Miscellany

Looks like the idea of sending robots to repair Hubble is gaining some steam. They wouldn’t be able to do everything you could do with a servicing mission, but they could install new instruments and gyros to keep the telescope running for quite a while longer. (Or not — if it’s deemed unfeasible, they might use a robot just to prepare the satellite for re-entry into the atmosphere.) It will be up to the engineers to build robots that can reliably do the job, which isn’t easy; but my bet is that it can be done. This challenge has actually energized a lot of folks at NASA, and fixing the Space Telescope is a goal everyone can agree on.

Chicago is a fantastic city in many ways; at some point I should do a series of posts on why this is the greatest city in the world to live in. One reason, believe it or not, is geography. In some respects, it’s not good to live on a large plain in the middle of a large continent; there are no mountains nearby to go climbing, and with no nearby oceans the weather can get pretty dramatic. (I once read that there are only three metropolitan areas with greater than five million people in which the temperatures regularly reached over 100 degrees F in the summer and below zero in the winter: Beijing, Moscow, and Chicago.) But there is an important benefit as well: it’s much harder to sneak up on an inland city with a nuclear weapon than it would be if we were on one of the coasts.

To be sure, Chicago is only about the fourth-ranked U.S. target that one would choose for a dramatic blowing-up; New York, Los Angeles, and Washington D.C. have to be ahead of us on the list. That, coupled with the difficulty of smuggling a nuclear weapon all the way into the interior, makes it seem relatively safe here. If I lived in one of those three coastal cities, I wouldn’t be nearly as sanguine. It’s one of those things we don’t like to talk about, but the chances of a terrorist group cobbling together the technology and raw materials for making a bomb have to be appreciable, given the half-hearted efforts that have been made to quarantine both resources and know-how thus far. (Not only have we gone quite easy on people who are known to share nuclear secrets, but our violations of the test-ban treaty and plans to build “small” tactical nuclear weapons have created a climate in which other countries do not feel encouraged to give up their own nuclear programs. Not to mention the fact that successfully building a bomb would be excellent proof against getting invaded.)

Mutually Assured Destruction, shaky as it was as a defensive doctrine under the best of circumstances, is nearly useless against terrorist organizations. There’s no way of guaranteeing we would even be able to pinpoint the true culprits, nor to counterattack if we could. If terrorists somehow get the bomb, they’re very likely to use it.

So what are the chances of a nuclear bomb being detonated in a U.S. city sometime in the next fifty years? One percent? Ten percent? These seem like reasonable numbers to me. What to do about it, I’m less sure.

Of course, risk analysis is notoriously difficult, and people tend to do a terrible job even when it’s easy. How many people would evacuate L.A. if scientists could guarantee that there was a 20% chance of a devastating earthquake (millions dead, city in ruins) in the next twenty years? I suspect not many; when the danger is so diffuse, it’s hard to take the tangible steps necessary to avoid it.

It was good to hear that Kerry is putting nuclear proliferation high on his list of foreign-policy priorities. (Even if he did choose to wear an old Monday Night Football blazer while doing so. Doesn’t he have wardrobe consultants on staff?) I don’t know how effective we can be, but doing everything conceivable to prevent a nuclear weapon from exploding in one of our cities seems like an easy priority to agree on.

I should tie up some loose ends (read: “potentially misleading intemperate statements”) in my post below about the anti-Big-Bang petition.

First, an actual physics point: Does Einstein’s general relativity really say that energy is not conserved? You will be unsurprised to hear that the answer depends on what you mean by “energy.” and what you mean by “conserved.” Before general relativity came along, when spacetime was thought of as a fixed, static background on which all the rest of physics played itself out, the answer was unambiguous; at any moment in time, there was a number we could compute (for any closed system) called the “energy,” and that number would be the same as at any other moment in time. (One way to derive this statement is as a consequence of the word “static”; time-translation invariance implies energy conservation.) Most often, we were lucky enough that the energy came in the form of an energy density defined at each point in space, which we could add up over the entire system to get the total energy.

GR changes the rules of the game. Spacetime is a dynamical object whose geometry responds to the presence of matter fields. We can now ask two separate questions: Is energy conserved for the matter fields in a given spacetime background? and Is the total energy of the universe, including matter and gravity (as manifested in spacetime curvature) conserved?

The answer to each question still depends on what you mean. Consider matter evolving in some background spacetime (so we ignore the possible energy of the gravitational field, whatever that may be). There is now no number we can calculate for a closed system that corresponds to “energy” and is conserved. This shouldn’t be a surprise, since we have violated time-translation invariance; the background geometry could be expanding or contracting, for example. In cosmology, there is no “total energy of the universe” which is supposed to be conserved — that’s why Lerner’s statement was so silly. On the other hand, there is a rule for “covariant” conservation of the local energy-momentum tensor (for experts, it’s D_aT^ab=0). This rule can be thought of as telling us exactly how the energy changes in response to changes in the background geometry, and it is what replaces the flat-spacetime notion of energy conservation. So the number of rules is the same in flat or curved spacetime; it’s not as if anything goes. But we can’t, once again, define a conserved total energy in any reasonable way.

So we should just include the energy of the gravitational field, obviously, right? The problem is there’s no good way to do that. If we blindly follow the rules for calculating the energy and apply them to general relativity, we find that they don’t give us an energy density at each point in space, but rather a boundary contribution defined solely at infinity. In other words, there is no local definition of energy density in general relativity. In the weak-field limit we can come up with good approximate notions of a gravitational energy density, and these are useful e.g. when calculating the energy lost through gravitational radiation in orbiting bodies. So perhaps we could give up on locality and stick with just a global definition. Given appropriate boundary conditions (typically that spacetime is flat at infinity) this makes sense, and we can define different notions of energy (the ADM energy, the Bondi energy) appropriate to different circumstances. But in cosmology the universe is not flat at infinity, so these circumstances don’t apply — there is generally, once again, no such thing as the conserved total energy. (In a closed universe there is — and it’s always exactly zero, for all the good it does us.)

The situation is thus a little ambiguous; whether energy is conserved in GR depends on the situation you are talking about, and what you would qualify as energy conservation. Don’t get me wrong: nobody who understands what’s going on has any disagreement about the equations or their solutions, it’s just that there are different words we can reasonably apply to them. This is actually a good example of what Thomas Kuhn talked about in The Structure of Scientific Revolutions, where he discusses how words mean different things before and after a paradigm shift. The notion of “energy” is very useful, but its status in GR is different than it is in flat-spacetime physics. The one thing we can all agree on is that background energy density that remains constant as the universe expands, and whose integral over space therefore grows, is perfectly consistent with everything we know about physics.

The other thing I wanted to revisit is my defaming remark that Big-Bang opponents aren’t very smart. Peter Woit points out a counterexample: Irving Segal, a well-known mathematical physicist who developed “chronometric cosmology” as an alternative to the Big Bang. Of course there are other counterexamples, notable among whom we should mention Sir Fred Hoyle, who did extremely important work in stellar nucleosynthesis, and later became well-known as a supporter of the Steady State model. (It was Hoyle who actually coined the term “Big Bang,” as a derogatory term to belittle the model we now know to be correct.) (Update: Another unfair slander! See the comments.)

I shouldn’t have given such a blanket indictment of the intellectual prowess of the anti-Bang folks. For all I know, Eric Lerner is a grandmaster at chess, a gourmet cook, and a crossword-puzzle wizard. What I should have simply said is that the criticisms leveled by these folks at the Big Bang are just not very smart. I can certainly imagine intelligent and reasonable arguments given against almost any scientific position; but the anti-Banging is generally done from a position of deep philosophical conviction, which tends to result in rather weak argumentation. Segal, for example, had a theory in which the apparent velocity of a distant galaxy should be proportional to its distance squared (rather than simply the distance, as in the conventional theory). He would insist that modern statistical techniques reinforced his result; typically, these techniques would involve tossing out the data that manifestly disagreed with his theory. He was extremely bright in some ways, but about this he was blind.

The point really is that the anti-Big-Bang crowd are not visionary mavericks being unfairly undermined by a narrow-minded scientific establishment; they are just crackpots. The difference can be quite subtle and even subjective, but in this case it’s pretty clear.

I think of myself as realistic and even cynical, but reality keeps surpassing my lowest expectations. The Poor Man points out something I didn’t believe until I checked for myself: the front page of the official George W. Bush campaign website features (on May 30, anyway) not a single image of George W. Bush. It does have four pictures of John Kerry, though. Lead with your strengths, I suppose.

PZ Myers of Pharyngula fame has pointed me to an online petition that was apparently first published in New Scientist. No, it’s not complaining about the Bush administration making a travesty of science (although David Appell points to one of those, too); it’s about the terrible dominance of the Big Bang model.

The complaints are not new. The Big Bang just rubs some people the wrong way, and they won’t believe in it no matter how many successes it accumulates. Some of the disbelief stems from religious conviction, but in other cases it seems to be a particular kind of philosophical outlook. Most of the skeptics, of course, have their own favorite alternatives. The most popular is undoubtedly the Steady-State model (or one of its increasingly twisted modern incarnations), but there is also something called the “plasma cosmology”, championed by the late Nobel Laureate Hannes Alfven. (His Nobel was for plasma physics, not cosmology; and the fact that he was Swedish didn’t hurt.) If you want to know in detail why the various alternatives are wrong, Ned Wright tells you.

Here is the kind of thing the petition says:

What is more, the big bang theory can boast of no quantitative predictions that have subsequently been validated by observation. The successes claimed by the theory’s supporters consist of its ability to retrospectively fit observations with a steadily increasing array of adjustable parameters, just as the old Earth-centered cosmology of Ptolemy needed layer upon layer of epicycles.

Really? How about acoustic peaks in the power spectrum of temperature fluctuations in the cosmic microwave background? And the polarization signal, and its spectrum? And the baryon density as deduced from light-element abundances agreeing with that deduced from the CMB? And baryon fluctuations in the power spectrum of large-scale structure? And the transition from acceleration to deceleration in the Hubble diagram of high-redshift supernovae? And the relativistic time delay in supernova light curves? These are just the very quantitative predictions that have come true in the last few years; the Big Bang has had a long history of many observational successes. (This is a very incomplete list; usually one doesn’t pay much attention to straightforward tests of the Big Bang framework, since they are taken for granted.)

But here is the important issue, again from the petition:

Whereas Richard Feynman could say that “science is the culture of doubt”, in cosmology today doubt and dissent are not tolerated, and young scientists learn to remain silent if they have something negative to say about the standard big bang model. Those who doubt the big bang fear that saying so will cost them their funding.

Something actually interesting is being raised here: at what point does a scientific theory become so well-established that it’s no longer worth listening to alternatives?

There’s no easy answer. Scientific theories are never “proven” correct; they simply gather increasing evidence in their favor, until consideration of alternatives becomes a waste of time. Even then, they are typically only considered correct in some domain. Einstein’s general relativity, for example, works very well in a certain regime, but that doesn’t stop us from considering alternatives that may be relevant outside that regime.

So, shouldn’t we devote a certain fraction of our scientific resources, or our high-school and secondary curricula, to considering alternatives to the Big Bang, or for that matter Darwinian evolution? No. Simply because resources are finite, and we have to use them the best we can. It is conceivable in principle that the basics of the Big Bang model (an expanding universe that was much hotter and denser in the past) are somehow wrong, but the chances are so infinitesimally small that it’s just not worth the bother. If individual researchers would like to pursue a non-Big-Bang line, they are welcome to do so; that’s what tenure is for, to allow people to work out ideas that others think are a waste of time. But the community is under no obligation to spend its money supporting them. And yes, young people who disbelieve in the Big Bang are unlikely to get invited to speak at major conferences, or get permanent jobs at research universities. Likewise astrophysicists who believe in astrology, or medical doctors who use leeches to fight cancer. Just because scientific claims are never proven with metaphysical certainty doesn’t mean we can’t ever reach a conclusion and move on.

And to be sure, the alternatives to the Big Bang are just silly. Usually I try to keep my intellectual disagreements on the level of reasoned debate, rather than labeling people I disagree with as “dumb” (that I reserve for the President); but in this case I have to make an exception. They just aren’t, for the most part, very smart. Consider this quote by Eric Lerner, petition signatory and author of The Big Bang Never Happened:

No Conservation of Energy

The hypothetical dark energy field violates one of the best-tested laws of physics–the conservation of energy and matter, since the field produces energy at a titanic rate out of nothingness. To toss aside this basic conservation law in order to preserve the Big Bang theory is something that would never be acceptable in any other field of physics.

Actually, there is a field of physics in which energy is not conserved: it’s called general relativity. In an expanding universe, as we have known for many decades, the total energy is not conserved. Nothing fancy to do with dark energy — the same thing is true for ordinary radiation. Every photon loses energy by redshifting as the universe expands, while the total number of photons remains conserved, so the total energy decreases. An effect which has, of course, been observed.

Just because a person doesn’t understand general relativity doesn’t mean they are dumb, by any means. But if your professional activity consists of combating a cosmological model that is based on GR, you shouldn’t open your mouth without understanding at least the basics. So if I get to decide whether to allocate money or jobs to one of the bright graduate students working on some of the many fruitful issues raised by the Big Bang cosmology, or divert it to a crackpot who claims that the Big Bang has no empirical successes, it’s an easy choice. Not censorship, just sensible allocation of resources in a finite world.

Will Baude at Crescat Sententia asks two profound questions that we at Preposterous are happy to answer.

First: What is the appropriate honorific for a professor at the University of Chicago? There’s a story one sometimes hears to the effect that everyone (students, faculty, presumably researchers) at the UofC refers to each other by Mr/Ms, in sort of a charming reverse-snobbery. (As Brian at That’s News to Me points out, the story is promulgated through the UofC student guide.) We’re all supposed to be a community of scholars or some such thing. But is it really true?

The existence of this story makes things more awkward than they should be, if anything; the transition from Dr/Professor to first names as students get to know professors better is ambiguous and difficult enough, and throwing the possibility of Mr/Ms in there muddles things beyond hope. But we can look at the data. A quick perusal of emails from students in my current undergrad class reveals about a 50/50 split between “Professor Carroll” and a complete absence of name (just “Hi” or some such thing). No “Mr. Carroll”‘s in evidence. But perhaps email is slightly more formal than face-to-face? I recall at least one student last quarter using “Mr.” Not that I care; students are welcome to call me by Sean, or Professor, or Dr. I would think that the rules should be close to what they are outside the academic environment; if you are meeting someone for the first time, the relevant title seems appropriate, and once you get to know them better you can use the first name. Note to students: not every professor feels this way, and some quite like being called “Professor.” And there’s no easy way to tell.

To be honest, I’m not always clear on what I should call other professors. In particular, if I am sending email to someone in my field, whose work I am familiar with but whom I’ve never met in person nor corresponded with previously, should I call them Dr/Professor or just use their first name, as would be common if we were introduced at a conference? For no especially good reason, I tend to jump right in with the first name if the person is actually in my field, but use an honorific for someone in another discipline. Presumably I feel as if we physicists are a band of brothers and sisters, all in this together and somehow all friends even if we haven’t actually been introduced. Whereas the more abstract ties of academia aren’t quite enough to allow for such assumed intimacy. I think this compromise is not unusual, actually, although I don’t have any real data.

(As I was writing this I noticed an update. Seems like the Professors are taking over.)

Will’s second question: Should an omnipotent God be omnicontracting (able to make any promise, but not to ever break those promises) or omnibreaching (able to do anything at any time, even break past promises)? That one is much easier. The concept of an omnipotent God is incoherent. There is no sensible way to define what is meant by “omnipotent.” That’s okay, because there doesn’t exist anything resembling an omnipotent God, so the logical impossibility of the concept shouldn’t bother anyone.

Never let it be said that we don’t tackle the important issues.

In case you had any doubt, the human rights situation worldwide is now the worst it’s been in 50 years. Ruben Bolling offers one possible explanation (click for more):

Don’t laugh, I’ve heard crazier ideas.

Yesterday we wondered out loud whether cosmological evidence for dark matter might actually be pointing to something more profound: a deviation of the behavior of gravity from that predicted by Einstein’s general relativity (GR). Now let’s ask the same question in the context of dark energy and the acceleration of the universe.

We have (at least) two problems to face. First, if you do a back-of-the-envelope estimate of what the vacuum energy (the energy density inherent in empty space, or equivalently Einstein’s cosmological constant) should be, you get an answer that exceeds the observationally allowed value by the ridiculous factor of 120 orders of magnitude (10¹²⁰). That’s bad, as far as agreement between theory and experiment is concerned. But nevertheless the universe is accelerating, which could be explained by a tiny amount of vacuum energy — about 10^-8 ergs per cubic centimeter, if you care. Or perhaps by something else.

For example, maybe general relativity works for ordinary bound systems like stars and galaxies, but breaks down for cosmology, in particular for the expansion rate of the universe. In GR the expansion rate is described by the Friedmann equation, which sets the expansion rate proportional to the square root of the energy density. Ordinarily the density drops as the universe expands, and the expansion rate follows suit; if the density is constant (as with vacuum energy), the expansion rate can stay constant. (We would then interpret that as “accelerating”, oddly enough. A distant galaxy has a recession velocity v=Hd, where d is the distance and the Hubble constant H tells us the expansion rate. If H is constant and d is increasing, we would measure v to be increasing.)

So maybe Friedmann was somehow wrong. For example, maybe we can solve the problem of the mismatch between theory and experiment by saying that the vacuum energy somehow doesn’t make the universe accelerate like ordinary energy does. There are different ways to make this happen, none of which strike you as perfectly compelling. Arkani-Hamed, Dimopoulos, Dvali, and Gabadadze have proposed a “filter” by which smoothly-distributed energy doesn’t affect spacetime in the same way as localized energy; it’s somewhat ad hoc, but definitely interesting. With Laura Mersini I suggested that the pressure of a substance, as well as the energy density, contributes to the expansion rate, in just such a way as to make vacuum energy (which comes with a negative pressure) cancel exactly and leave spacetime unaffected. We were inspired by models with extra dimensions of space, but the particular models in question don’t quite work, so I’ve since spent a lot of time looking for models that are strictly four-dimensional. No luck yet.

Solving the cosmological constant problem is hard, and a popular strategy is to ignore it and try to account for dark energy separately. That is, imagine that the vacuum energy is set to zero by some mysterious mechanism, and something else is responsible for the acceleration of the universe. There are different approaches to this possibility as well. One is to be largely phenomenological, and just write down alternatives to the Friedmann equation to see what might work. This approach (inspired again by extra dimensions, but basically phenomenological) has been pursued by Dvali and Turner, and by Freese and Lewis. One issue here is that ultimately it wouldn’t be possible to distinguish experimentally between a modified Friedmann equation and some model of dark energy; both would only show up in the behavior of the expanding universe.

So the complementary approach is to come up with a whole new theory of gravity that can make the universe accelerate, and see if what that theory has to say about other tests of gravity. I’ve been thinking about this recently, having spent the weekend talking to Mark Trodden. He and I have written a paper with Duvvuri and Turner that explores an especially simple approach to doing this. We just suggest that the curvature of spacetime somehow resists going to zero, and can bounce back to infinity when it becomes small. (There are actually a lot of equations involved, but that’s the basic philosophy.) Then we can compare our model to experiments. Sadly, it fails. The simplest way to see this was pointed out by Chiba, who rewrote our theory in a way that resembles other models, and showed that ordinary tests of GR in the solar system are incompatible with our suggestion. Basically, the orbit of Mars would look different. But that’s okay; it just goes to show that GR is actually quite robust, and even an attempt to change it exclusively in cosmology ends up affecting all sorts of other things.

A more elaborate approach has been suggested by Dvali, Gabadadze, and Porrati (see a recent review by Dvali for more details). They again use an extra dimension of space, imagining that our world is a three-dimensional “brane” embedded in a four-dimensional space (plus one time dimension, as usual). They have invented a scheme whereby gravity can behave differently on and off the brane, become much weaker in the four-dimensional “bulk.” But at very large scales the bulk begins to affect our universe. They claim that, if we choose parameters appropriately (there is always a great deal of unnatural fine-tuning involved in these scenarios), we can straightforwardly explain the accelerated expansion of the universe. Even better, they are not yet (as far as we know) ruled bout by solar-system tests, but improved measurements might be able to detect new affects from the extra dimensions in the orbit of the moon (see also this paper by Lue and Starkman). This theory is not very well understood as yet, and deserves a lot more work to be fully explicated; but it’s interesting and promising, so we’ll have to see what happens as people think about it further. (There is a nice popular-level exposition by Dvali in Scientific American, although you have to pay for the full article online.)

So we don’t have any extremely compelling alternatives to Einstein’s theory, but there are a lot of possibilities and we have our work cut out for us. The good news is that observed phenomena (the dynamics of galaxies and clusters, the cosmic microwave background, the accelerating universe) are pushing us to think of profound new scenarios for gravity and cosmology.

By the way (as it were), John Scalzi links here and suggests that GR is bound to give way pretty soon. I hope that’s not the impression I’m actually giving; I personally think it’s an incredible long shot, but one worth pursuing. Probably the “standard” story of cold dark matter and vacuum energy are exactly right; this is a robust model that makes many more predictions than there are free parameters, and it’s well-motivated (although far from completely understood) in fundamental physics. In contrast, when we start modifying gravity, we’re just flailing around, hoping some good will come of it. But that’s how science works; the flailing always looks a little silly until it smacks into a bit of miraculous insight, which we then clean up and proclaim to be genius. Right now there’s a lot of talk of modifying gravity, because it’s well worth considering; but if you’re going to bet, Einstein gets much better odds even than Smarty Jones.

Gravity is the most obvious of the four forces of nature (gravity, electromagnetism, and the strong and weak nuclear forces). It’s also the first for which we had a sensible physical theory: Newton’s law of universal gravitation. Now we have sensible theories for all four of the forces, and Newton’s theory has been superseded by an even better theory, Einstein’s general relativity (GR).

GR has passed a series of experimental challenges with flying colors: the precession of Mercury, deflection of light, gravitational redshift and time delay, gravitational radiation from the binary pulsar, and the expansion rate of the early universe during the nucleosynthesis era. But it doesn’t quite fit in with the rest of physics, since the other three forces seem to be compatible with quantum mechanics in a way isn’t so obvious for gravity. So very few people really believe that general relativity is the final answer; at some point we’ll have to invent a better model (string theory being the leading candidate) that is intrinsically quantum-mechanical yet reduces to GR in the appropriate regimes.

Usually in field theory, if a model works well in a certain regime, you might expect it to break down at shorter distances or higher energies, but continue to be successful at long distances and lower energies. Nevertheless, people have begun to ask whether general relativity might be okay in the solar system but break down on much larger scales (galaxy- or universe-sized distances). The primary motivation for such suggestions is the fact we need to hypothesize dark matter and dark energy to make sense of our universe if GR is correct. It is very likely that GR is correct, and dark matter and dark energy are both for real, but since we can’t be sure we consider the possibility that our understanding of gravity is to blame.

Of course, it’s easy to say “let’s modify gravity,” much harder to come up with a good model. Indeed, it’s not even obvious what issue you’d like your model to address — the need for dark matter in galaxies, clusters, and large-scale structure; or the perplexingly small value of the cosmological constant; or the acceleration of the universe conventionally attributed to dark energy.

Modifying gravity with the goal of replacing dark matter is a long-standing project that has met with mixed success, most famously pursued by Milgrom and his friends. Milgrom has an idea called “Modified Newtonian Dynamics,” or MOND for short. For some introductions see pages by Greg Bothun or Stacy McGaugh, or this review by Sellwood and Kosowsky. The idea is to slightly increase the Newtonian gravitational acceleration when that acceleration is very small, so that slowly-moving particles feel more force than they ordinarily would, mimicking the presence of unseen matter. This idea works extremely well for individual galaxies; indeed, Milgrom made predictions for the behavior of low-surface-brightness galaxies before they were directly observed, and the predictions were later confirmed very nicely.

Unfortunately, there are problems with the MOND paradigm itself. For one thing, it’s not really a “theory”, it’s just a rule for making predictions in a very specific set of circumstances — slowly-moving particles orbiting around massive bodies. (Just as an observational matter, it doesn’t even seem to work very well for clusters of galaxies, although it does quite well for individual galaxies.) Since it’s not a full-blown theory, it’s hard to make predictions for other tests you might like to do, like deflection of light or cosmology. So people have been trying to invent an actual theory that reduces to MOND in the appropriate circumstances. In a recent proposal, Bekenstein has claimed to succeed; now people are at work putting this idea to the test, to see both if it makes sense and if it agrees with other things we know about cosmology.

In addition to the theoretical difficulties, there is at least one model-independent reason to think that no modification of gravity will ever replace the idea of dark matter: we seem to be accumulating evidence (tentatively at the moment, to be sure) for gravitational forces pointing in directions where there is no ordinary matter. The most basic such clue comes from studies of gravitational lensing of clusters of galaxies, which can be used to reconstruct the distribution of dark matter in the clusters. The upshot is that the dark matter seems to be distributed much more smoothly than the ordinary matter; see this reconstructed cluster image for an example. Less direct evidence is found in the acoustic peak structure of the temperature anisotropies in the cosmic microwave background. (For an intro, see Wayne Hu’s tutorial.) Density fluctuations in the plasma of the early universe lead to sound waves, in which regions become more dense and therefore hot, and then bounce back and become less dense, in a repeating cycle; this leads to peaks in the plot of temperature fluctuation as a function of angular scale. But fluctuations in the dark matter don’t heat up (they don’t interact with light, since they’re dark), so they only increase with time. Consequently, odd-numbered peaks have ordinary matter and dark matter in phase, and even-numbered peaks have them out of phase. The out-of-phase oscillations are suppressed, so we expect dark matter to boost the odd-numbered peaks. This is exactly what appears to happen, as this figure indicates. At least a little bit; the data need to improve before we can be sure. But it’s hard to see how a modified theory of gravity could explain this phenomenon.

Of course, perhaps a modified theory of gravity could predict gravitational forces pointing in directions other than where there is ordinary matter; you’d have to tell me the theory first before we could say for sure. MOND doesn’t, though, and such a theory is even harder to imagine than one that simply fits the galaxy data.

Tomorrow I’ll talk a little about modified gravity and the issues of vacuum energy and the accelerating universe.

I’m thinking of starting a new tradition, declaring Friday to be Narcissism Day here at Preposterous Universe. A day we can take off from thinking about important world events and profound cosmic mysteries, and just think about me.

In this spirit, I offer this pointer to my first-ever (so far as I know) appearance in the society pages of a major newspaper. (To balance things out, here’s a media moment more relevant to my purported expertise. [Update: I found another one. What a media slut, hmm?]) The occasion was the Dinosaur Dinner I attended to benefit Project Exploration. Here’s more proof:

L to R: Sean, State Senator Barack Obama, Shureice Kornegay, Jean Claude Francois, Project Exploration Executive Director (and expectant mother) Gabrielle Lyon, Michelle Obama. I’m the one with the martini, to nobody’s surprise.

I have to admit that I didn’t see any evidence of the stalker that Jack Ryan’s campaign has assigned to follow around Obama twenty-four hours a day. Probably he couldn’t afford a ticket. The Obama campaign has started its own blog, which is worth a visit.