Books by Moffat, John W.

Moffat, John W. Reinventing Gravity. New York: Collins, 2008. ISBN 978-0-06-117088-1.

In the latter half of the nineteenth century, astronomers were confronted by a puzzling conflict between their increasingly precise observations and the predictions of Newton's time-tested theory of gravity. The perihelion of the elliptical orbit of the planet Mercury was found to precess by the tiny amount of 43 arc seconds per century more than could be accounted for by the gravitational influence of the Sun and the other planets. While small, the effect was unambiguously measured, and indicated that something was missing in the analysis. Urbain Le Verrier, coming off his successful prediction of the subsequently discovered planet Neptune by analysis of the orbit of Uranus, calculated that Mercury's anomalous precession could be explained by the presence of a yet unobserved planet he dubbed Vulcan. Astronomers set out to observe the elusive inner planet in transit across the Sun or during solar eclipses, and despite several sightings by respectable observers, no confirmed observations were made. Other astronomers suggested a belt of asteroids too small to observe within the orbit of Mercury could explain its orbital precession. For more than fifty years, dark matter—gravitating body or bodies so far unobserved—was invoked to explain a discrepancy between the regnant theory of gravitation and the observations of astronomers. Then, in 1915, Einstein published his General Theory of Relativity which predicted that orbits in strongly curved spacetime would precess precisely the way Mercury's orbit was observed to, and that no dark matter was needed to reconcile the theory of gravitation with observations. So much for planet Vulcan, notwithstanding the subsequent one with all the pointy-eared logicians.

In the second half of the twentieth century, a disparate collection of observations on the galactic scale and beyond: the speed of rotation of stars in the discs of spiral galaxies, the velocities of galaxies in galactic clusters, gravitational lensing of distant objects by foreground galaxy clusters, the apparent acceleration of the expansion of the universe, and the power spectrum of the anisotropies in the cosmic background radiation, have yielded results grossly at variance with the predictions of General Relativity. The only way to make the results fit the theory is to assume that everything we observe in the cosmos makes up less than 5% of its total mass, and that the balance is “dark matter” and “dark energy”, neither of which has yet been observed or detected apart from their imputed gravitational effects. Sound familiar?

In this book, John Moffat, a distinguished physicist who has spent most of his long career exploring extensions to Einstein's theory of General Relativity, dares to suggest that history may be about to repeat itself, and that the discrepancy between what our theories predict and what we observe may not be due to something we haven't seen, but rather limitations in the scope of validity of our theories. Just as Newton's theory of gravity, exquisitely precise on the terrestrial scale and in the outer solar system, failed when applied to the strong gravitational field close to the Sun in which Mercury orbits, perhaps Einstein's theory also requires corrections over the very large distances involved in the galactic and cosmological scales. The author recounts his quest for such a theory, and eventual development of Modified Gravity (MOG), a scalar/tensor/vector field theory which reduces to Einstein's General Relativity when the scalar and vector fields are set to zero.

This theory is claimed to explain all of these large scale discrepancies without invoking dark matter, and to do so, after calibration of the static fields from observational data, with no free parameters (“fudge factors”). Unlike some other speculative theories, MOG makes a number of predictions which it should be possible to test in the next decade. MOG predicts a very different universe in the strong field regime than General Relativity: there are no black holes, no singularities, and the Big Bang is replaced by a universe which starts out with zero matter density and zero entropy at the start and decays because, as we all know, nothing is unstable.

The book is fascinating, but in a way unsatisfying. The mathematical essence of the theory is never explained: you'll have to read the author's professional publications to find it. There are no equations, not even in the end notes, which nonetheless contain prose such as (p. 235):

Wilson loops can describe a gauge theory such as Maxwell's theory of electromagnetism or the gauge theory of the standard model of particle physics. These loops are gauge-invariant observables obtained from the holonomy of the gauge connection around a given loop. The holonomy of a connection in differential geometry on a smooth manifold is defined as the measure to which parallel transport around closed loops fails to preserve the geometrical data being transported. Holonomy has nontrivial local and global features for curved connections.

I know that they say you lose half the audience for every equation you include in a popular science book, but this is pretty forbidding stuff for anybody who wanders into the notes. For a theory like this, the fit to the best available observational data is everything, and this is discussed almost everywhere only in qualitative terms. Let's see the numbers! Although there is a chapter on string theory and quantum gravity, these topics are dropped in the latter half of the book: MOG is a purely classical theory, and there is no discussion of how it might lead toward the quantisation of gravitation or be an emergent effective field theory of a lower level quantum substrate.

There aren't many people with the intellect, dogged persistence, and self-confidence to set out on the road to deepen our understanding of the universe at levels far removed from those of our own experience. Einstein struggled for ten years getting from Special to General Relativity, and Moffat has worked for three times as long arriving at MOG and working out its implications. If it proves correct, it will be seen as one of the greatest intellectual achievements by a single person (with a small group of collaborators) in recent history. Should that be the case (and several critical tests which may knock the theory out of the box will come in the near future), this book will prove a unique look into how the theory was so patiently constructed. It's amusing to reflect, if it turns out that dark matter and dark energy end up being epicycles invoked to avoid questioning a theory never tested in the domains in which it was being applied, how historians of science will look back at our age and wryly ask, “What were they thinking?”.

I have a photo credit on p. 119 for a vegetable.

April 2009