Dark Matter: Still Existing
Sean at 3:41 pm, November 1st, 2007I 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.
good analogy
“Tell me right up front exactly how your theory explains how a force can point somewhere other than in the direction of its source,”
how a _gravitational_ force. Please do not start fueling a campaign against electromagnetism.
I’m a big fan of magnetism. If someone has a theory of gravity like that, and would like to use it to explain the Bullet Cluster, tell me how it works.
Your central objection to modified gravity seems so obvious that it cries out for an explanation. Have B&M offered even an attempt at squaring their theory with observations of the Bullet Cluster? I find it hard to believe that they wouldn’t defend their position.
I know that you are just baiting here Sean, but I will just point out what I consider to be blindingly obvious. Namely,
(Predicted matter distribution via our current understanding of general relativity) + (”Dark Matter” defect) + (”Dark Energy” defect) = observed matter distribution
Via a simple rearrangement, we can write
Predicted matter distribution via our current understanding of general relativity = Observed matter distribution - (”Dark Matter” defect) - (”Dark Energy” defect)
So, as you said, we have two choices: we might choose to believe that our data is incomplete and there is stuff out there that our instruments cannot detect, which seems to be the camp you fall in, OR, we might choose to believe that our data is more or less complete and our understanding of general relativity is lacking.
I am inclined to believe it more likely that the second case is true, and that there are errors in our current theoretical understanding that do not matter on the scale of our solar system but become glaring at galactic scale. I think that positing the existence of extra matter/energy sources to conform to a cherished theory, particularly when there are errors of ?95%?, seems to be stretching credibility just a little. After all, to throw your words back at you (and I hope you forgive me for it), the universe is notoriously uninterested in adapting its behaviour to conform to our wishes.
^”After all, to throw your words back at you (and I hope you forgive me for it), the universe is notoriously uninterested in adapting its behavior to conform to our wishes.”
strange that I felt the same way reading the last line.
In other words, Neptune was dark matter, and it was eventually discovered. But for Mercury, the correct explanation was modified gravity.
I love this analogy! And I’d never heard of Vulcan before… it’s a shame how many awesome things get left out of the grade-school science curriculum just because they don’t exist.
It really doesn’t help that their modified gravity theory is scalar-vector-tensor gravity, which is quite complex, vastly more so than just positing the existence of a new, weakly-interacting particle (something predicted by grand unified theories anyway). And I have to agree with Sean: they’re not bothering to state, in clear terms in their abstract, how they’re explaining the Bullet Cluster. From reading the abstract and skimming the introduction, there is no indication of an explanation that I could see, so I have to wonder why anybody would bother to pore through the full 28-page paper to figure out what in the world it’s saying.
Now that we’re pretty sure dark matter exists, have people given up on MOND theories, in which gravitational theory itself is modified - or is there still some reason to believe in the latter?
Also, what’s the latest on the Pioneer 10 etc. anomalies and their significance?
Finally, what about light itself exerting gravitational effect? It should, because of the mass equivalent of energy. There’s a contradiction if we allow light not to exert gravity. We could convert a lump of matter into light, and then the gravity from the matter would suddenly no longer propagate from that location - which creates problems (I don’t have time right now to explain why, most of you can fill in.) But the problem is, you can’t (?) have a field proceeding from something going at the speed of light, the field theory doesn’t work right (again, for reasons most can fill in.)
Oops, OK I sometimes don’t take enough time, since I see some people didn’t give up on MOND. But I’m still curious about the Pioneer 10 questions.
I agree with the sentiment of this post 100%. I just wish I knew how to persuade the editors of popular science magazines to start thinking this way. 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.
A recent New Scientist was trumpeting the proposal that gamma ray bursts are light that has travelled back in time around naked singularities. I guess mere colliding neutron stars and imploding hypermassive stars are so boring now that it’s only by biting the heads off chickens with time travel that you can get readers to pay attention.
“the idea that more or less everything is still up for grabs”
We only know about 4% of the Universe, which is ordinary matter, and I don’t think there are good dark matter candidates yet, let alone dark energy “theories.” I am not sure who you think have grabbed anything, but I think he/she didn’t grab much.
[…] Cosmic Variance explains what an honest to goodness “alternative theory” must do in order to be accepted by the mainstream of science. In this case, he is discussing “dark […]
I took up the question of the bullet cluster with Moffat about a year ago, and he admitted that his fit required there to be a coincidental alignment of what we see. Specifically, the centers of the overall matter distribution (which are inferred from lensing) and the centers of the distribution of optically visible galaxies (which have moved more or less ballistically) are very closely lined up. (There are two sets of centers, one for each of the clusters in the collision.) The optical and lensing centers don’t line up exactly, but their misalignment is exactly what you would expect from the fact that the interacting x-ray gas makes up a nontrivial part of the total mass. In Brownstein’s and Moffat’s model, the fact that these the centers of the galaxy distributions and the lensing centers are aligned is purely coincidence, which to my mind suggests strongly against their model.
I seem to recall a SciAm article from some years back proposing that “dark matter” is actually matter on another brane (or a fold of our brane), which interacts only gravitationally because only gravitons make it off the brane to influence matter elsewhere.
I have no idea what the current status of this model might be, except to note that I never hear about it in the context of the “dark matter vs. modified gravity” rumble. Perhaps for theoretical reasons it’s already been exluded, or maybe it’s just terribly unpopular. But if it still lives on in the work of some theorist or theorists out there, what does the Bullet Cluster observation have to say about such “brane world” models?
I’ve heard about the branes-leaking-gravity idea as well and find it to be fascinating. Does anyone have any more info on it?
I’m not sure I get the objection to positing modified gravity; it doesn’t seem absurd and I suppose (from the post) that it works out mathematically?
Neil B.,
Actually, general relativity does provide a very specific prediction as to the gravitational field emitted by photons.
In fact, early in the universe, the gravitational effect of radiation was the dominant effect. But since radiation dilutes faster than matter (1/a^4 vs. 1/a^3), rather early on matter came to dominate, significantly before the cosmic microwave background was emitted. Currently the photon density of the universe is around one part in ten thousand to one part in one hundred thousand of the total energy density.
As for the Pioneer anomaly, I don’t know. Never heard of the issue.
People (scientists, not just crackpots) are still working on the Pioneer anomaly — at least, a former student of mine is a postdoc in one such group, and I assume there must be more.
The last time I looked at this issue it seemed overwhelmingly likely though that there’s some explanation that just involves unmodelled properties of the spacecraft, like anisotropic thermal emission.
Dick,
The Bullet Cluster aside, I would like to say that complexity of modified gravity theory (as compared to dark matter postulate) is not a very convincing reason to ignore it. Sean’s example of Vulcan vs GR is an example.
You know this reminds me of that ancient story of people who believed that the Sun was the center. First they thought the Earth was the center, but eventually data piled up and forced people to believe that Jupiter had moons, and forcing those moons to orbit Earth would make things implausible as they had to force it to orbit in a weird and complex path around the Earth, rather than the simpler method: don’t let it orbit Earth in the first place. I guess the modified gravity-ists are trying to do the same thing - go for a much more complicated method rather than a simpler dark-matter method. Did I do this analogy right?
Is it possible that dark matter (which by now it’s pretty obvious does exist) is a stable “atom” cooked up within impending supernovae and comprising an iron nucleus with neutrinos orbiting in place of electrons?
If the neutrinos were tightly bound, almost skimming the nucleus instead of fluffed out like electrons, the structure would be invisible to all but possibly the highest photon frequencies and unlikely to interact significantly with normal matter even at its most dense.
This would explain why dark matter tends to clump round and in galaxies - it is formed within them, and why it is diffuse - it is flung out at high speeds in supernova explosions.
This hypothesis might be tested in a couple of ways: firstly by attempting to spot slight irregularities (dispersion or absorption?) in gamma sources viewed through a supposed clump of dark matter; also by seeing if galactic rotation speed band anomalies (explained by dark matter) are less for very distant and hence early galaxies, in which one assumes supernovae have had less time to produce this exotic exhaust!
John R Ramsden (#22):
Neutrinos don’t bind to nuclei; they either sail right through them, or, with some phenomenally small probability, induce beta decay.
With or without neutrinos around, iron nuclei would have the same charge as ever, and would have to be bound to, or associated in a plasma with, electrons.
Also, I thought there were aspects of the CMB suggestive of dark matter in the early universe (i.e. long before galaxies were formed) influencing structure formation.
Thanks Greg, yes shortly after posting I remembered neutrinos were neutral (DOH!) so it would have to be some other particle, negatively charged of course and stable (at least when bound in the conjectural atom - as for neutrons, that need not be the same as stable in isolation).
But if as you say dark matter was around before galaxies even formed that would blow the idea out of the water anyway.
Wouldn’t dark matter particles be rather easy to find if they carried charge?
Alex
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.)
[…] 2nd, 2007 by purplepenguin Sean Carroll over at Cosmic Variance has succintly explained why it is reasonable to believe in dark matter, in spite of the spate of recent modified […]
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.
[…] I am getting an increase in weight of 127% using spreading infrared radiation […]
Dan,
Well, as Sean explained, it’s pretty apparent that merely modifying how gravity drops off with distance is not ever going to explain the Bullet Cluster. The obvious way that you’d have to modify gravity to explain the Bullet Cluster would be to violate the equivalence principle at large distances. That is, despite there being vastly more baryons in the hot cluster gas, somehow you’d have to have most of the gravitational lensing be around the far fewer baryons in the compact objects (mostly stars) in the galaxies. But the Brownstein and Moffat paper doesn’t say anything about that in the abstract, despite the fact that it’d only take a couple of sentences to explain. Nor do they provide any other rough outline of an explanation in the abstract. So why bother to dig through a 28 page paper in detail when we don’t even know where it’s going?
I think Sean’s point is really excellent: especially if you have a theory that is on the fringes, or appears to have been ruled out, you really have to be able to at least provide an outline of a description so that scientists will bother to read further. If you don’t tackle the primary objections straight away, most scientists will just assume you haven’t actually explained anything of value and move on to something that seems more likely to be interesting.
“Dark Matter, Still Existing”
Right -something is there - but what?
Neptune was actually discovered, while Vulcan was not.
So all we have to do now is to actually discover DM in the laboratory, measure its properties and find that they are concordant with astrophysical (Galaxy rotation profiles, cluster dynamics, Bullet Cluster) and cosmological (Large scale structuring, ‘cuspiness’, CMB fluctuations) constraints and then and only then we will really know what we are talking about.
A third possibility to the non-baryonic DM or modified gravity scenarios is that the DM might be baryonic. This might be possible if the expansion history of the universe during the BBN epoch was elongated in time due to the action of an as yet unknown scalar field thus allowing the baryonic density to increase. But in that case the question would be; “Where is all this dark baryonic matter today and why can we not see it?”
Historical Note: although Neptune explained most of the anomalous motion of Uranus there was still a residual that led to the search for Pluto. However Pluto and other plutons have proved to be two OOM too small so that residual still remains.
Just a thought…
Garth
Garth,
How would a scalar field in the early universe not totally mess up big bang nucleosynthesis? And besides, proposing two unknown mechanisms (unknown scalar field and invisible baryonic matter) is quite uninteresting when one unknown mechanism (WIMP) does just fine.
Agreed, one question about WIMP is finding it in the laboratory.
I have no exact reaction rates but the ‘hand waving’ scenario would be the following:
BBN would be adjusted by the action of a scalar field or similar that delayed the expansion rate, so the proportion of neutrons would decrease as they decayed thus requiring the density of baryonic matter to increase to produce the same proportion of helium. Deuterium would be annihilated requiring the present abundance to have been produced at some later stage, such as spallation in shocks around the hypernovae of PopIII stars.
Garth
#52: “…it’s pretty apparent that merely modifying how gravity drops off with distance is not ever going to explain the Bullet Cluster.”
Certainly, I find it pretty believable that if you’re just naively considering modifications to the “1/r^{2}” law of Newtonian gravity you’ll run into situations where tweaking the power 2 to 2 + \epsilon(r) or whatever is not going to work. Like the Bullet Cluster. But geometrical theories of gravity of the level of complexity of GR are tensor theories, and they use this thing called a metric. That means, by my estimate, there are still 9 degrees of freedom you have to play with if you are modelling reality as a Lorentzian space.
If you can convince me that you have data that proves that it is impossible to tweak these 10 degrees of freedom to produce a theory in agreement within 5% error of what is observed, then I will be prepared to view this dark matter/dark energy stuff at least as a possibility. But as things stand, I find the “solution” to the problem - the postulation of a large amount of “something else” like WIMPs, nonbaryonic matter, heavy neutrinos!? somewhat bizarre and a bit contrived. Particularly since none of these candidates has ever been observed, even in particle accelerators.
I realize this sounds simplistic, but if space expands and the universe doesn’t, wouldn’t the consequence be external pressure on gravitational systems?
So? Even with tensors, gravity is still locally-defined. Unless your new theory of gravity violates the equivalence principle, then, you’re not going to have the galaxies appear to outweigh the cluster gas that has around ten times as many baryons, if there is no dark matter.
So, lots of fine tuning, plus additional extra unknown physical mechanisms? Sounds exceedingly unlikely to me. Now, if ever some evidence came to light that ruled out dark matter, then there might be a reason to delve into such theories. But when the vastly simpler explanation of dark matter is available, it seems our time would be better-spent elsewhere.
I’d suggest that a clue to the explanation of the galaxy rotation curve lies in the close relationship between Milgrom’s law and the rate of accelration of the universal expansion, which Lee Smolin says he was so struck by in his book The Trouble with Physics (Ch. 13).
Except that no theorist is likely to take my reasons for this suggestion seriously.
What close relationship between Milgrom’s law and the rate of acceleration of the expansion of the universe?
According to Smolin:
…there seems to be a region in in the interior of the galaxy where Newton’s laws work. Outside this region, things get messy.
The key question is: Where is the special orbit that separates the two regions? We might suppose that it occurs at a particular distance from the centre of the galaxy. This is a natural hypothesis, but it is wrong. Is the dividing line at a certain density? Again, the answer is no. What seems to determine the dividing line, surprisingly, is the rate of the acceleration itself. As one moves further out from the centre of the galaxy, accelerations decrease, and there turns out to be a critical rate that marks the breakdown of Newton’s law of gravity. As long as the acceleration of the star exceeds this critical value, Newton’s law seems to work and the acceleration predicted is the one seen. There is no need to posit any dark matter in these cases. But when the acceleration observed is smaller than the critical value, it no longer agrees with the prediction of Newton’s law.
What is the special acceleration? It has been measured to be 1.2 X 10^-8 centemetres per second per second. This is close to c^2/R [10^8 per second^2], the value of the acceleration produced by the cosmological constant!
The Trouble with Physics p. 210
#58: “So? Even with tensors, gravity is still locally-defined. Unless your new theory of gravity violates the equivalence principle, then, you’re not going to have the galaxies appear to outweigh the cluster gas that has around ten times as many baryons, if there is no dark matter.”
I might make the observation here that electromagnetic effects are relatively negligible in the cluster gas relative to galaxies, and if the final say on relativity includes anything to do with contributions due to the EM field that I’d say this would probably be part of your answer.
Unless I’ve misunderstood you, I’m not sure why you think it is impossible to describe gravity on large scales with a purely local theoretic description. Your point about the equivalence principle is a good one, of course, and well taken - but as far as I can see it is not really established with any mathematical rigor beyond the notion of a working hypothesis. When one has data that fly in the face of a working hypothesis, that were not taken at the scale the working hypothesis was originally tested, you have two options:
(i) You can continue to view the hypothesis as valid, and draw appropriate conclusions (dark matter/dark energy),
or
(ii) One can do a rethink of the fundamentals that led you to consider that hypothesis in the first place.
As far as I understand, good science involves thinking carefully about both options. Clearly (i) could well be right, particularly if it leads you to make predictions that are later confirmed (eg detection of new types of matter, or improvements in existing experimental technique that allow you to discover mass sources you previously missed, or made a hock out of the calculations, or something). However, if you make things so that it is almost impossible to detect these types of matter, or that one has no real clue what this stuff is, even if one views it as a simple solution — how can it possibly be a simple solution if you don’t even know what it is you’re looking for?
Andrew Daw,
Potentially interesting, but given that modified gravity doesn’t appear to explain Milgrom’s Law (due to the Bullet Cluster result), it seems more likely to just be a coincidence. There doesn’t, after all, appear to be any physical significance to the relative acceleration of an object sitting at the future horizon in a de Sitter universe.
Milgrom’s Law is more obvious, as it’s going to be directly related to the enclosed mass.
Tumbledried,
People have been thinking very hard about ways to modify gravity in order to account for the apparent existence of dark matter. And this pursuit was very important, until the Clowe et. al. Bullet Cluster result was published. Working with esoteric theories is absolutely vital to the pursuit of science, but that work needs to be informed by the data if it is to be useful.
Also, if the EM force had something to do with the difference, then that would be a violation of the equivalence principle. Remember that we have some pretty tight constraints on how photons gravitate from solar system experiments.
Oh, and by the way, after glancing at the Brownstein and Moffat paper again, I noticed that they are not attempting to explain the Bullet Cluster without dark matter. They now are trying to show how using both dark matter and modified gravity makes for a better fit to the data. But given that it’s only a two sigma improvement, and given that their modified gravity scenario adds a number of new unknown variables, one cannot conclude that modified gravity (on galaxy cluster scales) is remotely useful.
Really, the modified gravity people would, in my opinion, be making much better use of their time by attempting to look at potential modifications of gravity that would explain the current acceleration of the universe.
Jason,
Thanks for your response. You make some convincing arguments. I guess I just have an inherent bias against peculiar, trendy naming of unexplained phenomena, which may be impairing my judgement on these matters.
Incidentally, I was not really defending the Brownstein/Moffat paper per se - I was merely attacking this (relatively) new obsession with “dark matter”/”dark energy”. I find these concepts inelegant and unsatisfying for reasons that are perhaps not entirely logical, though you probably by now have the measure of my main counterarguments. I guess my fundamental grounding for this objection is more intuitive than anything else, and one fellow’s intuition is another’s scrapheap, so to speak.
Cheers.
Well, as far as dark energy (or modified gravity to explain the acceleration) is concerned, I have no opinion either way. The data just aren’t good enough yet. From looking at the proposed theories from a slight distance, it feels like the dark gravity people are having a hard time at it, while people suggesting that it might be some novel form of dark energy haven’t had any issues producing a wide range of at least self-consistent models that aren’t experimentally ruled out already. I honestly don’t know whether or not that should tell us anything about which is more likely to be correct.
But given the bullet cluster result, it just seems manifestly unlikely that you can in any way explain that without dark matter. And I also don’t see why it is interesting at all to attempt to show that both dark energy and dark matter are active. My reasoning is this: how do you know that your mass profile of the dark matter is accurate? Most people, when examining dark matter from lensing, tend to assume an isothermal profile. But we know that when a galaxy (or cluster) has recently undergone an interaction, it can take a while for the dark matter to relax into an isothermal profile. And since we know that the Bullet Cluster underwent a recent interaction, I’m going to be highly skeptical of any result that is going to depend upon the details of the mass profile, as any examination of modified gravity must (since weak lensing directly measures the mass profile, and if you are going to attempt to use weak lensing to determine the relationship between the underlying mass and gravity, you have to make some assumptions as to the mass profile..Bernstein and Moffat assumed isothermal, as I expected).
Slight correction: weak lensing does not directly measure the mass profile. It directly measures the gravity profile, from which we can infer the underlying mass profile given gravity. Bernstein and Moffat attempted to assume the underlying profile and from that infer gravity. But this sort of thing is doomed to failure when you assume an isothermal profile when your system recently underwent an interaction.
No matter how convincing the argument, if an investment advisor was trying to sell me on a company, 96% of whose assets I had to take on faith, I’d back out of there with my hand on my wallet.
Dark matter is to explain why the outer perimeter of galaxies spin faster then they should and dark energy is to explain why galaxies appear to be flying away faster then they should. I realize cosmology is at a point where theory says these dark forces are the best explanation, but maybe it is time to sit back and look at the theory.
Matter causes positive curvature of space, so why wouldn’t radiation cause negative curvature of space? A cosmological constant to balance gravity.
The data on redshift looks like it. The additional spin could as well be external pressure, as internal attraction. No need for dark energy, since the expansion of space is balanced by gravity.
Big Bang Theory, Inflation Theory, dark matter, dark energy. What will the next step be?
More on name.
So we have Sean’s picture.
We accept that there is evidence of the universe currently expanding more then it was before?
What currently in our universe would cause this? Are there times when the universe would “speed up” faster then other times?
I don’t quite understand how you can explain rotation curves via MOND without knowing how much dark matter there is in a galaxy? You’d need a different MOND depending on the amount. Or are they just assuming there’s very little?
Rob
Standard candle and expansionary rate of the universe?
Plato:
Was that an answer to my question? If it was I didn’t get it, so please elaborate.
John Merryman,
Dark matter explains much more than just galaxy rotation curves. If it was just galaxy rotation curves, you’d have a point, and we’d have no reason to prefer dark matter over modified gravity, or vice versa. The first major difficulty for modified gravity, however, came in with the CMB. Basically, it is quite difficult with modified gravity theories to explain the oscillations on the CMB, oscillations which are trivially explained by positing the existence of dark matter. Finding a modified gravity theory that works in both situations is a challenge, but with dark matter it “just works”. This made the modified gravity scenario seem rather contrived.
But now that we’ve got the Clowe et. al. Bullet Cluster result, modified gravity to fully explain dark matter’s effects just seems downright ludicrous, because the mass of the galaxy clusters is nowhere near where the baryons are.
The fundamental problem with your hand waving radiation explanation is that we understand how photons gravitate, and they don’t produce the effect you’re talking about. Photons, just like normal matter, produce positive curvature in overdense regions. The primary differences are that they don’t form structure, and their energy density is far too low during the current epoch to have any significant gravitational effect.
Plato,
The most reasonable explanation yet proposed for explaining the expansion without dark energy or modified gravity was to try to examine how the non-linearities of structure formation affect the apparent expansion. The idea here is that as structure forms, your overdense regions become smaller, while your underdense regions become larger. Thus the slightly larger expansion rate of the underdense regions makes the measured expansion rate appear to accelerate. As long as the structure formation is linear (as was the case in the early universe), these effects perfectly cancel and you see no additional acceleration. But at later times, as the structure formation goes nonlinear, the cancellation is no longer perfect, and you get some apparent acceleration. This has, so far, been investigated in spherically-symmetric inhomogeneous spacetimes (the only inhomogeneous spacetimes that have been solved), and the effect has been demonstrated. It remains, however, to show that the effect is large enough to explain the observed acceleration. Here is a (very) recent paper on the subject:
http://www.arxiv.org/abs/0710.5505
Rob,
Well, I presume it comes from varying the free parameters in the modified gravity theory.
Plato,
If the “picture” of our universe met the observations, why do we need to keep adding preposterous patchs to explain all the observations that don’t met our picture?
Inflation Theory? If space itself is expanding, why doesn’t the speed of light increase proportionally? Otherwise it is measuring a standard distance. The Doppler effect isn’t about expanding space, it’s about increasing distance in stable space. The train moves, the track does not stretch. The speed of light is the track. If it is increasing distance though, not expanding space, that would mean we are at the center of the universe.
Dark energy? Galaxies are being flung apart at an increasing rate, based on the redshft of a few photons of light, but these photons are not otherwise disturbed by this 70% of the total energy? Of course it can’t be an optical effect of light filling out enormous volumes of space, because we know light can’t be redshifted by anything other then recessional velocity. If we can propose spending enormous amount of time and money looking for this invisible energy, wouldn’t it also make some sense to spend some exploring the possibility that there might be some other explanation for redshift. Might it just be evidence of a cosmological constant that distorts the path of light, as gravity distorts the path of light? Rather then pulling it into a well, it stretches it out over a hill. If Omega=1, then the expansion is balanced by the contraction of gravity. Where is the additional expansion for the entire universe to expand?
Sometimes, when you just can’t fit everything into the frame you are using, it means it’s time to get a new frame, not play peek-a-boo with the evidence.
Jason,
I’m not arguing for modified gravity. As for my handwaving; we understand how photons gravitate, but is that the same as how lightwaves radiate? Radiation and gravitation would seem to be opposite sides of some larger cycle of expansion and contraction, so when we define light in terms of a particle, it conforms to the contraction side of the equation, but redshifting is a function of the expansion side of the equation. Particle or wave, but not both at the same time.
Sorry that I’ve been traveling and haven’t had time to join in the conversation. But Jason has basically covered everything I would have said.
And just to emphasize what Richard said above: dark matter isn’t just a stopgap or a fudge factor. It’s an extremely predictive hypothesis that fits a wide variety of data. The two big arguments against modified gravity are: (1) it’s hard to come up with a modification that changes the direction of the gravitational force in the weak-field regime without introducing new independently-propagating degrees of freedom [”dark matter”], and (2) the DM idea works so well that any new theory has to magically reproduce its predictions in case after case.
After all, there could actually be a planet Vulcan, too small and dim for us to detect. But not many people are expending resources chasing down that hypothesis.
In Tegmark’s mathematical multiverse, MOND would still be the correct theory in some sector. So, even if it turns out not to be relevant for our universe, one still has to study it in order to understand why we don’t find ourselves living in the MOND universe.
Let’s get real: if the universe really was just “mathematical” (and one among all the possible descriptions etc.), then anything at all could be true. With no inherent underlying principle, we could just as easily find ourselves in a world with the gravitational attraction being according to 1/r^2.001 as 1/r^2, etc. or even that changed with time in all kinds of ways, or even just arbitrary patterns (since they can all be logically “described,” albeit in ever more complicated ways.) A mathiverse gives no basis for predicting anything at all, despite the misleading intuitive implications.
John Merryman,
Photons don’t radiate. They have no electric charge.
Count Iblis and Neil B.,
If Tegmark’s mathematical universe is correct, then that doesn’t mean you can arbitrarily change constants or equations. Firstly, any set of equations that we can observe must have originated from some basic mathematics which are capable of generating new universes. Second, among those sets of mathematical setups which can generate new universes, we must exist in one capable of generating life. These place tremendous constraints upon what sorts of universes we can observe, and so if we knew how to connect fundamental theories (like string theory) to ideas like MOND as well as our own universe, then perhaps we would be capable of saying that there is a universe governed by MOND instead of dark matter. But I just don’t think that very hard work has yet been done for any truly fundamental theory (as I think string theory is the only such theory we have at the moment).
Hi Sean,
I was about to ask the same as Brian in #37: what is your take on the situation in Abell 520?
The Bullet cluster was a spectacular result, because it beautifully confirmed our assumptions about how dark matter, gas, and galaxies behave, [but] Abell 520 does the complete opposite,” comments Julianne Dalcanton of the University of Washington in Seattle.
Separation Anxiety: Cosmic collision may shed light on dark matter
By Ron Cowen
Best,
B.
Neil, the underlying principle for reality (including this universe) is that it needs to be self-consistent. Otherwise it cannot exist. That puts tremendous constraint on what can exist.
“A mathiverse gives no basis for predicting anything at all, despite the misleading intuitive implications. ”
How can this be true? Only a mathiverse would allow one to do calculations and predictions? That is what physics is all about.
There seems to be no alternatives to a mathiverse. Or maybe you can say what is the alternative?
Jason,
Maybe you could read what I asked, before responding; “we understand how photons gravitate, but is that the same as how lightwaves radiate? Radiation and gravitation would seem to be opposite sides of some larger cycle of expansion and contraction, so when we define light in terms of a particle, it conforms to the contraction side of the equation, but redshifting is a function of the expansion side of the equation. Particle or wave, but not both at the same time.”
Matter doesn’t radiate. Energy does. Is the photon the initial consolidation of mass out of energy?
John,
Well, I had assumed you were talking about EM radiation, which photons do not emit. Are you talking about some other form of radiation, such as gravitational?
John, radiation (like EM) carries energy, but energy as such does not radiate generally. Charged matter radiates EM when accelerated, and neutral matter is supposed to radiate gravitational waves when accelerated (difficult to measure though).
For those who want to read further on the issue of Dark Matter here is some information that has been helpful to me.
What is “Nothing” should help too
B and Brian, I don’t know much about Abell 520. It looks like a mess to me, and my strong suspicion is that we’ll need better data to figure out what is going on. The nice thing about Bullet cluster is that it’s pretty clear what is going on.
Brian Lacki –
Picking up on the sub-thread (strand?) in #29-35-38-41 above:
Yes, it has seemed to me that it’s hard to find a simple, true statement about the role of pressure, as distinct from mass-energy, as being a source of gravity, since it seems to behave that way in some examples but not others. I have personally put this question directly to a number of certified Big Brains, including at least one CV’er (not Sean), and not yet gotten a sensible answer. Perhaps we can attract Sean’s attention here?
Your reading in Peacock sounds quite to the point, but I can’t comment on it until you tell me whether rho is mass density or energy density (the latter would be expected, but the factor of 1/c^2 in (rho + 3p/c^2) suggests the former).
When was the book published?
Hoping for enlightenment,
Paul Stankus
Thanks, Sean. My question in post #37 wasn’t really “fair”, because all I think we can do right now about Abell 520 is speculate. I just took a fling - just wanted to hear what you would say.
Paul,
In what example does pressure not act as a source of gravity? Because that would pretty much falsify general relativity.
The only “simple, true statement” about the role of pressure is Einstein’s equation: G_uv = 8 pi G T_uv. Spacetime curvature on the left, stress-energy tensor on the right. Everything else is just words that we attach to specific solutions to give us a warm and fuzzy feeling — for example, “negative pressure causes the universe to accelerate.” Einstein’s equation relates tensors, not scalars, so there is no simple “source of gravity” in the Newtonian sense. But the equation itself is completely unambiguous; there aren’t any unsolved problems here.
Paul,
Here’s a reasonably simple way to think about pressure’s role in gravitational physics.
What matters in GR is the stress-energy tensor, T^{ij}, which tells you about the density of the i-th component of energy-momentum in a 3-volume orthogonal to the j-direction. So T^{tt} tells you the density of energy in a spacelike 3-volume orthogonal to the t direction, and (T^{xt}, T^{yt}, T^{zt}) gives you the density of the momentum 3-vector, again in a spacelike 3-volume orthogonal to the t direction. When we set j equal to a spacelike direction, say x, the 3-volume orthogonal to it includes time as one of its directions, so the “density” becomes a rate of change with time of energy or momentum per unit area. The rate of change with time of momentum is force, and force per unit area is pressure, so a component such as T^{xx} is pressure in the x-direction.
The stress-energy tensor of a blob of pressure-free matter is just rho u^i u^j, where rho is the mass density measured in the matter’s rest frame, and u is the matter’s 4-velocity. If you took a gas and computed the stress-energy tensor molecule by molecule this way (ignoring fiddly details of molecular structure such as bond potential energies, vibrations, etc.) and added up all the single-molecule stress-energy tensors, you would get the correct stress-energy tensor for the gas as a whole; because of the different directions for u for the different molecules, diagonal pressure terms like T^{xx} would appear automatically in the total, when written in a coordinate frame in which the gas was at rest. There is no extra term you need to add to T to account for the pressure.
The thing is, though, we don’t usually do the calculation that way: adding up rho u^i u^j for billions of molecules. Instead, we have macroscopic quantities describing the gas: its macroscopic density and its pressure, measured not in the rest frame of one molecule, but in the rest frame of the gas. If we want to construct T that way, we need to make sure that the density we use is the complete mass-energy density (i.e. it must take account of the kinetic energy of the molecules, not just their rest mass), and we need to explicitly make use of the pressure. We then get a tensor, in the rest frame of the gas, of the form diag(rho,P,P,P).
Similarly, when we’re dealing with an electromagnetic field we need to use the appropriate stress-energy tensor for that, which will generally contain both pressure and tension terms.
But however we end up constructing T, if there’s pressure or tension around there will be diagonal terms in T, and when T goes into Einstein’s equation as the source of spacetime curvature, those terms will make a difference.
Jason, Carl,
My initial understanding, aquired in thirty years ago, is that light is either waves or particles, but not both at the same time. That the process of measuring physically collapses the wave to particles, not that measuring simply discovers the particles contained within the waves and that they are actually both particle and wave at the same time. A possible analogy being that a lightning bolt collapses the energy in a cloud to a specific spot on the ground. Carver Meade wrote some interesting stuff that sounded similar.
A thread I tried starting in the recent god discussion, about the nature of time, ties into this. If time is a physical dimension along which physical reality travels from past events to future ones, then reality is both particle and wave because there is nothing to specifically define one from the other, but if time is a process by which motion in space creates events, then time is the wave of future potential collapsing into the particle of information that recedes into the past, as various fields interact, much like the interaction of the fields of sky and ground connect as lightning bolt, or tree. Both of which accrete energy to a specific point at the interface.
Admittedly my understand of physics is diluted by interaction with various other fields of study.
Sean,
MOG will not disappear until the day a press release is announced lauding the direct detection of dark matter particles. The discovery of dark matter is crucial, easily as much as the discovery of the CMB, for establishing the epistemological soundness of cosmology. Right now, anti-Big Bang folks use our lack of understanding of dark matter as yet another piece of evidence that we are really no further along in our understanding of the cosmos than we were generations ago. For them, dark matter is the 21st century version of the ether. Trust me, few events would be more devestating to an anti-Big Banger than the direct detection of dark matter particles. If the amount of dark matter directly detected matches the abundance implied by lensing, CMB, supernovae, and galaxy clusters, this would be one of the greatest scientific achievements of humanity. Until this happens, if it does, there will always be that discomforting lingering doubt that perhaps dark matter is a cosmic mirage after all.
I suppose it’s far too early to say, with the nature of dark matter still up in the air, but are there any respectable models in which the net proportion of dark matter is declining over time?
Could that explain the apparent acceleration of the Universe’s expansion, if dark matter acts as a gravitational brake but is gradually turning to some other form of mass-energy less effective as such (if that is physically possible)?
I guess in that case one would expect to see anomalous rotation more pronounced in galaxies the more distant they are. They would tend to be smaller though, which might muddy the waters somewhat.
On a related note, nobody has mentioned an intriguing idea mentioned a year or two ago, in New Scientist I think or maybe Scientific American, that dark matter is a kind of inverted and magnified (and perhaps time-shifted?) “image” of mass projected from the interiors of black holes. That was the gist of the proposal as I recall.
John Merryman,
Nope, not at all. All quantum mechanical particles, photons included, behave in a manner that makes them appear to be both particles and waves at the same time. This is basically just another way of saying that quantum mechanics is weird, and its behavior doesn’t actually coincide with anything we experience in the macroscopic world. The “particle” and “wave” behavior are really just analogies of the true behavior.
And wave function collapse, by the way, is merely an illusion. Representing the full wave function of the particle and its environment shows us that decoherence caused by interactions with the environment cause the different eigenstates of the particle to stop interfering with one another, causing the appearance of wavefunction collapse:
http://en.wikipedia.org/wiki/Quantum_decoherence
spaceman,
Sure, but where the science is concerned, big bang doubters really aren’t worth listening to. There’s more than enough evidence for dark matter, and the big bang theory in general.
John R. Ramsden,
I believe this is a general feature of dark matter theories. But they’re typically stable enough that it’s a very small effect. After all, if the annihilation of dark matter was too rapid, either it’d all be gone by now, or we’d be able to see the resultant radiation. There are a number of theorists who have proposed methods of detecting dark matter annihilation as a means to either test for interesting new physics, or just to detect the dark matter.
As for using galaxy rotation curves to test for this, well, there’s just far too much uncertainty in galaxy formation and structure for that to be useful at the current time.