.

Now walk around your house and observe those little guys in your cup. Notice something interesting? How about when you turn in a corner? When you do that, you can observe them rotating all together, collectively. Alex and I would now point at your cup and say solemnly, “That is Many Body Physics”. Most of you would then answer, “What?”.

So, what is this Many Body Physics we have been talking about? And if there is something which involves many bodies, there should also be a concept that involves few bodies, then there should be one for single bodies, right? Well, yes. In fact, you may remember it from school, or high-school, or even Physics 101 in college. Remember those never-problems with pulleys and falling blocks? That is part of few-body physics, which is the concept of treating the position and speed of individual objects and predict how they are going to move in the future, based on some initial data. in our field, these kind of problems are usually called “initial value problems”. It is jargon, yes, but we think it sounds cool. We also know it probably doesn’t.

I want to tell you how important are those ideas, and even if they sound easy and trivial, it took since the greek philosophers until Kepler and Galileo to start making sense of them. Almost two thousand years in the making!

But it was another guy who really understood this physics, and wrote down his famous Laws of Motion, upon which physics was completely based for two centuries. That guy was called Sir Isaac Newton. His ideas, which were developed — as he himself said — standing on the shoulders of the intellectual giants before him, helped humanity to understand, modify and predict how things moved, the science of forces (and the technology that comes with that knowledge), and even how and why the celestial bodies behave like they do.

These ideas and discoveries had one thing in common, all of them. They depended on the isolation of a few bodies in the problem. Normally two. One can easily calculate to very good accuracy how the Earth revolves around the sun without taking the other planets and the asteroid belt in account. It is an approximation of reality, but it is one which presents a very small error. (Why we can ignore this and be happy with it, are matters for future posts.)

So what happens when we can’t separate a part of the problem into little couples? Well then, there has to be a change in the way we think about it. And this incendiary transformation is, in fact, a very simple one. Should we care about a single molecule of water in the vastness of a glass full of them? The answer, as you may expect, is no. What should we care about, then?

The interesting part of this story is that this transformation of thought never happened as a historical event. No, it all happened alongside the development of the physics we were discussing before. Another field was rising, which was all about the liquid state of matter. Archimedes and his disciples were really into understanding how water behaved when pushed around. However, they never needed to understand how the fluids were subdivided into drops, or atoms, or molecules, or whatnots to understand how water worked. Why? Because they were interested in the general, overarching properties of the phenomenon. In modern physics, with a bit more of understanding over these matters, we would say that they were trying to describe the “macroscopic properties” of the fluid.

This kind of thinking was carried through the centuries, applied by countless people, such as da Vinci, Galileo, Torricelli and Bernoulli, even by Newton himself! You have to remember that during this time, these phenomena and the ones explained by single body physics were not really thought of as being the same. The atomic nature of matter had to be yet confirmed, and these polymaths didn’t regard them as being different faces of the same dice.

But this is when things get really interesting. During this time, electricity was becoming a booming area of research, and by the beginning of the 19th century both charge and current were well-stablished concepts. The first dealt with some property of matter which created an invisible force between bodies. For this, three possible states were identified: “positive” and “negative” charge, and also no charge, named “neutral”. Newton’s mechanical rules proved to be the correct framework to treat charges, and as an extra curiosity, Gravity and Electricity seemed to have the same behaviour if you exchanged mass with charge. But current was another topic, as it seemed to be something that flowed, that was dynamical, and liquid. Similar concepts and names were used to describe these flows.

It was not a long time until these intellectuals discovered that by moving, translating, rotating charges they could create the same effects as with their battery currents. This was the birth of Electromagnetism, which culminated in Maxwell’s work. But the change was already on the way. Particles with properties could create flows. Maybe water or air is the same. Can we calculate that?

Yes, we can.

But we still have to change our perspective. It is not the individual particles we need to know, but their statistical behaviours. We want to know the average energy, or velocity of them, to understand how hot the fluid is or the flow they create. This is called Kinetic Theory -a vital part of Statistical Physics-, which a very important area of our knowledge. This was the clash between two worlds. A clash that made us understand how the laws that rule the physics of single bodies can and will change the behaviour of the whole substance, but in exciting, unexpected ways. That the collectivity comes with new, “emergent” properties, that won’t show with the individual components.

Since then, we have understood that these properties can be found everywhere. Fluids, such as gases and liquids were investigated to help us with pipes and drains, but in the wild, in their natural state, they become so much sexier. They make up the ever-changing climate (so relevant right now, isn’t it?), they make up stars, they make up nebula and even the whole observable cosmos can be taken to be a fluid! But it doesn’t end there, since with the discovery of quantum mechanics, we have applied the same thinking to fascinating new questions, which can explain a lot of microscopically generated, but macroscopically observed phenomena. What am I talking about? Well, magnetism, for example, is one of those which we will cover eventually (so, stay tuned). We can also explore a lot of the physics of the nuclei, and even go deep into the core of a star, and try to explain what can happen if the star feels extreme amounts of pressure from gravity.

But you know, it is very curious, that this way of thinking was also applied early on the life sciences, namely population science. It has been used to understand the dynamics of predators and preys, as well as to investigate the peaks of infectious diseases. However, one could also use it to understand, and maybe predict, the behaviour of evolutionary science, not on the level of individual species, but on the appearance, rise and extinction of groups of them, and how different events could, for example, trigger mass extinctions.

However, physics and biology are not the only areas affected by these thoughts. It turns out that you can apply these ideas to almost everything that is comprised of a collective. Using them, one can explore the bulk properties of society, such as investigating rises and falls of markets, riots, ideological movements, you name it! Once, I even saw a paper trying to understand the flow of attendants to a concert, explained with fluid mechanics. Basically, if you are interested in some part of society, with a bit of thought, it can be modelled.

So this is how we close this first installment, as a “collective” of fascinating and booming areas of research we can dig into, in order to better understand our universe, life, society, planet, climate. From this, we can see that from pure love of knowledge up to the purely applied, from the microscopic, to climate and astrophysics, and passing through your cup, we can safely assure you that many body physics, is everybody’s physics.