QUANTUM STATISTICS

Enrico Fermi( left) and Paul Dirac. Both these scientists independently worked on the Fermi Dirac statistics. The particles which obey this statistics are called Fermions. This statistics follows the Pauli's exclusion principle.

Satyendra Nath Bose( right) who recognized an alternative arrangement of particle distribution called the Bose Einstein statistics. These particles were named  Bosons after him. His theory was later extended by Albert Einstein.

There are two very interesting concepts in Quantum Statistics namely, the Bose Einstein and the Fermi Dirac statistics. These are two popular theories that deal with probability distribution or the possible ways in which identical particles( similar looking particles) present in a given quantum system are distributed in a given quantum state of that system. For simplification let us call it as the energy state of the system.

To make it a little more simple let us consider an analogy. Suppose we have a box filled with chocolates. All the chocolates look similar to each other. So here, the box is our system and the chocolates are the collection of identical particles in this system. Now, inside the box there are tiny compartments such that only one chocolate can be placed in each compartment. These compartments are the energy states. This type of arrangement of particles is called the Fermi Dirac statistics. The particles which obey this statistics are the fermions. It is in accordance with the Pauli's exclusion principle which states that no two fermions can occupy the same quantum state in a given quantum system.( that is in our box system two chocolates cannot be present in the same compartment).

Now, in another situation consider the same box, but this time we have a collection of identical chocolates that are smaller in size, are cooled and kept very close to each other. Now in the same compartment, it is possible to fit more number of chocolates. This is similar to what happens in Bose Einstein statistics. These particles are called bosons and are different from the fermions. It is observed that at low temperature bosons condense together due to which more number of particles can occupy a given energy state.( more than one chocolate in a given compartment). The condensed form of particles is called the 'Bose Einstein condensate'.

While teaching this topic in an online class of Physical Chemistry, my Professor narrated a very interesting incident related to the two scientists who developed these statistical theories. Although there isn't any actual evidence about this incident, yet it is an interesting way of remembering the concept. Hence I am sharing it here.

It so happened that Enrico Fermi and Satyendra Nath Bose together had gone to attend a conference. While leaving for the conference Fermi realized that there were two cars waiting outside. When he questioned Bose about this, Bose said that one car was for Fermi and the other one was for Bose and his students. Listening to this Fermi said "Why are you travelling in a different car? "wont you be coming with me?" He demanded. To which Bose calmly replied" I have arranged this car for you. Only one person will sit in it just like your statistics in which a single particle is present in a given energy state. I will go in the other car along with my students since my statistics says that there could be more that one particle in a given energy state.

Although it appears as a simple gesture but this story had me thinking a lot. Isn't this true? How easily one can be at ease with their own opinions without disrespecting the point of view of the other person. Yet we spend our lives in proving our point to others. And go to extremes if someone refuses to agree.

There could be hundred people in a group with hundred different opinions. So what? It is never a question of whether you agree or disagree with a particular school of thought or an idea or a concept. As stated in the book Autobiography of a Yogi, 'The only scientific attitude one can have is whether it is true or not'. 

Do these ideas, facts and opinions take us to the truth we all are seeking? Do they in any way help remove or reduce the obstacles that we face in our day to day lives? After all that is the sole purpose. Be it building a new car, reforming a National policy, learning a difficult concept or making the vaccine for the covid virus, what we seek is the trueness of our results. Whether these opinions contribute to the trueness of these results is what we should be concerned about.

And if at all the opinions do not match, then, there is always a second car waiting in the parking. ultimately, both these cars reach the conference hall just like the theories proposed by both the great scientists sitting in these cars led to the basis of what we call the Quantum Statistics.

©Neha kanase

Sources:

1. Bose–Einstein statistics - Wikipedia

2. Fermi–Dirac statistics - Wikipedia

3. Image 1: enrico fermi and paul dirac photo together - Bing images

4. Image 2: satyendranath bose and albert einstein photo together - Bing images