How Einstein Proved that Atoms Existed. And How You will too. Part 1.2

Credit: Eliza Sankar Gorton. Baby and book by , Calabi-Yau manifold by , adapted under a Creative Commons license.

We talked by looking at pollen grains floating in water. In this post series you will understand how that comes about, we will do the calculations and the (virtual) experiments.

The first thing you should do before going on an adventure is to take a bird’s eye view and think about what kind of things you will encounter along the way. You can’t, of course, plan all the details, it wouldn’t be an adventure otherwise!!

Things are very similar in physics, it is very much an adventure when you embark on a journey to understand atoms, before anybody was sure that they existed. What we will do in this post is to first build intuition about what to expect along the way, and understand what are the things that Brownian motion will depend on. In other words we are defining the the main characters

Meeting the Cast

Imagine we had a microscopic particle suspended in water, it could be a sphere like in the simulation above or it could be a cube or whatever shape. The particles is moving around randomly because of all the atoms that are hitting it every instant from every direction. We don’t know how many atoms will hit it on each side exactly, sometimes 1000 atoms will hit from the right and 1010 will hit from the left and so on. All we know is that on average a certain number of atoms will hit. This means that in order to be able to predict something about the motion of this particle we must know how to calculate with probabilities, which is one of the main characters we encounter on this Journey.

The particle which we can watch under the microscope will experience a force in the left direction whenever more particles hit from the left than the right. The strength of the force will depend on how fast the atoms are moving when they collide with it. The relation between the speed of atoms and the temperature of the water is another one of the miracles of physics. This is explained by the second main character: Thermodynamics and Statistical Mechanics, here is what Einstein had to say about this:

It is the only physical theory of universal content, which I am convinced, that within the framework of applicability of its basic concepts will never be overthrown.

With Statistical mechanics we can now determine the probability that a molecule will have a speed of 1000 m/s for example, we can also find the probability that it is moving to the left vs. the right. After knowing how many molecules are moving at a certain speed and how many molecules are hitting our friendly particle from each direction, we will need to sum up the contribution from all the different molecules with different speeds. The process of summing many little things is known as Integration.

Newton, one of the people who pioneered our modern way of doing physics, also invented calculus!! This should tell you that without calculus it is difficult to predict a lot of the phenomena of nature. We will briefly introduce integration, just enough for us to be able to understand how to measure the size of atoms!!!

Your Challenge:

The goal of this article is for you to build intuition about the phenomenon of Brownian motion. Pause reading for a second take out a piece of paper and draw a picture of what is happening during this phenomena, explain to yourself why the particle is moving in a random way. Then write down the three main cast of characters we talked about, and explain to yourself how they are important to the phenomena in the picture you drew.

Share your answers in the comments section and if you still have questions about this, I will help you answer them.

What Comes Next

The next post will be about probability; how to make predictions when things are uncertain. There will be many guided challenges that you will have to do. And there might be a game that you can play that will help you experience and play with the cool concepts of probability theory.

Until then, have lots of fun and understanding!!

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As you see in the picture the cows are completely grass-fed and grass-finished (meaning they are not artificially fattened up with grains).




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