* The Fermions
Fermions are one set of fundamental particles and the other one are
bosons. The distinguishing factor between bosons and fermions is
that the fermions have half integral spins, whereas the boson have
integral spins. Their names suggest that the bosons were discovered
by S N Bose, an Indian physicist and fermions by E Fermi. Now
another this is that the fermions follow what is known as the Pauli
exclusion principle. That is to say you cannot have two fermions
which have all the quantum numbers same.
The Pauli exclusion principle is a quantum mechanical principle formulated by the Austrian physicist Wolfgang Pauli in 1925. In its simplest form for electrons in a single atom, it states that no two electrons can have the same four quantum numbers; that is, if n, l, and ml are the same, ms must be different such that the electrons have opposite spins. More generally, no two identical fermions (particles with half-integer spin) may occupy the same quantum state simultaneously. A more rigorous statement of this principle is that for two identical fermions, the total wave function is anti-symmetric.
http://en.wikipedia.org/wiki/Pauli_exclusion_principle
And electrons are fermions It is this principle which decides the electronic
configuration in atoms. The filling up principle or the aufbau
principle works according to the exclusion principle. So when near
to each other the electrons will tend to have different quantum
numbers. If all the quantum numbers are same for a given pair of
electrons, then they must have the spins opposite. But now if a
third electron is to be arranged in the same orbit, it simple cannot
be accommodate; it has to go in a different orbit. So that the
electrons behave, as if they do not like the proximity of each
other.
* Local trains
Now when observing humans when they are in a crowded environment
like a local train in Mumbai, I feel that the humans do behave
exactly like fermions. That is to say that they do not like the
proximity of each other, just like the electron do not like
proximity of each other in the electronic orbits. I have observed
this many a times in the local trains. Usually the trains are very
crowded. Even to get a position to stand comfortably is a privilege,
especially in the peak hours.
When you board the train at the starting station like the VT, then
what follows is closely analogous to filling up of the electronic
orbitals in the atom. The seats that are usually taken first are the
window seats. In the atom it would correspond to the first filling
of the principal quantum number. In the window seats also the
preference is to the seats for the windows which face the incoming
air, that is facing towards the direction of travel.
Then the seats are filled in the order of least occupancy. People
want to sit at the seats which are least occupied. Normally the
seats can take 3 people, and 4 with a bit of difficulty. But the
norm is that 4 people are seated on a single seat. Once all the seats
are filled up to 4 occupants, then people tend to stand in between
the seats. The analogy does not extend to the people who are
standing at the doors, there it is more like an ensemble of free
particles, which are jumping in and out of the compartments.
So coming back to the seating arrangements what I have observed is
that once the seats are filled with 4 occupants. That is the maximum
that our 'seat' orbital can take. The rest are occupied in between
states. They are like virtual states, ready to jump into the empty
seats as soon as one gets empty.
* The Law of 3
Lets assume that the people standing in between are like the
electron sea in metals. Now lets assume a situation in which there
are a few people who are standing in between seats and all the seats
are seated by 4 people. Now lets see what happens when one of the
person who is sitting stands up to get off the train. As soon as the
seat gets empty, one of the persons who is standing goes to fill in
the empty seat. As more and more people get off, the people who are
standing take up their seats. Finally we reach a state when there
are no more people who left are standing. Now all the seats have
four seated occupants. Now if a single person gets up. There is one
seat with just three people, but people don't tend to move to that
seat. It just not worth the effort, by going from a 4 seated seat
again to a 4 seated seat, you don't gain much. So you remain seated
where ever you are. But if you are one of the people who are seated
on the seat where the person just left from, you surely feel
relieved.
Now let us try to visualize the situation if 2 people from a single
seat leave off. Two people leaving from 2 different seats will not
help. It has to be 2 people who were seated on the same seat. After
this what we have is that, there is a seat where only 2 people are
seated and rest of the seats have 4 people seating on them. As soon
as this happens, a person from a 4 seater, will try to get to the 2
seater seat. This results in two 3 seater seats, whereas the rest
are 4 seaters. Even more if 3 people from the same seat go away, the
resulting changing of seats by people results in maximizing the
number of 3 seater seats. This is the law of behavior of people in a
local train ;). I call it the Law of 3. This just also touches on
the idea of what is called in psychology as personal space. We
are comfortable only within a certain distance from each other. And
make it a point to bring this into existence we make the movements.
Well this is just a vague analogy, to the actual behavior of the
fermions is much more involved, but nonetheless the analogy is worth
observing.
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