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Wednesday, November 21, 2012

Reading List: Feynman Lectures on Gravitation

Feynman, Richard P., Fernando B. Morinigo, and William G. Wagner. Feynman Lectures on Gravitation. Edited by Brian Hatfield. Boulder, CO: Westview Press, 1995. ISBN 978-0-8133-4038-8.
In the 1962–63 academic year at Caltech, Richard Feynman taught a course on gravitation for graduate students and postdoctoral fellows. For many years the blackboard in Feynman's office contained the epigram, “What I cannot create, I do not understand.” In these lectures, Feynman discards the entire geometric edifice of Einstein's theory of gravitation (general relativity) and starts from scratch, putting himself and his students in the place of physicists from Venus (who he calls “Venutians”—Feynman was famously sloppy with spelling: he often spelled “gauge” as “guage”) who have discovered the full quantum theories of electromagnetism and the strong and weak nuclear forces but have just discovered there is a very weak attractive force between all masses, regardless of their composition. (Feynman doesn't say so, but putting on the science fiction hat one might suggest that the “Venutians” hadn't previously discovered universal gravitation because the dense clouds that shroud their planet deprived them of the ability to make astronomical observations and the lack of a moon prevented them from discovering tidal effects.)

Feynman then argues that the alien physicists would suspect that this new force worked in a manner analogous to those already known, and seek to extrapolate their knowledge of electrodynamics (the quantum theory of which Feynman had played a central part in discovering, for which he would share a Nobel prize in 1965). They would then guess that the force was mediated by particles they might dub “gravitons”. Since the force appeared to follow an inverse square law, these particles must be massless (or at least have such a small mass that deviations from the inverse square law eluded all existing experiments). Since the force was universally attractive, the spin of the graviton must be even (forces mediated by odd spin bosons such as the photon follow an attraction/repulsion rule as with static electricity; no evidence of antigravity has ever been found). Spin 0 can be ruled out because it would not couple to the spin 1 photon, which would mean gravity would not deflect light, which experiment demonstrates it does. So, we're left with a spin 2 graviton. (It might be spin 4, or 6, or higher, but there's no reason to proceed with such an assumption and the horrific complexities it entails unless we find something which rules out spin 2.)

A spin 2 graviton implies a field with a tensor potential function, and from the behaviour of gravitation we know that the tensor must be symmetric. All of this allows us, by direct analogy with electrodynamics, to write down the first draft of a field theory of gravitation which, when explored, predicts the existence of gravitational radiation, the gravitational red shift, the deflection of light by massive objects, and the precession of Mercury. Eventually Feynman demonstrates that this field theory is isomorphic to Einstein's geometrical theory, and could have been arrived at without ever invoking the concept of spacetime curvature.

In this tour de force, we get to look over the shoulder of one of the most brilliant physicists of all time as he reinvents the theory of gravitation, at a time when his goal was to produce a consistent and finite quantum theory of gravitation. Feynman's intuition was that since gravity was a far weaker force than electromagnetism, it should be easier to find a quantum theory, since the higher order terms would diminish in magnitude much more rapidly. Although Feynman's physical intuition was legendary and is much on display in these lectures, in this case it led him astray: his quest for quantum gravity failed and he soon abandoned it, and fifty years later nobody has found a suitable theory (although we've discovered a great number of things which don't work). Feynman identifies one of the key problems here—since gravitation is a universally attractive force which couples to mass-energy, and a gravitational field itself has energy, gravity gravitates, and this means that the higher order terms stretch off to infinity and can't be eliminated by clever mathematics. While these effects are negligible in laboratory experiments or on the scale of the solar system (although the first-order effect can be teased out of lunar ranging experiments), in strong field situations they blow up and the theory produces nonsense results.

These lectures were given just as the renaissance of gravitational physics was about to dawn. Discovery of extragalactic radio sources with stupendous energy output had sparked speculation about relativistic “superstars”, discussed here in chapters 13 and 14, and would soon lead to observations of quasars, which would eventually be explained by that quintessential object of general relativity, the black hole. On the theoretical side, Feynman's thesis advisor John A. Wheeler was beginning to breathe life into the long-moribund field of general relativity, and would coin the phrase “black hole” in 1967.

This book is a period piece. Some of the terminology in use at the time has become obsolete: Feynman uses “wormhole” for a black hole and “Schwarzschild singularity” for what we now call its event horizon. The discussion of “superstars” is archaic now that we understand the energy source of active galactic nuclei to be accretion onto supermassive black holes. In other areas, Feynman's insights are simply breathtaking, especially when you consider they date from half a century ago. He explores Mach's principle as the origin of inertia, cosmology and the global geometry of the universe, and gravitomagnetism.

This is not the book to read if you're interested in learning the contemporary theory of gravitation. For the most commonly used geometric approach, an excellent place to start is Misner, Thorne, and Wheeler's Gravitation. A field theory approach closer to Feynman's is presented in Weinberg's Gravitation and Cosmology. These are both highly technical works, intended for postgraduates in physics. For a popular introduction, I'd recommend Wheeler's A Journey into Gravity and Spacetime, which is now out of print, but used copies are usually available. It's only if you understand the theory, ideally at a technical level, that you can really appreciate the brilliance of Feynman's work and how prescient his insights were for the future of the field. I first read this book in 1996 and re-reading it now, having a much deeper understanding of the geometrical formulation of general relativity, I was repeatedly awestruck watching Feynman leap from insight to insight of the kind many physicists might hope to have just once in their entire careers.

Feynman gave a total of 27 lectures in the seminar. Two of the postdocs who attended, Fernando B. Morinigo and William G. Wagner, took notes for the course, from which this book is derived. Feynman corrected the notes for the first 11 lectures, which were distributed in typescript by the Caltech bookstore but never otherwise published. In 1971 Feynman approved the distribution of lectures 12–16 by the bookstore, but by then he had lost interest in gravitation and did not correct the notes. This book contains the 16 lectures Feynman approved for distribution. The remaining 11 are mostly concerned with Feynman's groping for a theory of quantum gravity. Since he ultimately failed in this effort, it's plausible to conclude he didn't believe them worthy of circulation. John Preskill and Kip S. Thorne contribute a foreword which interprets Feynman's work from the perspective of the contemporary view of gravitation.

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