I love telling the stories of Neptune and Vulcan. Not the Roman gods, the planets that were originally hypothesized to explain the mysterious motions of other planets. Neptune was propsed by Urbain Le Verrier in order to account for deviations from the predicted orbit of Uranus. After it was discovered, he tried to repeat the trick, suggesting a new inner planet, Vulcan, to account for the deviations of the orbit of Mercury. It didn’t work the second time; Einstein’s general relativity, not a new celestial body, was the ultimate explanation.
In other words, Neptune was dark matter, and it was eventually discovered. But for Mercury, the correct explanation was modified gravity.
We’re faced with the same choices today, with galaxies and clusters playing the role of the Solar System. Except that the question has basically been answered, by observations such as the Bullet Cluster. If you modify gravity, it’s fairly straightforward (although harder than you might guess, if you’re careful about it) to change the strength of gravity as a function of distance. So you can mock up “dark matter” by imagining that gravity at very large distances is just a bit stronger than Newton (or Einstein) would have predicted — as long as the hypothetical dark matter is in the same place as the ordinary matter is.
But it’s enormously more difficult to invent a theory of modified gravity in which the direction of the gravitational force points toward some place other than where the ordinary matter is. So the way to rule out the modified-gravity hypothesis is to find a system in which the dark matter and ordinary matter are located in separate places. If you see a gravitational force pointing at something other than the ordinary matter, dark matter remains the only reasonable explanation.
And that’s precisely what the Bullet Cluster gives you. Dark matter that has been dynamically separated from the ordinary matter, and indeed you measure the gravitational force (using weak lensing) and find that it points toward the dark matter, not toward the ordinary matter. So, we had an interesting question — dark matter or modified gravity? — and now we know the answer: dark matter. You might also have modified gravity, but one’s interest begins to wane, and we move on to trying to figure out what the dark matter actually is.
But some people don’t want to give up. A recent paper by Brownstein and Moffat claims to fit the Bullet Cluster using modified gravity rather than dark matter. If that were right, and the theory were in some sense reasonable, it would be an interesting and newsworthy result. So, you might think, the job of any self-respecting cosmologist should be to work carefully through this paper (it’s full of equations) and figure out what’s going on. Right?
I’m not going to bother. The dark matter hypothesis provides a simple and elegant fit to the Bullet Cluster, and for that matter fits a huge variety of other data. That doesn’t mean that it’s been proven within metaphysical certainty; but it does mean that there is a tremendous presumption that it is on the right track. The Bullet Cluster (and for that matter the microwave background) behave just as they should if there is dark matter, and not at all as you would expect if gravity were modified. Any theory of modified gravity must have the feature that essentially all of its predictions are exactly what dark matter would predict. So if you want to convince anyone to read your long and complicated paper arguing in favor of modified gravity, you have a barrier to overcome. These folks aren’t crackpots, but they still face the challenge laid out in the alternative science respectability checklist: “Understand, and make a good-faith effort to confront, the fundamental objections to your claims within established science.” Tell me right up front exactly how your theory explains how a force can point somewhere other than in the direction of its source, and why your theory miraculously reproduces all of the predictions of the dark matter idea (which is, at heart, extraordinarily simple: there is some collisionless non-relativistic particle with a certain density).
And people just don’t do that. They want to believe in modified gravity, and are willing to jump through all sorts of hoops and bend into uncomfortable contortions to make it work. You might say that more mainstream people want to believe in dark matter, and are therefore just as prejudiced. But you’d be laboring under the handicap of being incorrect. Any of us would love to discover a modification of Einstein’s equations, and we talk about it all the time. As a personal preference, I think it would be immeasurably more interesting if cosmological dynamics could be explained by modifying gravity rather than inventing some dumb old particle.
But the data say otherwise. So most of us suck it up and get on with our lives. Don’t get me wrong: I’m happy that some people are continuing to work on a long-shot possibility such as replacing dark matter with modified gravity. But it’s really a long shot at this point. There is a tremendous presumption against it, and you would have to have a correspondingly tremendous theory to get people interested in the possibility. I don’t think it’s worth writing news stories about, in particular: it gives people who don’t have the background to know any better the idea that more or less everything is still up for grabs. But we do learn things and make progress, and at this point it’s completely respectable to say that we’ve learned that dark matter exists. Not what all of us were rooting for, but the universe is notoriously uninterested in adapting its behavior to conform to our wishes.
Accepting “equilibrium states” within context of the universe, one could easily accept the contrast of Sean’s “Tell me right up front exactly how your theory explains how a force can point somewhere other than in the direction of its source…”
Understanding sun/earth/moon relations in terms of Lagrangian, it is not to unlikely that we can see this relationship “to source?”
It is what is pervasive at the “basis of reality” that gravity can speak to “all things?” 🙂 Just trying to apply “my logic,” and maybe even wrap “magnetism.”
Alex wrote:
>
> Wouldn’t dark matter particles be rather easy to find if they carried charge?
Certainly, but I proposed a neutral “atom” comprising an iron nucleus surrounded by negatively charged particles other than electrons (muons or tau particles perhaps, kept stable somehow in this bound state?)
However, as Greg pointed out, characteristics of the microwave background indicate that dark matter was around before galaxies and hence supernovae and hence iron formed. So it’s back to the drawing board..
Good post…thanks! Let us keep in mind, “the simplest possible scheme that can bind together the observed facts” was Einstein’s dictum. Maybe information has mass! Ba-dum-dum!
John,
I think the problem with nuclei of any kind is that the total number of baryons allowed by Big Bang Nucleosynthesis will be far less than any cosmological distribution of dark matter.
Neil and Jason,
I’ve always been fascinated by Tolman’s derivation (Phys. Rev. 37, p. 602, 1931) that a mass will (gravitationally) accelerate towards a pencil of radiation with *twice* the magnitude of acceleration as it would towards the equivalent mass density source of gravity. It’s consistent with the finding that light bends around the Sun twice as much as an equivalent mass density. Both of the above are derived in the weak-field limit.
so…
Does anyone know, at some fundamental level, where that factor of 2 comes from? Why should radiation be twice as effective at “producing” gravity as matter? Is it just some relativistic effect that approaches 2 for photons, or what? It seems to be terribly interesting to me, but perhaps mistakenly.
The other point about dark matter that most people miss is that it is “unified theory” which explains several completely disparate observations. The classic example where it is needed is galactic dynamics, but it is also needed to explain the acoustic peaks in the microwave background – and these are a successful *prediction* of the “dark matter hypothesis”, whereas modified gravity theories are typically making post-dictions at best. And in addition to the dynamics of galaxies, dark matter neatly accounts for both weak and strong lensing, as well as the formation and merger history of galaxies.
All of these thing get explained by ONE hypothesis which has genuine predictive power — and, better yet, a hypothesis that is completely consistent with our current understanding of particle physics.
By contrast, any of these effects can be explained by a modified gravity theory, but each effect typically requires a *different* modification. And for some reason when I think of that, I want to type the word “epicycles” 🙂
My own feeling when I first came face to face with the TeVeS model (a “proprer theory” which was designed to reproduce the empirical predictions of MOND, which) was that it so baroque that its main purpose was simply to demonstrate how contrived these theories were, and were thus not likely to be a fruitful field of enquiry. (Constructing these theories is a major intellectual accomplishment, but having done this, the sensible thing seems to be to try something else).
Off the back of my head could the factor of 2 come because fermions have spin = 1/2 and bosons have spin =1 ?
Chemicalscum, that’s interesting, but I don’t remember if (or how) the spin couples to the expression of the field. It would be cool if superfluids gained extra weight during a phase transition. 🙂
“But you’d be laboring under the handicap of being incorrect.” Whew, I love that one!
Tad,
Please bear in mind that this really is little more than an educated guess, as I’m not really a gravity guy. But one obvious thing to look at is the shape of the field around the particle. With a massive object that is stationary with respect to the frame we’re looking at, the field is spherical in nature. If the object is, instead, moving at the speed of light, then that spherical field gets compressed along the line of movement into a narrow shock wave. My guess is that the factor of two has to do with the details of how this difference in the shape of the gravitational field affects accelerations.
The reason that radiation has twice the gravity of normal matter is because of radiation pressure. As it turns out, in General Relativity, the effective gravitational “charge” isn’t the energy density itself, but e + 3p, where e is the energy density and p is the pressure. Pressure and energy density have the same units, so that works out. So objects with high pressure actually produce more gravity than pressureless objects (which does come into play with, say, neutron star structure).
For radiation, p = e / 3. So the gravitational charge of radiation is e + 3 * e / 3 = 2e, which is where the factor of two comes from. Highly relativistic particles, such as neutrinos just after the Big Bang, I think, also have p ~ e / 3.
This can also be generalized, by saying that, in general, things have an equation of state of p = w e. For normal matter, in which the thermal motions of the particles are not relativistic, w is very near 0. For photons, w = 1/3. A cosmological constant, though, has p = -e, so w = -1. In that case the effective gravitational charge is e – 3 * e = -2e, so a (positive) cosmological constant is gravitationally repulsive, even though it has positive energy density — it has enormous negative pressure. That’s how it accelerates the Universe’s expansion. You’ll sometimes hear cosmologists talking about determining w as a way to describe what dark energy actually is.
Jason, et al
Yes GR does describe gravity from photons, but IIUC that is considering such as a photon “gas” where they are moving in all directions. But if you consider a single photon, the “wake” and other oddities of having attraction coming from something (even if delocalized) that moves (its center of likely occurrence, at least) that moves at c is problematical, isn’t it?
Sean,
What is your take on the situation in Abell 520? That just seems quite the anomally unless the researchers made a mistake in their analysis of the gravitational lensing.
Brian — (replying to #35 above)
Your conclusion that radiation has more gravitational “pull” than matter because its sum e+3P is larger — exactly twice as large for a radiation gas as for a cold matter gas — is quite compact and elegant. However, I don’t think the whole story can be this simple.
Positive pressure may, in a sense, be said to generate positive (ie attractive) gravity in a smooth, continuous Friedmann universe, since we know that the sum e+3P is the “figure of merit” for the deceleration of the universe’s expansion: more pressure, more deceleration, and hence more gravity. I don’t disagree with any of this; but once you leave the example of the smooth continuous distribution I don’t think you can carry the same notion with you. In particular, for localized objects one can show quite directly that (an increase in) positive pressure does _not_ result in (increased) attractive gravity.
Consider a static, localized, spherically symmetric distribution/body of matter surrounded by vacuum. We know that the exterior metric must be Scwarzschild with some mass parameter M, which is what any observer in the vacuum would assign as the body’s mass based on its gravitational pull. Now suppose the material is actually an explosive of some kind, which we then set off simultaneously throughout its volue (in an appropriate frame). At each spot within the distribution the mass-energy density e is the same just before and just after the explosion, but the pressure P has clearly increased. (If you are willing to postulate a matter-antimatter explosive, aka a positronium bomb, then P can increase by the maximal amount from 0 to e/3.)
If we follow your general line, then we would expect the increased pressure to result in an increased gravitational pull between the now-hotter body and distant objects (possibly after a causality lag), ie the external metric is still Schwarzschild but with a higher M than before. However, this kind of change would constitute a “monopole wave,” which we know are _strictly_ forbidden in General Relativity. (You can also prove this via Birkhoff’s theorem, which effectively says that spherically symmetric vacuum metrics must be part of a Schwarzschild metric, and hence completely static: the M parameter can never be seen to change by an observer out in the vacuum.)
So I have to disagree with the claim that “higher positive pressure leads to higher attractive gravity” as a general statement; it’s true for the smooth continuum case, but not the isolated object case. So I don’t think this can be the fundamental reason for the factor of x2 question asked above.
Best regards,
Paul Stankus
John, another problem with dark neutral “atoms” composed of charged particles is that EM radiation will interact with the atom via the energy transitions.
Brian,
Thanks, that was so obvious an answer I can’t believe that I forgot it.
Neil B.,
I don’t see why that’s a problem at all. Aircraft traveling at faster than the speed of sound still produce sound, do they not? Same principle.
Paul Stankus —
Yes, your example does make sense. I can think of an even more intuitive example to prove your point, now that I think about it. A 3 solar mass stellar core will form a 3 solar mass neutron star, even if it’s near the limit when its particles are relativistic. And if it collapses into a black hole, the black hole will still act like a 3 solar mass object, even though at some point inside the event horizon, the particles had to be going relativistically.
My main exposure to general relativity has been through an undergrad introductory course and a smattering in cosmology courses. So I’ll concede that my GR knowledge is limited, and there is something about pressure’s relationship to gravity that I’m missing. I was looking through Peacock’s Cosmological Physics when I posted, and I did notice the passage on page 25 where he gives the Poisson equation for the weak-field limit, in which the Laplacian of the potential is proportional to (rho + 3p/c^2). Then he says
If I’m reading that correctly, that seems to be saying that it’s not necessary to assume homogeneity for the pressure argument to work. I suppose it could also be that the (1 + u^2/c^2) factor doesn’t have to do with pressure — I don’t think the factor applies to dark energy, for example — but I think it would describe a contribution from thermal pressure. Correct me if I’m wrong.
Of course, there is a difference in the situation here, in that the (1 + u^2/c^2) factor is applying to a test particle moving in some other potential, rather than generating the potential itself. But on the other hand, ultrarelativistic objects don’t become black holes simply because they’re moving very fast. That would violate Lorentz invariance. So the (1 + u^2/c^2) factor doesn’t actually apply to the gravity generated by moving objects, and it would be wrong to apply it recklessly.
So, is it necessarily the smooth, homogeneous fluid assumption that’s breaking down, or something else? Since I’m still trying to figure out why positive pressure seems to increase gravity in some cases, but not others.
(And does this have anything to do with the fact that spatial curvature in the FRW metric only depends on density and not pressure, so that a positive cosmological constant can accelerate the Universe’s expansion but also make it flat instead of open? I’ve never actually seen the full GR derivation for k, only the hand-waving Newtonian argument.)
(Also, I’m not the Brian of comment 37, just so there isn’t any confusion.)
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Sean,
Have you any reaction to the review article by Stacy McGaugh in the Aug 3 2007 edition of Science?
Of course she goes on to say that MOND still requires dark matter.
The conjectured Higgs Particle, reportedly five types, three neutrals, and two charged, that connect to all other particles in the “universe” replaces Newton’s Gravitational constant, G, with a poetically named Higgs Universal Gravitational Strings (HUGS) which must play some part of Super Symmetry both locally and at a distance.
Dark Matter (Black Hole for starters) from my reading is matter at absolute zero degrees, thus does not itself radiate except for those particles glancing the BH and radiating information about BH mass and area from the acceleration of the glance. The HUGS between the source and BH and observer’s equipment may interact with the BH HUGS, perhaps like a field.
So gravitational lensing where images are split or surround a BH. I think that strings from one particle when crossing those from another, can pass through each other, but at best so far, when passing through, I assume the individual string’s outer sheath are charged negatively charged and inside balanced with positive charges. Multiple loops, may need to be examined, since it might prove that their magnetic fields cancel. A neutrino may be a candidate?
Some string theory essays state that transverse movements ™ of a string are the electromagnetic forces, the longitudinal movements (lm), the gravitational. But this construction should be “seamless” or “continuous” in the transfer of source construction to receiver instrument detector constructions.
Our human eye appears to respond to a single “photon”, an amazing fact of nature, to imagine that our eyes in viewing a star at night are so sensitive as to have their own graininess, the dark room noise.
A quick note on double deflections.
The derivative of a second order of x, the photon path, is the power, 2, times the change, so der(x^2)/der(r)=2*x(dx/dr). Last time I drew a parallel ray passing by a sun circle pass, that is how I answered the “2 times” deflection.
But these are words, not diagrams and explicit math.
Best, rmuldavin
Dark energy, still existing?
http://www.nature.com/news/2007/071102/full/news.2007.215.html
Hey all,
Sorry for hijacking the thread somewhat, but if you’re interested:
I’ve been checking back into it today, and I have it on some authority that the “physical” reason radiation is twice as effective as matter at producing gravitational fields is due to the extra contribution from the Poynting flow of energy. This is fascinating.
Wayland @ 43:
What McGaugh is referring to are the difficulties current galaxy formation models (which assume and use dark matter) have at reproducing certain galaxy properties and correlations. These are important problems, and it’s good to keep poking the modelers to improve things.
However, these aren’t necessarily show-stoppers. Galaxy formation models involve a lot of simplifying assumptions about the detailed physics, and it’s quite possible that things will improve with a) better resolution in the models; and b) better physics in the models (e.g., better hydrodynamics to describe what the gas does, better models for star formation, etc.).
(Incidently, it’s actually “he”; Stacy McGaugh is a man.)
What if the cosmological constant, as negative curvature of space, doesn’t actually cause the universe to expand, but that the expansion of space results in uniform increase of pressure on galaxies? Wouldn’t this cause the outer perimeter of galaxies to spin faster? That way, galaxies appear to be flying away from each other, as the space between them expands, but this expansion falls into the gravity wells of galaxies. This would explain why everything is redshifted as if it were flying away from us, without having the earth as the center of the universe and without proposing that space is expanding from a singularity. (If space expanded from a point, the speed of light would have to increase proportionally, otherwise it isn’t expanding space, but increasing distance.)
So we have a convective cycle of collapsing mass and expanding radiation, with galaxies as gravitational storms, the black holes being the eye of the storm and the smoothness of the CMBR as the dew point at which radiation starts to condense back into mass.
>”There seems to be little enthusiasm left in most publications for explaining in any depth what we already know fairly well; the only thing that rates coverage now is the drama of theory X slogging it out against theory Y, and nobody really cares whether theory Y is a significant contender or has just sprouted some new epicycles and free parameters since the last fight.”
I was taken aback recently to come across a magazine down here in Australia that claims, in their cover story no less, that the Bullet Cluster is the nail in the coffin for dark matter, and that it proves modified gravity. I was like, it does? That’s not what I heard… I’ll try to track down what magazine it was and provide a link.
I fail to see the problem with exploring why modifications to GR might account for phenomena such as the Bullet cluster. I’d guess that it’s the press coverage rather than the actual paper which has antagonised you somewhat? Otherwise, I’d contend that a thorough investigation into accounting for these anomalies in terms of “actual stuff” can only serve to cement the case for DM in the long run.