October 11, 2005


General relativity versus exotic dark matter (Physics Watch, Cern Courier)

Determinations of the rotation speed of stars in galaxies (galactic rotation curves) based on the assumption that Newtonian gravity is a good approximation have led to the inference that a large amount of dark matter must be present - more than can be accounted for by non-luminous baryonic matter. ... Now F I Cooperstock and S Tieu of the University of Victoria have reworked the problem using general relativity in place of Newtonian gravity, and they find no need to assume the existence of a halo of exotic dark matter to fit the observed rotation curves.

This is because even for weak fields and slow speeds, well-known nonlinearities change the character of the solution dramatically. The success of Newtonian mechanics in situations like our solar system can be traced to the fact that in this case the planets are basically "test particles", which do not contribute significantly to the overall field. However, in a galaxy this approximation is not a good one - all the rotating matter is also the source of the gravitational field in which everything rotates.

The anomalous galactic rotation curves were the first, and still considered the strongest, evidence for the existence of "dark matter", an assumption which now seems unnecessary, indeed unwarranted. Since, contrary to the assertion, it has long been known that Newtonian mechanics is not even sufficient to account for the motions of the solar system (the precession of the perihelion of Mercury, planetary ephemeri produced by JPL since 1982 require the general relativistic numerical integration of the planets and the 5 largest asteriods), the reliance on Newtonian theory for galactic motion can perhaps best be attibuted to mathematical sloth.

Modern astrophysics and cosmology have recently given us several "entities" which arise only from the need to somehow reconcile our current theories to observations: dark matter, dark energy, and inflation, none of which have any theoretical basis and are by definition unobservable except for their effects in the relevant equations. If dark matter is not only invisible but now possibly non-existent, what is the likely future of those other ad-hoc concepts?.

Posted by J. D. Watson at October 11, 2005 7:45 AM

JD: Great post (although in the future you might want to pay more attention to the custom of posting on things about which we know nothing).

Even using general relativity, isn't there still a need for inflation to explain the growth of the universe in the first few nanoseconds after the Big Bang?

Posted by: David Cohen at October 11, 2005 8:16 AM

jd - General relativity is barely studied among physicists, and not at all by astronomers. It's totally different from the rest of physics theory, and few experiments are made on gravity since it's such a weak and long-range force. Since only a few know how to make calculations with it, it's not surprising that "mathematical sloth" has occurred. In any case, the calculations could not have been made before high-powered computers were available.

David - Inflation helps explain the relative uniformity of the cosmic microwave background and the rough magnitude of the amount of matter in the universe. So its attraction is that it reduces two observational mysteries to one "ad hoc concept".

Posted by: pj at October 11, 2005 8:48 AM

Dammit JD, I was going to post this!

This raises a number of questions, the foremost being: why hasn't anyone computed this before? Was it simply never considered, or considered and mistakes made in the computations (or assumptions) that caused GR to be rejected as having sufficient explanatory power for galactic rotation?

If this proves out, it is quite embarrassing for physics.

Posted by: Bruce Cleaver at October 11, 2005 8:49 AM

It's not embarassing for physics, only specific physicists. Science theories routinely get tossed away as new data disproves old theories. This doesn't invalidate science, it confirms it. We are constantly marching out of ignorance.

Posted by: Chris Durnell at October 11, 2005 11:29 AM

The division of science into ever narrower sub-sub-disciplines creates barriers to scientific progress. Astronomers need to work with relativity physicists, molecular chemists need to work with biologists, etc.

Posted by: Gideon at October 11, 2005 11:37 AM

One of the things that theoretical physicists love to talk about is the "elegance" of their theories. How will we know when someone hits on the correct Grand Unified Theory that will fix all the (ever increasing...) loose ends in the current Standard Model? It will be so beautiful & obvious that everyone will just slap their foreheads and exclaim "Of course this is the answer!" Given this, it is rather perplexing that pretty much all modern academic physicists are atheists, but I suppose that's attributable to a combination of ego and group-think...

Posted by: b at October 11, 2005 11:53 AM

"Dark matter" always had the smell of phlogiston to it, and I'm surprised that it was allowed to persist so long. (It also violates the "elegance" rule, which should have been another indication of its problems.)

As for the computer simulations, they're hard. It's often a lot easier to take someone else's code and tweak it rather than to start from scratch. (Especially if it's "open source" and the researchers have better things to do than write all the support code needed.) This tends to turn certain assuptions of convience into axioms as everyone includes the same mistakes in their simulations.

In this case, I wouldn't be surprised that all the simulations that showed a need for "dark matter" were started back in the supercomputer equivalent days of 8-bit processors and no hardware floating point. The results were so grainy that GP didn't matter, or slowed the simulation down so much to make it unusable. Since then, as machines got bigger and faster, instead of adding more accuracy (by including GP), people concentrated instead on using that memory and speed to add more particles and smaller increment. Which only made things worse.

It wouldn't surprise me to find out that "inflation" is artifact of floating point error and sloppy programming. And is why I also have so little faith in the "global warming" simulations.

Posted by: Raoul Ortega at October 11, 2005 12:53 PM

Raoul: You don't need a computer to find the "need" for dark matter. All you have to do is measure a rotation curve for a galaxy (using radio measurements, generally), take an optical picture, and use Kepler's Laws to show that in order for the outer regions to be rotating as fast as they are, you need much more mass than you can account for from the amount of light you see. Therefore, you need lots of mass that puts out no light, i.e. "dark matter". There is of course no doubt that dark matter exists--you and I are fine examples. The question is how much there is, and how important it is on various scales.

Of course, the "therefore" in the above paragraph assumes that the simple Keplerian calculation applies to the situation at hand. Some have speculated that it does not because of unknown modifications to the 1/r^2 gravitational law. But scientists are in general a very conservative lot, and it's much easier intellectually to fall back on dark matter and try to figure out what it might be then to take on Sir Isaac. These authors appear to propose a different reason on why the calculation is misleading.

Inflation is also motivated by simple observations--opposite ends of the observable universe seems to "know" quite well what the other is doing when they really shouldn't. Inflation is one attempt at an explanation of why that could be...

Posted by: b at October 11, 2005 1:18 PM

Of course, one _other_ possibility remains: The authors of the paper (Cooperstock/Tieu) made a mistake rather than other people.

Posted by: Bruce Cleaver at October 11, 2005 1:58 PM

"General relativity is barely studied among physicists, and not at all by astronomers."

I don't think that is true. I roomed with a couple of phyiscs grad students when I was an undergraduate, and they were studying General relativity. There was a course that covered it in my daughters ciriculum before she switched to Math.

Posted by: Robert Schwartz at October 11, 2005 2:09 PM

Bruce: Always a possibility. As noted by pj, 99% of astronomers will look at these abstracts, have their eyes glaze over when they see something like "a stationary axially symmetric pressure-free fluid in general relativity" (similar to the reaction you get from oj whenever math is brought up), and figure that the theorists will tell them in a few years if it's anything they need to worry their pretty little heads about...

Posted by: b at October 11, 2005 2:40 PM

jd and b: looking at the references cited I see one from 1999, one from 2001, nothing else recent. I'm wondering two things: (1) was there anything to prevent this result from being derived, say, 10 years ago; and (2) how recent a hypothesis is cold dark matter anyway -- did it come before or after we started getting data from COBE? Thanks in advance.

Posted by: joe shropshire at October 11, 2005 7:42 PM

Having now ploughed through the original Cooperstock/Tieu (C/T) paper and Korzynski's (K) criticism mentioned by b above, perhaps I can clarify some of the issues discussed.

First (Raoul), this is not a computer simulation of galactic motion using General Relativity (GR), but rather an attempt to derive a closed form solution for the simple galactic model of a rotating, self-gravitating disk of dust. C/T arrive at a closed solution involving a sum of orthogonal Bessel functions. They then show that solutions of this form can rather impressively account for the observed rotation velocity curves of the Milky Way and three other galaxies, and as a result obtain reasonable estimates of the galactic masses and diameters of visible disk, all without invoking any "dark matter".

K criticizes this. While admitting "the set of equations they (C/T) derive is essentialy correct", he argues that the solution is non-physical (i.e., a poor model) because of a discontinuity at the galactic plane. But C/T were aware of this, and stated in footnote 11: "While this produces a discontinuity in Nz at z = 0, it is important to note that this has no physical consequence since ... Nz does not play a role in the equations of motion. Moreover, the metric itself is continuous. ... In principle, other coordinates could be found to render the metric and its first partial derivatives globally continuous but this would be counter-productive as it would unnecessarily complicate the mathematics." K discounts this, for reasons that are not at all clear to me.

"Dark matter refers to hypothetical matter particles, of unknown composition, that do not emit or reflect enough electromagnetic radiation to be detected directly" (definition from Wikipedia), so it is very different from ordinary, non-luminous matter (b).

All things considered Bruce, I prefer an explanation using a commonly accepted theory (GR) which naturally accounts for the observations, rather than one using a limited formalism (Newtonian mechanics) that needs to invoke undetectable hypothetical objects (dark matter) having no other theoretical basis. I'm sure there are mathematical details to be worked out, but it's an impressive first try, and much more elegant.

"Inflation" is necessary in the Standard Model to account for the variation in cosmic background radiation and the formation of galaxies. Again, from Wikipedia: "Primordial fluctuations are density variations in the early universe which are considered the seeds of all structure in the universe. These variations originated as quantum fluctuations, and grew from the rapid expansion which occurred during cosmic inflation. The observable universe is thought to have been in thermal equilibrium prior to inflation. Thus, without these fluctuations, the universe would be completely homogeneous, and galaxies and galaxy clusters would not have formed." And what caused this inflation? "... the exact nature of the particle or field that generates the vacuum energy density for inflation (the "inflaton") remains a mystery: inflation is understood principally by its detailed predictions of the initial conditions for the hot big bang, and the particle physics is largely ad hoc modelling."

Sorry for the length and obscurity of this post -- if it's too much, just ignore it.

Posted by: jd watson [TypeKey Profile Page] at October 11, 2005 7:56 PM

I saw nothing which hasn't been standard relativistic analysis for much longer than 10 years -- the only innovation was applying GR instead of assuming Newtonian mechanics was sufficient.

I believe the cold dark matter (CDM) hypothesis preceded COBE, but I'm not sure.

Posted by: jd watson [TypeKey Profile Page] at October 11, 2005 8:39 PM

A quick reality check:

Astronomers don't study GR? Completely untrue. Many don't have a deep grounding in it, but nearly all have some background in it.

Dark matter is "by definition unobservable." Hmmm, maybe you should talk to the dozen or so groups around the world who are running experiments to search for dark matter particles.

Dark matter was invoked to explain galaxy rotation curves, just as Neptune was invoked to explain the orbit of Uranus. We found Neptune, so it was no longer considered an ad-hoc explanation. If we find dark matter particles, the same will apply. It's too soon to make sweeping statements about the failure of dark matter.

Evidence for dark matter also comes from observations of velocity dispersion in galaxy clusters, gravitational lensing in galaxy clusters (a GR effect studied by...astronomers!), and hot gas in clusters. Cooperstock and Tieu do not address these lines of evidence.

Evidence for dark energy comes from measurements of the Hubble constant at different cosmic epochs, as well as from measurements of harmonics in the cosmic microwave background. There are several layers of interpretation at work here, and it's quite possible that dark energy is not what it seems, but the existence of dark energy was inferred from observation, not from theory--and in fact, the theorists had spent the better part of a century arguing that it should not exist. This is a case of theory bowing to observational data, not the other way around.

Posted by: CoreyP at October 17, 2005 3:27 PM