# Gell-Mann’s innovative thinking| The Eight Fold Way|

May 25, 2019

Note: This post is a tribute to Murray Gell-Mann a physicist who passed away yesterday-24th May 2019. A man who used innovative thinking and intuitiveness to tame the particle zoo that terrified physicists in 1950s.

Chaos is merely order waiting to be deciphered Jose Saramago

Humans have had the tendency to breed chaos ever since the first nomads started fighting for food. But there are few among us who found order among all of the chaos. Mendeleev was one of them and so was Dr. Murray Gell-Mann.

It was in 1869 when the Russian Chemist Dmitri Mendeleev organized the known chemical elements in a table and found order among many known elements -metals and non metals alike- making a periodic table.

Doing that Mendeleev not only had an easy way to classify different elements but also predicted various elements which were not yet known and predicted their properties.

Murray Gell-Mann did a similar thing but for Particles (Bosons and Fermions), proving the importance of Innovative thinking and how out of the box thinking can lead you to wonders.

## Murray Gell-Mann

Dr. Murray Gell-Mann had an inherent curiosity as he was growing up in Manhattan. When he was a kid he and his elder brother- who was 9 year older- used to go bird-watching where he encountered his various interests. Including Nature, Archaeology, Etymology and even literature. He pondered through and read James Joyce’s Finnegans Wake an Irish novel which played an important role in the future(unknowingly).

Gell-Mann found elementary physics difficult and he wanted to go with Biology and Linguistics as his major while filling for the university, but his father told him to reconsider and opt for Engineering (as it would be easier to earn a living with it and he won’t starve). Gell-Mann then replied to him: “I’d rather starve. Besides, if I design anything, it will fall down, fall apart.” (you can find this in CalTech’s oral History Project here)

Vocal about his dislike of the subject his father then advised to find a middle ground with Physics. As he narrates in his interview:

So then I said, “Well, what do you suggest?” My father said, “What about a compromise? What about physics?” And I said that that course in high school was a disaster. It was the only course in which I did badly in high school, and I hated it. He said, “Oh, that doesn’t make any difference. At the university, you’ll study quantum mechanics and relativity, and you’ll love it. It’s marvelous.” So I took physics, and after a while I got to like it. And I found that my father was right, in fact—uncharacteristically, he was quite right. Quantum mechanics and relativity were marvelous.

There’s a life lesson to be learnt from Mr. Gell-Mann here, A subject that he really disliked, it grew up on him and went on to become his passion. He never gave up on it. And of-course his father helped him on. He fondly remembers a few of his teachers and professors that helped on the way.

He did went on to pursue his PhD from MIT and started teaching at University of Chicago. In 1950s he started his work on Particle Physics and Quantum Electrodynamics which was the upcoming branch of physics that was giving incredible results with physicists like Feynman, Schwinger.

Murray Gell-Mann teaching at CalTech

## It’s raining Particles and they are strange

In 1940-50s there were a slew of particles that were discovered in UK as well as in CalTech by Carl David Anderson in cosmic rays (Radiations coming from outer space).

Then in 1952 first particle accelerator that could accelerate particles up to energy order of few GeV started operating and many other baryons were introduced to the array of particles. They were dubbed strange particles because they showed a few behaviors which other particles never did. These particles were always produced in pairs and were produced by Strong Interaction (Time Scale ~ $10^{-23}$ s) and decayed by Weak interaction.(Time Scale ~ $10^{-10}$ s)

Particles from Cosmic Rays interacting in Atmosphere

In 1953 Gell-Mann and Nishijima proposed a new property that these new particles must have assigned to. They called it Strangeness. It was a qunatum number much like Charge, Lepton Number or baryon Number which already existed back then. The number is conserved in Strong interactions while not in weak interactions thus explaining the weird behavior of strange Particles. Gell-Mann also working with Richard Feynman proposed a vector/axial vector (VA) Lagrangian for weak interactions. Without going into much more detail let’s get back to the particles.

By the end of 1960s there were more than 100 different particles that had been discovered in last two decades and which confused physicists across the world. Some physicists started calling it “particle zoo” .Each particle was an elementary particle. And there could not have been as many elementary particles.

## The Eightfold Way

Gell-Mann : "Anyway, in those years I was thinking a lot about approximate symmetries—going beyond isotopic spin and forming very approximate families, which we can call supermultiplets. Wigner invented that term, for something slightly different, in 1936 and ’37. And I use that term sometimes myself for this slightly different physical concept. The idea was to put these particles, which were already in isospin families, into bigger families. It’s much like classification in biology. But here it has dynamical consequences and dynamical origins. "

In the academic year 1959-60, Gell-Mann took on the problem that was troubling the physics world. He started meddling with Symmetries of Weak interaction. The SU(2) times U(1) symmetry was giving results which were not coherent with the eight particles. An year later he discarded the global symmetry he was working on and started on the lie algebra of SU(3) group.

He identified the Symmetry present in the particles and then in January 1961 proposed the so called Eight-fold way to arrange the particles. While the group representation of SU(3) holds complicated mathematics and lie algebra which is complicated. It is very simple to see how the eight-fold way works and arranges particles as their properties.

Gell-Mann and Nee’man independently discovered the eight-fold way to arrange Baryons and Mesons in complex geometrical patters according to their properties.

Meson Octet

In this arrangement each property as you go from left to right (Strangeness) or top to bottom (Isospin) or diagonally (Charge). ( As we had groups in Mendeleev’s Periodic Table)

Eight particles are arranged in Hexagons called as Octets and ten particles are arranged in a triangle and is known as a decuplet.

Baryon Octet

Each octet and Decaplet had Spin and parity constant. As we go down an octet or a decuplet the mass of particles increase and the mass is almost constant horizontally. For constructing the baryon Decuplet ,The principles of the eightfold way also applied to the spin-3/2 baryons .

Gell-Mann found that at the bottom of the figure there was a particle with -1 Charge and -3 Strangeness that should exist. But it had not been discovered yet. He proposed that the particle will have mass of 1650 MeV. In 1964, particle researchers detected a particle corresponding almost exactly to Gell-Mann’s description.

Note: It says a lot about Gell-Mann’s understanding across multitudes of subjects that he called it the Eight-Fold way based on the Eight-Fold way of achieving Nirvana in Budhist Philosophy.

## Quarks exists

Yes the Eight-fold way led to physically good looking geometrical arrangements of known particles. They arrived from symmetries that were shown by the particles. But why did they follow the symmetry in the first place.

Protons and Neutrons are made up of three quarks

In 1964 Gell-Mann and George Zweig independently proposed that all hadrons (Mesons and Baryons) are made up of more elementary particles which Gell-Mann called Quarks while Zweig called them Aces.

Each Baryon is composed of three quarks while each meson is composed of two quarks.

The quarks were propsed with fractional charge which many physicists thought to be absurd and thus did not accept Quark theory and rejected Gell-Mann’s hypothesis.

Gell-Mann named the particles quark from a line in James Joyce’s book that we talked about in the starting. In his book The Quark and the Jaguar Gell-Mann writes:

In 1963, when I assigned the name "quark" to the fundamental constituents of the nucleon, I had the sound first, without the spelling, which could have been "kwork". Then, in one of my occasional perusals of Finnegans Wake, by James Joyce, I came across the word "quark" in the phrase "Three quarks for Muster Mark". Since "quark" (meaning, for one thing, the cry of the gull) was clearly intended to rhyme with "Mark", as well as "bark" and other such words, I had to find an excuse to pronounce it as "kwork". But the book represents the dream of a publican named Humphrey Chimpden Earwicker. Words in the text are typically drawn from several sources at once, like the "portmanteau" words in Through the Looking-Glass. From time to time, phrases occur in the book that are partially determined by calls for drinks at the bar. I argued, therefore, that perhaps one of the multiple sources of the cry "Three quarks for Muster Mark" might be "Three quarts for Mister Mark", in which case the pronunciation "kwork" would not be totally unjustified. In any case, the number three fitted perfectly the way quarks occur in nature.

In 1967 at Stanford Linear Accelerator (SLAC), in experiments of Deep Elastic scattering of an electron and a proton proved the existence of quarks and Gell-Mann’s hypothetical particles were accepted by the Scientific Community.

SWEDEN – DECEMBER 12: King Gustaf VI Adolf of Sweden awarding the Nobel Prize for Physics to Dr. Murray Gell-Mann of the California Institute of Technology for his contributions and discoveries concerning the classification of elementary particles and their interactions. (Photo by Keystone-France/Gamma-Keystone via Getty Images)

In 1969 Gell-Mann received the Nobel Prize in Physics for “his contributions and discoveries concerning the classification of elementary particles and their interactions.”

Since, Quarks are fermions, there can’t be three particles of the same type together. But we had some baryons which had three same quarks like $\Omega^-$ had three strange quarks. To solve this conundrum, Gell-Mann and some other physicist described Color quantum number that allowed three quarks to exist together in a small space. This gave rise to a new branch in Quantum theory: Quantum Chromodynamics.

Gell-Mann was not only a famous and successful scientist. he found that success starting from difficult circumstances. In his interview series ( You can watch it on YouTube here )

His is the prime example as how if you think outside the box. If you keep your mind open, keep your curiosity alive and never give up. You can achieve incredible feats. Here is a Ted Talk by the man himself to inspire you

Sources:

• https://www.achievement.org/achiever/murray-gell-mann-ph-d/

• https://www.nytimes.com/2019/05/24/obituaries/murray-gell-mann-died-.html

• https://en.wikipedia.org/wiki/Murray_Gell-Man