Book Review: Elementary Particles and the Laws of Physics

Elementary Particles and the Laws of Physics by Richard P. Feynman and Steven Weinberg (Cambridge University Press, 1987) is based upon lectures given by the authors in 1986 at Cambridge University as the inaugural entries in a series of endowed lectures in honor of P.A.M. Dirac, one of the fathers of quantum mechanics.

These two distinguished physicists were instructed to deliver their lectures at a level suitable for an undergraduate student who had taken an introductory course in quantum mechanics. By and large, I think they succeeded, although I would not have minded a bit more mathematical detail. There were occasions upon which certain intermediate steps were glossed over, leaving room for a bit of confusion.

The book is a quick read, weighing in at only 110 pages. (The two lectures from which it was drawn were only about an hour long each.) With such brevity, it could really be considered two essays (which I shall discuss separately below. Despite that brevity, each of the two contributors weighed in on some rather heady topics, although not in great depth.

“The reason for antiparticles” by Richard P. Feynman

It is entirely fitting that Feynman should have been chosen to give the very first of the Dirac Memorial lectures, as it was Dirac who laid the groundwork for quantum electrodynamics (QED) in a 1927 paper, and it was Feynman who filled in the gaps to turn QED into a useable theory with his 1942 dissertation on the path-integral formulation of QED. Feynman’s stated goal for his lecture was to demonstrate how Dirac’s 1928 unification of quantum mechanics with special relativity (resulting in the Dirac Equation) inevitably lead to the prediction of antiparticles. Interestingly enough, he managed to do this without actually invoking the Dirac Equation itself. Feynman also provided a secondary goal for his lecture, that of demonstrating the origins of the Pauli Exclusion Principle as a direct consequence of the existence of fermions (fermionic behavior also being a direct consequence of the Dirac Equation).

I should note that a video of Feynman’s lecture is available:

The video noise at the beginning can be ignored and does not cut into the content. Unfortunately, the resolution of the video is far too low to allow the diagrams and equations on the overhead transparencies to be read. Personally, I find it somewhat enjoyable to watch the video (to get the benefit of Feynman’s charismatic delivery) while following along in the book (to see the equations and diagrams).

While Feynman’s exposition did an admirable job of explaining the origin of antiparticles, I feel that it fell somewhat short with the secondary goal regard spin-statistics. He unfortunately glossed over the mathematical reasons for half-integer spins resulting in a sign change of the wave function upon particle exchange (or, equivalently, upon a 360 degree rotational coordinate transformation), although he touched upon other arguments for this, particularly in the context of charge, parity, and temporal transformations.

As for the primary goal, though, Feynman was in fine form, bringing to his lecture the clarity that has always been a hallmark of his lectures. As an added but unstated benefit, his approach to the problem presented some insite into the origins of his famous Feynman diagrams and their mathematical underpinnings. Peppered throughout the lecture are proto-Feynman diagrams (missing only the photons, which are replaced by unspecified “disturbances” due to an imposed potential) meant to enumerate the contributions to a standard perturbative expansion in quantum mechanics, whereas proper Feynman diagrams are a method of enumerating the contributions due to various interactions to a Lagrangian in the path-integral formulation of QED. In both cases, the diagrams serve as bookkeeping devices for catching all of the leading terms of an infinite series expansion.

“Towards the final laws of physics” by Steven Weinberg

The second half of the book is from Steven Weinberg, who built upon Feynman’s work and extended the principles of QED to realm of weak nuclear interactions to create electroweak theory. The focus of Prof. Weinberg’s contribution was at a somewhat higher lever, focusing on what we can glean from current current physical models to predict what an eventual “theory of everything” might look like. He started off with a brief, greatly over-simplified overview of quantum mechanics (in which he obliquely managed somewhat pull off what Feynman failed to do regarding the sign change of the wave function of fermions, which for me was the high point of his contribution). He then proceeded to go into an overview of using dimensional analysis to discuss divergent terms in the Standard Model Lagrangian and how such methods are used to predict energy ranges at which gravity must operate in order to be incorporated into quantum theory. Weinberg also touched upon the importance of symmetry rules in constructing a final theory. He then closed with a quick introduction to String Theory, which, at the time of the lecture, was just beginning to strongly capture the interest of theorists (despite having been around for a decade and a half at the time).

All in all, this quick little book is a worthwhile diversion for someone with a smattering of an interest in the topic and who isn’t afraid of a handful of equations.

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About Glen Mark Martin

MCSE-Messaging. Exchange Administrator at the University of Texas at Austin. Unrepentant armchair physicist.
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