An Anecdote by C. N. Yang

The question of the gauge-field mass problem was raised by Pauli when Yang was invited to present the Yang-Mills results at the Princeton Institute in February 1954. As Yang relates:

Wolfgang Pauli (1900-1958) was spending the year in Princeton, and was deeply interested in symmetries and interactions.... Soon after my seminar began, when I had written on the blackboard,
Yang and Pauli ( - iB)

Pauli asked, "What is the mass of this field B ?" I said we did not know. Then I resumed my presentation but soon Pauli asked the same question again. I said something to the effect that it was a very complicated problem, we had worked on it and had come to no definite conclusions. I still remember his repartee: "That is not sufficient excuse". I was so taken aback that I decided, after a few moments' hesitation, to sit down. There was general embarrassment. Finally Oppenheimer, who was chairman of the seminar, said "We should let Frank proceed". I then resumed and Pauli did not ask any more questions during the seminar.

Wolfgang Pauli and C. N. Yang

Thus Pauli also was aware of the non-triviality of the mass problem. But some other interesting information is revealed by the following sequel to the episode:

I do not remember what happened at the end of the seminar. But next day I found the following message:

February 24, Dear Yang, I regret that you made it almost impossible for me to talk to you after the seminar. All good wishes. Sincerely yours, W. Pauli.

I went to talk to Pauli. He said I should look up a paper by E. Schrodinger... it was a discussion of space-time dependent representations of the matrices for a Dirac electron in a gravitational field. Equations in it were, on the one hand, related to equations in Riemannian geometry and, on the other, similar to the equations that Mills and I were working on. But it was many years later when I understood that these were all different cases of the mathematical theory of connections on fibre bundles.


The problem with the missing mass was finally resolved by the Standard Model in the mid-1970s, according to which all the elementary particles are massless when they emerged from the moment of Big Bang. This is the symmetric phase for the Higgs fields at high temperature. About 10-10 sec after the Bang, the Higgs fields made a phase transition to the Higgs phase at low
Higgs Condensate temperature (~ 100 Gev). In the Higgs phase, the spin 1 Higgs bosons bound together to form something like the superfluid in the lowest energy state. Although we are not aware the existence of such directly, it is this condensate that endows mass to the elementary particles and ultimately our weight. The mass is generated via the interaction with this Higgs condensate as shown in the drawing. The top quark (red circle, the size is proportional to the interaction strength) is heavy because its coupling is large - the dragging manifests the effect as mass. The electron (little blue circle) is much lighter, while the photon, which has zero mass, can move freely through the condensate. It seems that the Higgs condensate is only a mathematical odd-ball, since it is portrayed to be everywhere even at room temperature but we don't feel a thing about it. Its existence has been finally proven to be real on July 4, 2012 at LHC after spending

Higgs Field Condensate
[view large image]

US$ 4.5 billion just for building the machine alone. The Higgs boson with a mass of 125 Gev was detected by bombarding the Higgs condensate with high energy protons, some of which excited the Higgs bosons to a detectable level for a fleeting moment.