Sunday, September 15, 2013

Klein and Gell-Mann: birthdays

Today, we celebrate the birthdays of two true heroes of physics, at least according to the hitparades administered by your humble correspondent. Oskar Klein belongs to the history textbooks but Murray Gell-Mann is happily with us. Congratulations!

Oskar Klein

Oskar Benjamin Klein was born near Stockholm to a rabbi's family on September 15th, 1894. You shouldn't confuse him with Felix Christian Klein, a Prussian mathematician who lived half a century earlier.

Oskar Klein was a student of Svante Arrhenius, the guy who found out that the greenhouse effect was logarithmic. Oskar worked at the Nobel Institute and wrote papers about chemistry as a high school student.

In 1914, he wanted to do research in Paris but as the number indicates, he was drafted to the world war. After a couple of years, his service ended so he returned to Arrhenius. But he also met Hendrik Kramers who was a student of Niels Bohr. In 1918, he began to visit Copenhagen with a fellowship. He fixed some bugs in Bohr's work on molecular collisions and wrote a thesis on molecular motion, extending the Brownian motion to ions, in 1921.

When he got his PhD, he began to write semi-popular, blog-style texts on physics. One of them explained why Swedish philosophers who opposed relativity were wrong. In 1923, Klein married Gerda Koch and with Bohr's help, he got a job in Ann Arbor, Michigan.

In Michigan, he quickly understood the anomalous Zeeman effect: the splitting of spectral lines is proportional not just to \(L\) but to \(L+2S\) where \(S\) is the spin. Klein continued with the angular momentum of molecules and, while teaching the effects of electromagnetism and gravity at the same moment, he was getting ready to tackle the unified field theory in 1924.

Klein and compact dimensions

If you read the 1919 paper by Kaluza, it seems pretty clear that Kaluza knew how the classical equations of GR and electromagnetism in four dimensions can be obtained from GR in five dimensions. But he really didn't know that the extra dimension should be compact. What he did was a dimensional reduction, not a real compactification.

It just happened that Oskar Klein came to the idea of a fifth dimension independently: he was thinking about massless particles in five dimensions: the mass seen in four dimensions is simply the fifth component of the momentum.

Back in 1921, Einstein allowed Kaluza's original paper to be published. Badly enough for Klein but happily for science, Klein contracted hepatitis in Copenhagen in 1925. That allowed him to return to serious work. Wolfgang Pauli told him about Kaluza's results and Klein "tried to rescue what he could from the shipwreck".

At that time, it was realized in the quantum community that the momentum is discrete if the dimension is compactified. Klein was able to use this result in the context of Kaluza's theory. That's great. So he realized that the dimension had to be compact and identified its isometry with the electromagnetic \(U(1)\).

Klein also found it natural for the radius of the dimension to be close to the Planck length, a fact that would soon lead to the falsification of the simplest Kaluza-Klein theory, because of the unbearable lightness of being of the electron. (By the way, no, I don't know whether Milan Kundera was really an informer.)

At that time, Nature was publishing top research in theoretical physics. His article appeared there in 1926 and intrigued people like Fock, Rosenfeld, de Broglie, and Struck. However, people at that time had to understand a lot of other, more elementary and down-to-Earth ("testable") physical phenomena so the interest in his unified field theory unfortunately faded away at that time. Dirac thought that Klein was trying to solve too many problems at the same time.

In 1926, Klein became the closest collaborator of Bohr and arguably contributed to complementarity, correspondence, as well as the uncertainty principle. Heisenberg later admitted that Klein knew why the uncertainty relations and complementarity were morally the same thing.

Still in his great year of 1926, while recovering from hepatitis, Klein wrote their famous Klein-Gordon equation. Schrödinger did so earlier, as a relativistic mutation of his normal equation, but didn't publish it because he realized that the fine structure of the Hydrogen atom comes out incorrectly. See also an article about Vladimir Fock, the Soviet co-discoverer.

Around 1927, as Lars Brink reported, Klein was recommended to focus on teaching. Nevertheless, he continued with his research, together with Pascual Jordan: second quantization was one of his topics. He clearly became the world's #1 in these matters, as we will emphasize later. Yes, as you can see, Jordan had no trouble to work with Jewish physicists such as Klein.

Klein and Jordan found the link between the quantum statistics and quantum fields, while second-quantizing Schrödinger's equation. Jordan-Klein matrices are named after them. Klein and Yoshio Nishina worked on Compton scattering and Klein clarified some misunderstandings about the nature of positrons and perfect transmission of electrons ("Klein paradox"). The Rydberg-Klein-Rees method is a reverse algorithm to decode some potential energy curve from the position of lines in the diatomic molecular vibrational-rotational spectra.

In 1930, Klein returned to Stockholm. In the decade that followed, he helped some physicists-refugees including Walter Gordon (from their equation). Since the 1930s through 1960s, Klein attended many conferences and the most fascinating one was the 1938 Warsaw Conference. We will look at his picture of the world in 1938 more closely.

In the 1960s, Klein co-fathered the Klein-Alfvén cosmology with an equal amount of antimatter "cleverly" (?) separated from the regions of matter.

Warsaw 1938

If you know what "Klein" means in German, you may figure out which physicist has both the linguistic authority and expertise to write captivating things about Oskar Klein and other physicists as seen in 1938. Yes, see:
Gross about Klein (PDF)
Yes, I definitely recommend you this article because it is one of the cutest analyses of the history of physics as made by a true professional.

David Gross shows that all the big shots, including Heisenberg (who wasn't present physically), Bohr, de Broglie, Eddington (who was already a full-fledged crackpot at that time), Gamow, Fowler, and others were immensely confused about some very basic matters. They generally and unreasonably believed that quantum mechanics would or should break right behind the corner. Moreover, they had no understanding that the particle/field duality applied both to fermions as well as bosons (i.e. the electromagnetic field). In fact, you can see that the very concept of a "photon" was still controversial in 1938.

On the other hand, what Oskar Klein presented in 1938 was arguably on the same conceptual level as the Standard Model. He was just so damn close! He fully understood that there are bosonic and fermionic fundamental fields that should be second-quantized and that generate particles. He knew that the exchange of bosons is responsible for forces.

Moreover, he sorted the elementary fermionic particles of his era - electrons and neutrinos; protons and neutrons - into \(SU(2)\) doublets (realizing that they have anti-particles, too). And he supplemented the \(U(1)\) electromagnetic field with a whole \(2\times 2\) matrix of other bosonic fields that are responsible for other forces. More concretely, he would identify the off-diagonal elements with Yukawa's pions (rather than the W-bosons: the different types of nuclear interactions were not really understood well).

All this reasoning was obtained by a careful conceptual analysis of the Kaluza-Klein theory. There were many subtle technical bugs - he didn't realize that the \(SU(2)\) symmetry was there at the fundamental level (only \(U(1)\) was his organizing principle) but conceptually speaking, his theory was in the same universality class as the electroweak theory. Nothing essential for the construction was missing.

With his ideas currently viewed as basic tools of string theory, Oskar Klein was 30 years ahead of his time. If you see how relatively clear his picture of the world was before the war began, you may share my feelings that many of the later developments in physics - when Yang-Mills symmetries etc. had to be re-discovered - were just far too slow: pathetically inefficient.

From the modern perspective, it seems so obvious that Oskar Klein knew what he was talking about much more so than any of the "more famous" guys. I wonder whether there was any way to "prove them that they should listen" and "force them to listen" to Klein. That could have sped up physics by 25 years or so.

Later years

Klein later worked on cosmology, with Hannes Alfven, and wrote popular books and books about religion and science. Nevertheless, his amazing visions in 1926 and 1938 make him one of the finest theoretical physicists of the 20th century. He died in 1977.

Murray Gell-Mann

Murray Gell-Mann is an amazing scientist. I met him at Sidneyfest in 2005. So of course, I asked him about his cute commercial for Enron (Keep Asking Why) ;-) as well as about Feynman's opposition to teeth brushing: yes, Feynman really believed it was a superstition. But let us start at the beginning.

Murray Gell-Mann was born into a family of Jewish immigrants on New York's Lower East side on September 15th, 1929. The surname is an idiosyncratic way to translate a Russian Jewish last name, Gel'man.

He has been a child prodigy from the start. When he was 15, he graduated valedictorian and entered the Harvard for dummies, as Yale is called in Cambridge. ;-) He earned a Bc in physics when he was 19- and a PhD from MIT when he was 22-. After a postdoc job, he became a professor in Chicago and Caltech 3 years later.

We're already in the 1950s. A lot of cosmic ray particles were observed: see Brian Cox's video for the context. He introduced a new quantum number, the strangeness, that would also later lead him to a classification scheme of the particles based on the \(SU(3)\) flavor symmetry. Independently of George Zweig in 1964, Gell-Mann postulated the existence of quarks.

There were many things that led him to the quarks, including the 1955 Gell-Mann-Nishijima formula,\[

Q = I_z + \frac{B+S}{2}

\] Because his term "the eightfold way" - also a title of a book with Yuval Ne'eman - originated in Buddhism, it shouldn't be shocking that the term "quark" was imported from James Joyce's "Finnegan's Wake". Zweig called quarks "aces" - a term that became as popular as "screwing string theory" for "matrix string theory".

Gell-Mann, together with Harald Fritzsch, improved the ideas of Nambu and Han about the quarks' colors and wrote down the theory of quantum chromodynamics, without realizing that it was asymptotically free. Anyway, the key role that Gell-Mann played in the understanding of the strong force seems unquestionable, especially once I also mention his discovery of current algebras and nonlinear sigma models for pions, so let me move on.

Together with his colleague and rival, Richard Feynman, Gell-Mann has found essential things about the weak interactions, too. Independently of Sudarshan and Marshak, they realized that the weak interactions were of the \(V-A\) type (vector minus axial vector: this combination was appreciated as a candidate since the Yang-Lee discovery of the parity violation), i.e. that the gamma matrices you have to insert in between the Dirac spinors, to create a current (whose square enters the four-fermion interaction sketched by Fermi), have an odd number of indices.

You may remember Feynman's stories about the experimenters who claimed that the interaction was of the \(S-T\) type (scalar - tensor) but the experimenters were proven wrong because they were only building on inferior minds and experiments while Feynman and Gell-Mann were building on superior minds and a robust theory. More precisely, the experimenters' conclusion relied on the last point in their graph which should never be trusted. ;-)

In the 1970s, Gell-Mann's authority was essential to keep string theory alive at Caltech, one of the centers at that time. Nevertheless, Murray couldn't protect John Schwarz from Feynman's jokes in the elevator - e.g. "How many dimensions do you live in today, John?" :-)

Since the 1990s, he studied complexity and has been associated with the Santa Fe Institute. Many people love to say many fashionable things about emergent phenomena but you can check that Gell-Mann thinks, just like I do, that all these emergent phenomena are derived from a more fundamental theory: "you don't need something more to get something more". :-)

Gell-Mann is a keen bird-watcher and linguist who is even able to teach Chinese colleagues how their own names should be properly pronounced. :-) He is thrilled by the question whether all the languages have a common ancestor. There are lots of articles on this blog related to Gell-Mann but let me remind you about two videos:
Google talk: On Creative Ideas
TED talk: On Beauty and Truth in Physics

Dozens of TRF blog entries mention the full name of Oskar Klein and the same thing holds for Murray Gell-Mann.

Dear reader, do you feel a deja vu? Long-time TRF readers without sclerosis should. ;-)


  1. Klein was surely ahead of his time. I might be mistaken but I read somewhere that the real father of gauge theory was Hermann Weyl (Maxwell had no idea about gauge invariance). In fact, the somewhat confusing name "gauge" comes from him (scale invariance). There is a nice website dedicated to Weyl and it containes some very clear presentations of his ideas, among others a nice intruduction to Kaluza-Klein theory

    I recently became interested in quantum mechanical phase. Gauge theory is basically invariance under local phase transformations. The complex numbers forming a wave function can be understood as real number (aplitude) + phase (U1, little rotating arrows by Feynman). Especially cool is the geometric description of the gauge theory (in terms of fibre bundles)

    Aharonov-Bohm effect and the Berry phase show that the phase is something more than just an arbitrary appendage to the wave function. Last week I read a cool paper from Dirac about quantum phase, Dirac monopoles and Dirac strings

    Have you written some blog entry about quantum phase or Berry phase that I could read?

  2. LOL @ the Kundera reference. Don't worry, Lubos, staunch TRF readers, like myself, read all of your posts word by word and sentence by sentence. On average, it's just worth the time. I guess that's what you wanted to probe?!
    And yes, I did remember the Klein / Gell-Mann birthday post from 2008, though not its specific contents.
    It's kind of sad to hear that Feynman thought that tooth brushing is a superstition. I always thought Feynman was sensible in just about every aspect of life...

  3. LOL, from a German point of view the title of the Gross about Klein (PDF) paper is excessively funny :-)))

    Was just scrolling through and look forward to enjoy this post in depth later today ... :-)

  4. Feynman figured that if the girls would still kiss him brushing was unnecessary. ;)

  5. Lubos, is Gell-Mann the same Gell-Mann after whom Michael Crichton named the "Gell-Mann Amnesia effect"?
    I think Crichton's observation is a key to understanding and engaging in debate and discussion, particularly in our information-flooded world.

  6. Yup, Eric! It's the same physicist Murray Gell-Mann. Quote:

  7. Lubos, what do you thing about Clifford algebra approaches to physics? There are some attempts to formulate even string theory on Clifford spaces. They say that it elimates the need for the compactified hidden dimensions.
    Here a guy claims that he can reconstruct Kaluza-Klein theory from a Clifford space
    Here someone tries to construct a string theory on a Clifford space
    I find the Clifford algebra appealing because it treats vectors, spinors and tensors in a unified way.
    Is it all crackpottery or is it worth my time trying to understand these approaches?

  8. Dear Mephisto, I will avoid resolute conclusions on the paper because I haven't read the whole paper or the whole thesis.

    I don't understand in what sense a Clifford algebra is a general "physical object". For me, it's just the algebra of gamma matrices that is obeyed - for certain group representation theory reasons - by the gamma matrices; and for other reasons - fermionic harmonic oscillators - by the modes of fermionic fields etc.

    Already these two representations have very different physical interpretations. This simple algebra and similar others are obeyed by various matrices and operators in physics. Sometimes the objects are more naturally clumped to the algebra elements, sometimes it's more a bookkeeping device. At any rate, they're not new in physics and I don't understand what is the "big picture" that is meant to make them more important than they are.

    I surely don't think that Clifford algebras are as rich and important for physics as e.g. Lie algebras.

  9. Thanks for the answer. Clifford algebras form Spin and Pin groups and every Lie algebra can be represented by spin groups
    Clifford algebra (geometrical algebra) may not be a new physical object but it provides a new unifying language for the reformulation of existing physics. And every new language can offer new insights which were not visible in the old language (Newton machanics vs Hamiltonian mechanics).
    Maybe even the new work of Hamed-Arkhani could be formulated in terms of geometric algebra, it certainly can describe twistors

  10. I am not able to make any sense of the paper about "Lie groups as spin groups". What's important is that general Lie groups are not isomorphic to any Spin(M,N) groups.

    We say that a new language may offer new insights but we mean a new physical language, like your example with the Hamiltonian vs Newtonian mechanics. But human language, like English, can't offer new physics insights that can't be obtained e.g by Czech language.

    As far as I can see, the case of the Clifford algebra is closer to the "human language" example. I just don't see any physics beef - any new physics principle - in the comments about "physics as Clifford algebras". I don't know what you and others may possibly mean by such a combination of words. Clifford algebras are mathematical objects.. I haven't seen any physics principle linked to that structure. All the papers trying to worship the Clifford algebra look physically meaningless to me. The Clifford algebra has no universal physical interpretation in these pictures.