The amazing Julian Schwinger

After a long gap, I'm back to this blog. I don't know if I have any readers left, let alone whether any of them are physicists. On this one occasion I want to point out something that physicists should find fascinating if they didn't already know it (other readers may or may not follow some details, sorry about that).

During the past year I gave a few talks on the discovery of the Higgs particle during the peak periods of public interest (i.e. just after the discovery, and just after the Nobel announcement). In the process I waded through a large number of original papers. The one that surprised me the most is Julian Schwinger's 1957 paper "A theory of the fundamental interactions" published in Annals of Physics 2 (1957), 404-434. At the time Schwinger had already done his path-breaking work on quantum electrodynamics and was, so to say, awaiting a Nobel prize that would finally be given in 1965.

In the 1957 paper Schwinger attempted to create, almost by pure thought, what today we call the Standard Model of fundamental interactions. He did not succeed, lacking many ingredients (Yang-Mills theory was around but he didn't use it  and maybe didn't know of it, concepts like spontaneous symmetry breaking and the Higgs mechanism had not been developed and the right symmetries and multiplet structure were not known). Yet the paper certainly influenced most of the subsequent work and laid down an approach that bore fruit a mere decade later. This fact is widely acknowledged, but the surprise for me was the amazing level of insight in the paper and the sense it conveys of being very far ahead of its time.

The paper starts with a quote from Einstein: "The axiomatic basis of theoretical physics cannot be extracted from experience but must be freely invented". At face value this would infuriate a lot of people. Today it even reads like a sales pitch for string theory! But examine the sentence more carefully and nuances emerge. It is not that physics itself must be freely invented, but rather that theory cannot be extracted directly from experiment, there is an "inventive" stage in between - one that Einstein superbly implemented while converting Michelson and Morley's experiment to the Special Theory of Relativity.

I don't want to summarise Schwinger's entire paper but will just highlight its opening and closing sections. Phrases in italics are direct quotes from the paper. The very first paragraph is a manifesto of sorts. Here Schwinger proposes the following principles:

(i) Spins 0, 1/2 and 1 are fundamental in nature, having exceptional simplicity and allowing for the construction of "unique" theories (the sense in which he intends "unique" is not made precise).

(ii) "If the spin values are thus limited, the origin of the diversity of known particles must be sought in internal degrees of freedom"

(iii) "The various intrinsic degrees of freedom are dynamically exhibited by specific interactions, each with its characteristic symmetry properties..."

(iv) "...the final effect of interactions with successively lower symmetry is to produce a spectrum of physically distinct particles from initially degenerate states"

(v) If you know what the Higgs mechanism is, be prepared to be amazed by this line: "Thus we attempt to relate the observed masses to the same couplings responsible for the production and interaction of these particles."

Today we know that the mass of each particle is proportional to how strongly the Higgs particle couples to it. But how on earth did Schwinger guess this, or something that sounds like it? I find this amazing.

The paper develops the idea that an intermediate vector boson (which he calls Z, though in today's language it is really the W) should be responsible for weak interactions, and concludes modestly as follows:

"What has been presented here is an attempt to elaborate a complete dynamical theory of the elementary particles from a few general concepts. Such a connected series of speculations can be of value if it provides a convenient frame of reference in seeking a more coherent account of natural phenomena."

If by "frame of reference" he meant "a way of thinking about things" then his hope was more than fulfilled: the intermediate vector boson idea permeated the work of many including Englert-Brout and Higgs, Glashow and of course Weinberg who in 1967 essentially wrote down the correct theory.