Elementary Particles and the Laws of Physics: The 1986 Dirac Memorial Lectures [Paperback]

This short book, Elementary Particles and the Laws of Physics, offers two lectures: Richard Feynman's The Reason for Antiparticles and Steven Weinberg's Toward the Final Laws of Physics. These two talks comprise the 1986 Dirac Memorial lectures at Cambridge University. Both presentations are cogently structured and make fascinating reading.

The talks were directed at an advanced audience, one that was familiar with quantum mechanics. Unlike many popular presentations by Feynman and Weinberg, these lectures are not suitable for the general layman.

However, these lectures are accessible to a persistent (perhaps, stubborn) layman with a calculus background and a deep interest in particle physics. I am not a physicist, but I did take my share of physics, chemistry, and math courses several decades ago. I encountered Schrodinger's equation in more than one class, but not relativistic quantum mechanics. However, having recently read Bruce Schumm's wonderful review of particle physics (titled Deep Down Things), I was sufficiently motivated to work my way through both Dirac memorial lectures.

Richard Feynman's lecture, The Reason for Antiparticles, is decidedly the more difficult. Feynman first demonstrates that quantum mechanics and relativity together require the existence of antiparticles, and then shows that they also establish the spin-statistics connection. Within a few pages advanced mathematical expressions appear and then persistently stay in the foreground for nearly the entire talk.

Although understanding Feynman's mathematics is critical for a full and deep appreciation of his exposition, with careful, repeated readings the stubborn layman will have sudden moments of enlightenment and can come away with a deeper understanding of antiparticles and spin statistics. For readers engaged in some self-tutorial readings, it may prove helpful to return occasionally to this classic Feynman lecture to qualitatively measure progress. I have no doubt that, on a deeper level, Feynman's lecture will similarly challenge and enlighten physics majors as well.

Steven Weinberg discusses his speculations on the shape of a final underlying theory of particle physics. Initially, his talk is deceptively easy as few mathematical expressions are used. However, about midway a Lagrangian density equation appears, ratcheting the difficulty several notches, as Weinberg considers a theoretical framework based on quantum mechanics and a few symmetry principles, that is also mathematically consistent with the Lagrangian dynamical principle. After discussion of some limitations of the Standard Model, Weinberg concludes his talk with a somewhat mathematical introduction to string theory.

This slender volume comprises the first two Dirac Memorial Lectures, endowed by St. John's College, Cambridge, in honor of one of its most distinguished alumni, Paul Dirac, one of the originators of quantum mechanics, and the first to successfully meld quantum mechanics with special relativity to produce what eventually became quantum field theory and the Standard Model of particle physics. The first lecture is by Richard Feynman, who helped perfect quantum electrodynamics, that portion of quantum field theory dealing with interactions of electrons and photons, the modern view of electricity and magnetism. The second is by Steven Weinberg, who pioneered the unification of electromagnetism with the weak nuclear force, pointing the way towards the Standard Model and beyond to an as-yet-unrealized dream of a Grand Unified Theory encompassing all of physics including gravity.

The lectures themselves are terrific. This review is focussed on Feynman's lecture, which is the reason I bought the book. The target audience for the Dirac lectures according to Weinberg (page 67) was "undergraduates who have had a first course in quantum mechanics". Such a course would typically not include a lot of the material covered by Feynman. His lecture concerns itself with two very deep topics in quantum electrodynamics: how the inclusion of special relativity predicts antiparticles, and the relationship between a particle's spin and its behavior in aggregates (statistics). Basically, he starts by showing how a simple mathematical theorem requires that if we restrict our analysis of particle interactions to include only particles with positive energies, then particles travelling faster than the speed of light must be included in the analysis. It is then shown that in some reference frames these particles will be seen to travel backwards in time, which can be interpreted as antiparticles. Using a particularly simple particle interaction as an example, he then shows how in order for the probabilities of all the possible variations which must be included in the analysis to add up to one, particles with spin zero (and other whole integer numbers of spin) obey one kind of behavior in groups (Bose-Einstein statistics, hence the name bosons), whereas particles with spin 1/2 (and other half-integer spin numbers) follow a different kind of behavior in groups (Fermi statistics, hence the name fermions). He shows that a particle obeying Bose-Einstein statistics enhances the probability of a copy of itself spontaneously appearing, whereas a particle obeying Fermi statistics suppresses the probability of a copy of itself spontaneously appearing. The former behavior leads to a phenomenon called stimulated emission, which is the basis for lasers (not discussed further in this lecture). The latter behavior is the basis of the Pauli exclusion principle, whereby no two electrons can occupy the same state in an atom, which in turn is the basis for the periodic table of the elements and all the phenomena of chemistry.

Feynman presupposes that the audience is familiar with the basic mathematical formalisms of quantum mechanics, such as the arithmetic of complex numbers, calculation of amplitudes, and their relation to probability. He also presupposes an acquaintance with special relativity, Minkowski diagrams, etc. He uses ingenious simplifications to make the calculation of the amplitudes and probabilities in his simple example more clear.

Which brings me to why I give this book as opposed to the lectures only one star. It's not suitable for the general reader. Yet it masquerades as such. The name Feynman is displayed in large letters across the top, as bait. Look in the science section of any good general bookstore and only four scientists will have any prominence: Darwin, Einstein, Feynman, and Hawking. These are the only four who have achieved significant name recognition with a general audience. Anyone who buys this book thinking they're getting something on the level of "Surely You're Joking" or "Six Easy Pieces" or "QED" will be disappointed. No attempt has been made to add any material which will improve the comprehension for the general reader. Not so much as a simple statement that -i times -i equals -1, let alone any definition of amplitudes, or their relationship to probability, or what a light cone is, etc., etc. This is a disservice and smacks of exploitation of the Feynman name.

Then the publisher uses the trick of shrinking the size of the pages to try to hide the fact that if the book had regular-sized pages it would be too thin without supplementary material to look worth the price being charged.

Plus, despite having gone through at least 8 printings since first published in 1987, there are still typos! Not trivial ones, either. On page 7, Figure 1 has x1 and x2 labelled backwards. On page 14, Figure 3, the sign of the sum on the left hand side should be positive, not negative. On page 18, line 11 should read "those from Fig 7c, d, and f should cancel", not Fig 7c, d, and e.

As usual, the best physics books are short and to the point, as is this one. The two Dirac lectures may serve as a perfectly good mini physics course all by themselves. I always enjoy a Feynman lecture, and this is no exception. He cuts to the chase without sacrificing the plot. But, I must say, in this case the Wienberg lecture is the better of the two. Weinberg's style has a particular grace & beauty about it that gently exposes the aesthetic meaning of the search for a picture of nature.

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