Chaos: The problem of Sun-Moon-Earth.

In the last article, we left you wondering what chaos is, in this article, we will explain Chaos. If you have not read the first article in this series then its link is given in the bottom.

Chaos in a general colloquial sense is understood as unpredictability. If you would have ever travelled (or heard stories of travelling) through Mumbai local or Delhi Metro at very crowded hours, you would surely know that when the train arrives at a platform, there is a huge gushing of passengers in and out. Now if you would be in the group of extremely experienced commuters, like me, you would know that there is a sweet spot right beside the gate of the train or metro which remains undisturbed by the motion of commuters, which we prefer to occupy. Now, if you were a newbie who is unaware and may be slightly absent-minded, and you just missed that sweet spot by a few inches, the wave of commuters will hit you hard and the swarm will carry you to a very different place altogether from your initial position. In this case, a small change of the initial condition can lead to a drastic change in the final position. This is Chaos. When we are able to talk about systems which just by small changes in their initial conditions can lead to huge and unforeseen effects in final conditions, such systems are called chaotic. This is how unpredictability looks like. Real-life systems like crowds, buses, career markets, populations, animal behaviour, a human heart, weather and even the love life of a PhD student exhibits chaos. Studying and understanding their nature means understanding such complex real-life problems, and giving solutions to traffics, economics, health or maybe even lesser lonely PhD students. Understanding even one of these problems gives us the insight to solve other problems because they are of the same class.

So, we now understand why three body problems are interesting to study. Our interest is to see the simplest three body nucleus, the nucleus of Tritium atom (Hydrogen 3), or Triton. Hydrogen atom just has one proton in the nucleus and one electron orbiting around it. Triton has an additional of two neutrons sitting in the nucleus. Since the charge of the nucleus is given only by the proton and the neutrons are electrically neutral, the neutrons just increase the mass of this hydrogen nucleus. Such forms of the same atom having different masses (and different number of neutrons) are called as isotopes. This gives us a single proton and two neutrons sitting closely together and bound inside this nucleus, making it a three body problem.

What makes it more interesting is something to do with the small size of this nucleus. To get a perspective of the size of this object, if we take one meter and slice it in Quadrillion (one followed by 15 zeros) equal parts, one of the part will be the size of this object called as Triton. At such small scales of length, we observe something very interesting. Any particle-like object of such small scale, exhibits significant wave nature. What it means is that if we take a collection of such particles and pass them through a sieve which has only two slits, instead of piling up in front of these two slits like particles, they will show beautiful alternating patterns of varying intensity, just as if a water wave hit those two slits and both the slits became individual source of another wave coming out from them and they merged to form a pattern. Such small particles follow something called as Quantum Mechanics.

In the final part of the article we will touch upon the topic of Quantum Mechanics.

Nishchal Dwivedi

Nishchal Dwivedi is a Theoretical physicist at Bhabha Atomic research Centre (BARC) and a TEDx Speaker 


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