Reinventing gravity

December 19, 2008

Reinventing Gravity
John W. Moffat ( Thomas Allen, 2008 )
286 p.  First reading.

In the first half of the nineteenth century astronomical observations of Uranus indicated that its orbit was deviating somewhat from expectations.  Careful measurements confirmed the discrepancy, and in the 1840s Urbain Le Verrier in Paris and John Couch Adams in Cambridge, both believing that the orbit was being perturbed by a previously unseen planetary body, used Newton’s law of gravitation to predict the properties and orbital characteristics of a new planet.  In 1845, Neptune was discovered, more or less where they had predicted.

Later in his career, Le Verrier applied the same method to the orbit of Mercury.  It had been known for some time that Mercury’s orbit exhibits a peculiarity called perihelion precession: its elliptical orbit does not close on itself, but rotates a little with each revolution of the planet.  This irregularity, Le Verrier reasoned, was caused by a new planetary body between Mercury and the Sun, and he used Newton’s gravitation to predict its orbital properties.  The new planet was called Vulcan.  Astronomers looked for it, and even mistakenly discovered it several times, but in the end it was concluded that it does not exist.  The real resolution of the puzzle required Einstein’s theory of general relativity.  Mercury’s orbit does not agree with the predictions of Newtonian gravity because, in the relatively strong gravitational field in which Mercury moves, Newtonian gravity is wrong.  What was needed to understand the observations was not unseen (or “dark”) matter, but a new — in this case, radically new — theory.

These two case studies serve as a good introduction to the argument of Reinventing Gravity.  Today we are again faced with a variety of astrophysical and cosmological observations that differ from the naive predictions of Einsteinian gravity.  One possible response to these problems is the “Neptune” response: to propose that there exist other gravitational sources, generically called “dark matter”, which are unseen in telescopes, but which nonetheless exert a gravitational influence that accounts for the peculiar observations.  This is the response favoured by the vast majority of physicists today.  But another possible response is to propose that our theory of gravitation is wrong, and that the correct theory of gravitation would not require us to posit any “dark matter”.  This is the response favoured by John Moffat and his collaborators.  This book is a popular-level account of his ideas, and of how they are faring in the contemporary academy.

Moffat’s new theory of gravity, which he calls Modified Gravity (MOG), is inspired by general relativity insofar as it treats gravity as spacetime curvature, but it modifies Einstein’s gravitational field equations in significant ways (technically, by introducing a scalar and a vector field, but the details are not important for our purposes here).  These changes result in a modification of Newton’s gravitational law on large distance scales: the attractive force of gravity is stronger than predicted by Newton out to some distance scale, and then it dies off.  This modification is just the sort of thing needed to explain, for instance, galactic rotation curves without introducing dark matter.  (Whether it actually works is an empirical question, of course, but it’s the right sort of change.)

The theory has other, more startling consequences as well: it contains no spacetime singularities, which means that black holes and event horizons do not form.  Moffat argues that the evidence for black holes is “circumstantial at best”, and contends that existing candidates, such as the famous Cygnus X-1 source, could be some other type of super-massive dense object permitted by MOG.  A further, even more dramatic difference between MOG and Einsteinian gravity is that MOG predicts no Big Bang.  Instead, it predicts an eternal universe which began as flat, empty spacetime which at some point, due to quantum fluctuations, began to expand and produce matter.  This matter creation is a variant on the old “steady state” model of cosmology. I wonder if MOG requires a flat initial spacetime in order to answer the flatness problem, and, if so, whether that constitutes fine-tuning.

Moffat reviews a variety of problems for which dark matter has been proposed as a solution — galactic rotation curves, galactic supercluster dynamics, cosmological density — and argues that in each case his theory has a competing explanation in terms of modified gravity, without any need to introduce dark matter.  Obviously, whether or not that is true is a question for experts to evaluate.  The way he tells the story, he has some difficulty getting the larger physics community to take his theory seriously.  The main ingredients of the standard cosmological model are: Einsteinian gravity, Big Bang, inflation, dark matter, and dark energy.  Moffat’s theory does away with all of them, so it is perhaps not too surprising that it is not looked on favourably.

Indeed, the book raises interesting questions about the sociology and philosophy of science.  Physicists often say that one ought to choose the simplest explanation, but it is not always clear which of two competing ideas is simplest.  Is dark matter a simpler idea than modified gravity?  I don’t know.  Moffat’s account of his own search for a modified theory of gravity, with all its false starts and dead ends, also teaches the reader much about how science is done, and especially about the way in which non-empirical principles, such as an aversion to “monstrous” fine-tuning or an adherence to the so-called “Copernican principle” — that there is nothing special about us — influence what does or does not count as a legitimate theory.  (I might point out that the historical Copernicus’ principle was simply “heliocentrism”, and he would probably have contested the modern “Copernican principle”.)  Furthermore, scientists are subject to fads just like everyone else, and sometimes new ideas, if they are not the “right” new ideas, have a hard time breaking in.  String theory is a prime candidate for a theory that attained wide popularity, but still has not really proven itself, and it is quite edifying to hear Moffat wax eloquent against it.

The last half of the book, then, is devoted to a description of Moffat’s theory, the considerations that led him to it, the evidence it has to confront, and its reception.  The first half of the book sets the stage with a history of astronomy and cosmology from the Greeks to the twentieth-century.  It is quite fascinating, and is especially strong on the developments in gravity and cosmology in the last hundred years.  Some of the discussion of early modern history might be misleading. For instance, he states that Copernicus refrained from publishing his theory until he was near death because he “realized that his revolutionary ideas would be viewed as heretical”.  I believe that he can have had little reason for supposing that: his book was widely read, but nobody seems to have thought it heretical for several generations, until Galileo came on the scene.  Moreover, the book was dedicated to the pope, which hardly seems the thing to do if you are a heretic trying to avoid notice.  Again, the discussion of Giordano Bruno leaves the reader to infer that Bruno was executed for, among other things, heliocentrism, claiming that the universe was infinite, and believing that other worlds exist.  In fact we do not know precisely why Bruno was executed — the legal proceedings have been lost — but in any case to paint Bruno as a proto-scientist is quite misleading.  He did hold the positions attributed to him, but not for scientific reasons.  It is also worth noting that the medieval church formally condemned the proposition that other worlds cannot exist, which at least complicates the charges against Bruno.  But these are fairly minor concerns about an otherwise very interesting and well-told story.

For his whole career Moffat has been something of a gadfly in the physics world, questioning received opinions, proposing creative alternatives, and restlessly searching for new ideas.  In MOG he has developed a very interesting set of ideas addressed to some of the most important problems in contemporary science.  What readers will gain from his book is not knowledge of whether he is right or wrong — that is for experts to decide on the basis of the evidence — but rather they will be exposed to the excitement of theoretical physics, and become familiar with a man whose dedication to his science and desire to know what is are exemplary.

(Full disclosure: I am distantly acquainted with the author.)

10 Responses to “Reinventing gravity”

  1. Adam Hincks Says:

    I think modified theories of gravity are a worthy endeavour, but I also have to say that I think it’s becoming more and more of a dead-end. We now have precise astrophysical observations of gravity on many scales, and putting all these data together, MOG starts looking, at least to my eyes, fairly contrived. Take for example Fig. 2 of this recent paper by Moffat — you can’t motivate a theory adequately simply by interpolating data. (Full disclosure: the Bullet Cluster discussed in this paper is an object of great interest to me.)

  2. cburrell Says:

    Thanks, Adam. I’m sympathetic to the idea of modifying gravity as well, but I hope it’s clear that I stop short of endorsing Moffat’s particular theory. I don’t deny that it may be starting to look contrived; in fairness, I think that dark matter explanations can look contrived too. Time will tell.

    The Bullet Cluster is fascinating, isn’t it? To the untrained eye it looks like an ordinary gas cloud, yet when examined closely it contains such a wealth of information, and may even be telling us about new physics. Wonderful.

  3. Adam Hincks Says:

    I think one must separate the hypothesis of dark matter from theories of dark matter. The hypothesis that there exists dark matter is simple, and it precisely explains the observed phenomena using only Einstein’s gravity. Its putative existence is also what helps us explain the cosmological growth of structure in a convincing way.

    Theories of what dark matter could be is where things can become contrived. However, there are good experiments searching directly for it, and of course, the LHC might shed light on the issue, should it be a particle. One can always go the string theory route, but then you might not be much better of than a MOG . . .

    The Bullet was the first cluster we detected with the ACT.

  4. Vince Velocci Says:

    “Physicists often say that one ought to choose the simplest explanation, but it is not always clear which of two competing ideas is simplest. Is dark matter a simpler idea than modified gravity? I don’t know.”

    I think Occam’s razor deals with principles rather than theories. I think we ought to choose the theory that is based on the simplest set of principles rather than the simplest theory. For example, GR is based on the equivalence principle. Actually, I don’t know if MOG obeys the equivalence principle exactly or if it holds approximately. Well, I guess you can modify Einstein’s equations by having terms with higher derivatives of the metric tensor (and still obey the equivalence principle), but they would be very very suppressed. Does MOG have terms like this, or is it just GR with variable G and c constants?

    By the way, I am a friend and former classmate of Adam.


  5. cburrell Says:

    Yes, that’s one interpretation of Occam’s razor, and not a bad one. Glancing again through the book I can’t see if John claims that MOG continues to respect the equivalence principle or not. The Lagrangian differs from GR by the introduction of scalar and vector fields that couple to the metric tensor, but you’d have to look at his papers for the details. There was nothing in the book to suggest that he introduces higher derivative terms (no talk of a new high energy scale, for instance). As you can see, I haven’t spent much time looking at the scientific papers, so I’m somewhat in the dark.

    Were you a classmate of Adam’s at Princeton, or in Toronto?

  6. Vince Velocci Says:

    We were classmates (same graduation year) at U of T.

  7. Adam Hincks Says:

    And Vince actually studies GR, so he is the authority so far in these comments . . .

    As far as I remember, the essential feature of Moffat’s MOG is that the gravitational term G is not constant, but scales with size, i.e., G = G(r). In the paper I read, G(r) was interpolated from data, not predicted by the theory itself.

  8. Vince Velocci Says:

    Since Adam (for now) knows as much GR as I do, and since he actually read a paper on this topic, I will let him be the authority in these comments.

  9. cburrell Says:

    I don’t say that it is necessarily true, but I have found that it is generally safe to regard Adam as an authority. 😎

    Adam, if the variability of G(r) is really just an arbitrary fit to a set of data, then I agree that that is not convincing. I guess I should look more closely at the papers.

  10. […] reading: John W. Moffat – Reinventing […]

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