Bengali-Italian Great Divide

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This is the greatest of all Great Divides!

All other Great Divides like East-West, North-South, Black-White pale before this.

Bose and Fermi sit across their dining table and spin ALL the elementary particles that come along to build this Universe.

And pocket them between themselves leaving nothing to others.

Bose's collection are called 'Bosons' and Fermi's 'Fermions'.

What an honor for an Indian! All other Indians maybe forgotten (if not forgiven) but as long as Intelligence survives in this Universe Bose will be remembered thus, no escape.

The behavior of a collection of bosons is as different as can be than that of a collection of fermions.

Bosons are gregarious. The more the merrier. All are welcome!

Fermions are unsocial. Keep off!

We already saw that Pauli with his stick keeps electrons apart. That is because electrons happen to be fermions. He couldn't do it with bosons.

That is why normally, you can't crowd electrons in as thick bundles as you wish. But you can do it with bosons. Photons (light particles) are bosons. So, you can have as intense a spot of light as you wish, say in a laser.

But, occasionally, electrons and other fermions pair-up and act like bosons. Then you CAN crowd many of them. This is what gives rise to exotic effects like superconductivity and superfluidity.

The 'spin rule' is simple to state but hard to prove.

It says that bosons have 'integer' spins while fermions have 'half-integer' spins. (There are no other spins like 3.337).

Feynman worried that a rule as simple to state as this has no 'simple' proof (although he too contributed to it). He bluntly states that this simply means that we (he) hasn't understood the thing clearly (yet). He says that the proof is deeply embedded in the recondite nooks of Relativity and Quantum Field theory.

There is what is called the 'spin-statistics theorem' (note that no name is attached to it like the Pythagoras Theorem; which means that several names are there).

I guess the difficulty is that it is a 'negative' theorem. Like the 'no-win theorem' (The Second Law of Thermodynamics). Simply put, it says that it is impossible to build a 'consistent' theory that can cheat this Great Divide.

Long Live Bose and his alma mater Presidency College of 1915 (?) .

[Aside: For folks like me who have strayed into Physics without any aptitude for it, everything is difficult and needs laborious understanding, if that.

I knew that electrons can have spin as well as orbital angular momentum when their charge clouds whirl around a nucleus.

But I was told that so is the case with photons, although they don't whirl around any nucleus (forget black holes where Einstein's Gravity squeezes bosons as well as fermions in a Great Crunch).

So, what could this 'orbital' angular momentum of photons be?

The clue I got was from a stray remark that unlike electrons, photons have no wave function in the coordinate space, but only in the momentum space.

Momentum space wave function simply means 'angular distribution'.

Ah! There you are!

Photons come in various flavors: dipole, quadrupole, of the electric, magnetic varieties and various polarizations.

Then I remembered that photons are generated by electron jumps from various orbitals obeying various selection rules and carry away their angular momenta splits.

Then I chanced to read Akhiezer and Bertetski. It has everything you ever wanted to know about photons and electrons.

A cigar is a smoke but a good book is great joy!]
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