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Every particle is either a boson or a fermion, depending on its spin, and the word boson carries the name of Satyendra Nath Bose. In 1924, teaching in Dacca, he found a new way to count particles of light. Einstein translated his paper and extended the idea, which led to a state of matter first made in a lab in 1995 and is linked to superfluids and superconductors, as the Nobel Prize summary for 2001 explains. Here is the story and the counting idea itself, worked through with two particles.
Who was S. N. Bose?
Bose was born on 1 January 1894 and died on 4 February 1974, according to Jagdish Mehra's biographical memoir for the Royal Society. The MacTutor biography records that he became a Reader in physics at the University of Dacca in 1921 and was professor and head of the physics department there from 1927. Earlier, at Presidency College, Calcutta, he was one of the students of Jagadish Chandra Bose, as D. T. Emerson notes in his IEEE paper on the elder Bose.
What did Bose send to Einstein?
Planck's law describes how much light of each frequency a hot object gives off. MacTutor notes that neither Planck nor Einstein was satisfied with the existing derivation. Bose derived the formula a new way, from the statistics of light quanta and, as his covering letter put it, "independent of classical electrodynamics."
Mehra's memoir says Bose sent the paper to Albert Einstein early in June 1924. Einstein "recognized its merit, translated it into German, and had it published in the Zeitschrift für Physik." It appeared that year as "Plancks Gesetz und Lichtquantenhypothese" (Zeitschrift für Physik 26, 178-181), only four pages long. MacTutor quotes the start of Bose's covering letter: "Respected Sir, I have ventured to send you the accompanying article for your perusal and opinion."
Einstein then applied Bose's counting to atoms. The Nobel Prize summary for 2001 explains that he predicted that, if enough of these particles come close enough and move slowly enough, they will all fall into the lowest energy state together. That is Bose-Einstein condensation. Mehra adds that Bose's work was Einstein's "point of departure" for this prediction.
Why are particles called bosons?
According to MacTutor, Paul Dirac coined the term boson for particles that obey these statistics. The Nobel summary gives the modern rule: particles with integer spin are bosons, and those with half-integer spin are fermions. Photons are bosons; electrons are fermions. The arrangement of electrons in atomic shells, and so the periodic table, depends on electrons being fermions.
Bose-Einstein condensation took about seventy years to observe directly. Eric Cornell, Wolfgang Ketterle and Carl Wieman achieved it in dilute gases of alkali atoms in 1995 and shared the 2001 Nobel Prize in Physics for it.
Worked example: counting two particles in two boxes
The heart of Bose's idea is how you count. Take two particles and two energy states, call them state 1 and state 2. Assume every distinct arrangement is equally likely.
Case A: distinguishable particles (classical). Call them a and b.
Both in state 1.
Both in state 2.
a in 1, b in 2.
a in 2, b in 1.
Four arrangements. Two of them have both particles together, so P(same state) = 2/4 = 1/2.
Case B: identical bosons. Swapping two identical particles gives the same arrangement, so 3 and 4 merge into one.
Both in state 1.
Both in state 2.
One in each.
Three arrangements. P(same state) = 2/3. Bosons are more likely to share a state than classical particles.
Case C: identical fermions. No two can share a state, so only "one in each" is allowed. P(same state) = 0.
Push Case B to many particles at very low temperature and that preference for sharing becomes condensation. Push Case C and you get electrons filling shells one by one.
This is exactly the question that trips students up in permutations and combinations. Our guide to probability mistakes in JEE maths works through it with dice and balls.
What to take from Bose's story
A short paper can matter. Four pages, written, as MacTutor puts it, in isolation from the mainstream developments in Europe.
Ask for a reader. Bose wrote directly to the physicist best placed to judge his work.
New counting, new physics. He did not add a new force or particle. He changed how arrangements are counted, and the results changed.
If quantum ideas such as photons and spin still feel abstract, the Fermi Concept Library has a lesson for every concept in physics and shows where each sits in the map, so you can trace spin back to what you have already learned. To connect light quanta to exam problems, start with our guide to photoelectric effect problems.
