But that might be about to change. We’re very happy to have Marc Sher, a particle theorist at William and Mary, explain an interesting new initiative that hopes to provide a much lower-cost alternative to the mainstream publishers.

(Update: I changed the title from “Open Textbook” to “Nonprofit Textbook,” since “Open” has certain technical connotations that might not apply here. The confusion is mine, not Marc’s.)

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The textbook publishers’ price-gouging monopoly may be ending.

For decades, college students have been exploited by publishers of introductory textbooks. The publishers charge about $200 for a textbook, and then every 3-4 years they make some minor cosmetic changes, reorder some of the problems, add a few new problems, and call it a “new edition”. They then take the previous edition out of print. The purpose, of course, is to destroy the used book market and to continue charging students exorbitant amounts of money.

The Gates and Hewlett Foundations have apparently decided to help provide an alternative to this monopoly. The course I teach is “Physics for Life-Scientists”, which typically uses algebra-based textbooks, often entitled “College Physics.” For much of the late 1990′s, I used a book by Peter Urone. It was an excellent book with many biological applications. Unfortunately, after the second edition, it went out of print. Urone obtained the rights to the textbook from the publisher and has given it to a nonprofit group called OpenStax College, which, working with collaborators across the country has significantly revised the work and has produced a third edition. They have just begun putting this edition online (ePub for mobile and PDF), completely free of charge. The entire 1200 page book will be online within a month. People can access it without charge, or the company will print it for the cost of printing (approximately $40/book). Several online homework companies, such as Sapling Learning and Webassign, will include this book in their coverage.

OpenStax College Physics’ textbook is terrific, and with this free book available online, there will be enormous pressure on faculty to use it rather than a $200 textbook. OpenStax College plans to produce many other introductory textbooks, including sociology and biology textbooks. As a nonprofit they are sustained by philanthropy, through partnerships, and print sales, though the price for the print book is also very low.

Many of the details are at a website that has been set up at http://openstaxcollege.org/, and the book can be downloaded at http://openstaxcollege.org/textbooks/college-physics/download?type=pdf. As of the end of last week, 11 of the first 16 chapters had been uploaded, and the rest will follow shortly. If you teach an algebra-based physics course, please look at this textbook; it isn’t too late to use it for the fall semester. An instructor can just give the students the URL in the syllabus. If you don’t teach such a course, please show this announcement to someone who does. Of course, students will find out about the book as well, and will certainly inform their instructors. The monopoly may be ending, and students could save billions of dollars. For decades, the outrageous practices of textbook publishers have not been challenged by serious competition. This is serious competition. OpenStax College as a nonprofit and foundation supported entity does not have a sales force, so word of mouth is the way to go: Tell everyone!

And it may very well turn out that the behavior of gravity on large scales does not precisely match the prediction of ordinary general relativity. Nevertheless, I think that by now we’ve accumulated enough data to conclude that the universe cannot be explained solely by modifying gravity; there is ample evidence of gravitational forces pointing in directions where there isn’t any (ordinary) “stuff” to create them, leading us to accept the existence of some form of dark matter. About a year ago I put up a post that explained this point of view, and took aim in particular at the popular framework known as MOND.

This led to some good discussion in the comments, and also to a behind-the-scenes email exchange between Rainer Plaga, Stacy McGaugh, and me. It’s a bit of old news, but I thought there would still be some interest in our discussion, so (with permission) I’m posting our emails here. Seeing how the sausage is made, as it were. It’s a bit of a long read, sorry about that.

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Rainer, March 1:

Dear Sean,

I discussed your recent vigorous defense of CDM your blog with Stacy, and he encouraged me to send you my – absolutely objective – position.

On the one hand I am with you that if Stacy uses terms like “serious fine-tuning problem for LCDM” in his newest paper’s abstract (which are then interpreted by science journalists in the way you exhibit), he had to quantitatively compare the expected properties of galaxies under the assumption of \LambdaCDM with his data set. If he wants to criticise an idea he has to deal with the idea not with alternatives to it. Alas, he does not do that in this paper.

On the other hand I strongly disagree out of principle to require statements like: ?of course we have more than sufficient evidence to conclude that dark matter exists, we?re just trying to understand how it works and what else might be going on.? from anybody. Really Sean, this sounds like a caricature of the holy inquisition to me, “philosophers can speculate as long as they accept that the final truth is already known from the holy scriptures ”.

Your statement: “Dark matter is real … there’s no reasonable doubt about the dark matter.” is misleading. Stacy and I of course know that dark matter in the form of massive neutrinos does exist beyond reasonable doubt. But that does not answer a crucial question. Crucial questions are: what flattens the rotation curves in galaxies? What creates the third CMB peak? CDM, MOND or something else?

In my opinion the final verdict on these questions is not in, yet. Allow me to argue why your top 3 arguments for the existence of CDM do not convince me, perhaps yet.

1. “MOND is ugly”: The alternative is not “theory for MOND” vs. GR but “theory for MOND” vs. GR + “theory for CDM particle”. The number of exhibited equations then becomes similar. How do you know that TeVeS is uglier than the “theory for CDM particle”?

2. “Clusters require DM anyway” If one could make a case that they require nonbaryonic cold dark matter, I would consider the case settled in favour of CDM. However, the dark matter required for MOND in clusters might be the ca. 40% fraction of baryonic matter that we anyway know is currently missing in clusters (even in LCDM). Do we agree? How can the argument be clinching then?

3. Your strongest argument is the one from the CMB. But still, replacing “MOND” with “CDM”, couldn’t your statement:

“Can some clever theorist tweak things so that there?s a MOND version that actually fits? Probably. Or we could just accept what the data are telling us.”

be used just as well to comment on the well known problems of CDM to reproduce the detailed properties of galaxies?

Wouldn’t this be a great topic for another “great debate” a la Shapley/Curtis 1920 between u and Stacy? In that case it turned out both were partly right and wrong, my personal bet: it would be the same this time .

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Sean, March 1:

Hi Rainer–

Ten years ago, it was perfectly respectable to speculate that there was no such thing as dark matter, just a modification of gravity. (It couldn’t have been MOND alone, which was ruled out by clusters, but it could have been some more elaborate modification.) That’s no longer true. The Bulltet Cluster and the CMB both provide straightforward evidence that there is gravity pointing in the direction of something other than the ordinary matter. The source for that gravity is “dark matter.” It could be simple, like an axion or a thermal relic, or it could be quite baroque, like TeVeS + sprinkles of other dark matter as required, but it’s definitely there.

If people want to contemplate that there is dark matter and also a modification of gravity, that’s fine. If people want to point to features of galaxy/cluster phenomenology and say that these features must be explained, that’s absolutely fine. But if people want to cling to the possibility that dark matter doesn’t exist, that’s not being appropriately cautious, it’s just ignoring the data, and it’s a disservice to the public to pretend otherwise.

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Rainer, March 2:

Dear Sean,

I do not fully understand your argument: do you argue that the bullet cluster proves that _nonbaryonic_ DM exists? To me Stacy’s argument – that MOND might work only with the baryonic cluster DM which is an additional problem even within LCDM – cannot be currently excluded (see 2. in my previous e-mail). Do you disagree with his argument, and if yes, why?

For your convenience let me summarize Stacy’s general argument in my own words (Stacy please protest if I misrepresent it):

a. even within LCDM generally uncontested facts are that in clusters of the size of the bullet cluster (< 10(13) M_sun):
1. ca. 50% of the cluster's _baryonic_ matter is probably in some invisible form
2. the hot gas is a minor component of the total baryonic matter (see e.g. fig.1 here: http://arxiv.org/abs/1007.1980)

b. suppose that this baryonic cluster DM is in some non-collisional form (e.g. jupiters). Then a.1. would quantitatively explain MOND’s missing cluster DM and a.2. the observational fact that the bullet’s cluster mass is concentrated on the galaxies and not the hot gas.

It is somewhat paradoxical, but seems clear: if you want to rule out MOND you have to deal with its details, if Stacy wants to rule out CDM he has to deal with its details. Neither of you guys is really doing this, and I can understand why: both of you would feel you are wasting time on a wrong concept. But you would not .

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Sean, March 2:

Hi Rainer–

We know how much baryonic matter there is from BBN. It’s not enough to explain the Bullet Cluster or the CMB, even with MOND. Not to mention that you would have to come up with some way to turn the large majority of baryonic matter into some collisionless form. (The paper you just cited says ” the baryons are not missing, they are simply located in cluster outskirts” right there in the abstract.)

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Rainer, March 2:

Hi Sean,

We know how much baryonic matter there is from BBN. It’s not enough to explain the Bullet Cluster or the CMB, even with MOND.

They claim ca. a factor 2 more dark baryonic matter than seen is needed in the clusters. What problem would that pose with BBN? (Don’t forget that the baryonic matter/CDM ratios derived from LCDM in clusters are meaningless if MOND were the answer).

Not to mention that you would have to come up with some way to turn the large majority of baryonic matter into some collisionless form.

Yes, this would need some ad-hoc gastrophysics to produce enormous amounts of e.g. jupiters especially in the cluster centre. Not nice, but not impossible, cooling flows etc… But if all that were true, the bullet cluster would be OK.

(The paper you just cited says ” the baryons are not missing, they are simply located in cluster outskirts” right there in the abstract.)

But that’s exactly what is needed also for MOND: the dark baryons are really hiding somewhere… They are not claiming a detection of these baryons! But let us take a step back on this paper:

What it discusses is the fact that clusters need some dark baryonic matter even in LCDM, ca. 30% of the baryonic matter is apparently unseen. This was unexpected, some gastrophysics will be needed to explain it. (They mention “AGN feedack” and stuff…)

MOND’s problem is more severe, ca. 70% of the baryonic mater would apparently be unseen in the central parts of the clusters. This was unexpected some gastrophysics will be needed to explain it.

Sorry, Sean, this seems like an open problem to me both for LCDM and MOND, admittedly a bigger one for MOND (but then clusters are their worst problem…), but not the ultraclean evidence for CDM that you are claiming…

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Stacy, March 2:

OK, I think at least we all agree that BBN tells us the baryon density of the universe. Lets deal with one thing at a time, the dark matter in clusters. If I understand you, you are saying MOND is falsified because there is dark matter in clusters. Rainer is suggesting that a logical way out of this is if the excess mass in clusters is in some dark, baryonic, collisionless form. I agree it is tough to imagine what that would be (and have consistently said as much) but I am not willing to grant that I know it to be impossible. So the real leap to falsify MOND is to say that the dark mass in clusters is not just dark baryons, but WIMPs (or whatever non-baryonic particles compose CDM). And that follows how? Because Omega_m > Omega_b?

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Sean, March 3:

MOND without non-baryonic DM is falsified by clusters, because you can’t fit them with the baryons implied by BBN regardless of what form they take. That’s admitted by most people, e.g. Sanders’ paper.

More interesting is the question of whether you could get around the need for non-baryonic DM with some other theory of modified gravity. The Bullet Cluster and CMB, again to most people, imply not. Could you wriggle out of that conclusion by combining some new as-yet-unformulated modification of gravity with a huge population of mysterious intergalactic Jupiters? No, because you would still be completely wrong on the CMB. It’s time to accept what the data are telling us and move on.

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Stacy, March 3:

MOND without non-baryonic DM is falsified by clusters, because you can’t fit them with the baryons implied by BBN regardless of what form they take. That’s admitted by most people, e.g. Sanders’ paper.

Ah. I thought this was the conceptual error you were making. Clusters you certainly could fit just with baryons. They’re rare systems. If that is the only place we need dark baryons, then do the integrals. You can satisfy the residual mass discrepancy in clusters in MOND without making much dent in the BBN missing baryon budget.

Do I *like* such a solution? Certainly not. Neither do I like that fact that clusters are the only systems that come close to having the right baryon content in LCDM. Whay are galaxies missing more than half of their baryons? Dwarfs > 90%? I can imagine how this might happen, but the solutions are comparably contrived. The more basic point is that I am not willing to condemn a theory for needing some dark baryons if its competitor also needs dark baryons.

More interesting is the question of whether you could get around the need for non-baryonic DM with some other theory of modified gravity. The Bullet Cluster and CMB, again to most people, imply not. Could you wriggle out of that conclusion by combining some new as-yet-unformulated modification of gravity with a huge population of mysterious intergalactic Jupiters? No, because you would still be completely wrong on the CMB. It’s time to accept what the data are telling us and move on.

The CMB is really interesting. I correctly predicted the amplitude of the second peak (a prediction that is still quantitatively correct) by making the ansatz that there was whatever generally covariant theory might grow out of MOND looked just like GR in the early universe. Obviously that has to change later in order to grow structure, but at least it gives some proxy for what MOND might do with the CMB. At the time, I discussed some of the ways in which this would inevitably fail.

The response initially was that MOND itself made no prediction for the CMB, therefore we should disregard the chance success of this prediction. Now you want to treat the low third peak as an absolute prediction of MOND. You can’t have it both ways. Which is it?

A low third peak would have falsified LCDM. It survives that test. That does not automatically falisify MOND. It just means that the relativistic parent theory (whatever that might be – it is not obvious to me it has to be TeVeS) has to have a net forcing term a la CDM. Does that seem reasonable to me? No, and (as I said with the ultrafaint dwarfs) I too was ready to write off MOND on this point. But Skordis & Ferreira showed that the scalar field in TeVeS might have just such an effect. So I can not, in good conscience, say it is impossible.

You should not accuse me of ignoring data. I have written papers on these subjects. Indeed, one of the things that surprised and impressed me about MOND, when I first got over my initial revulsion and started to look into it, was what a great breadth and wealth of data it did quite in explaining. From the tone of your statements, I imagine you have no idea what I’m talking about. You really ought to check your facts before making ignorant statements to the effect that “MOND only does rotation curves.”

Indeed, you yourself appear to be ignoring facts. Why do any MOND predictions come true? Let’s suppose it is only true that all MOND does is fit rotation curves. That demands an explanation – one you nowhere attempt to provide. Your reasoning appears to boil down to “We’re sure that CDM exists, so somehow it must work out.” Well, I’ve tried – very hard – to see how it could work out. It aint easy. I won’t say it is impossible. But it is as absurd as some of the above dodges are with MOND. Dark matter in galaxies is like epicycles – you can fit anything you like, but it doesn’t explain why a simple formula does better.

You may find it hard to believe, but I started from exactly the same perspective as you. I am far more comfortable with CDM than with MOND. I will breathe a great sigh of relief if and when WIMPs are detected in the laboratory. Then we’ll know the answer, and we won’t have to have these bitter debates. However, I am not being unreasonable in holding the theory to a high standard of proof. If you want to convince me that, for sure, the universe is filled with some till-now hypothetical particle from a hypothetical dark sector outside of the Standard Model of particle physics, then show me a piece. Until then, you are over-reaching.

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Sean, March 3:

You can’t just wave your hands and say that a mysterious “forcing term” will help explain the CMB. If there is no non-baryonic dark matter, there is no way that even-numbered peaks can be different from odd-numbered peaks; the configuration of baryons is precisely analogous. You can mimic the situation in TeVeS (although the numbers don’t seem to work out) because you’ve introduced an independently propagating scalar degree of freedom whose energy density doesn’t follow the baryons. You can give that scalar whatever name you like, but it is “non-baryonic dark matter.” A particularly contrived version, but that’s what it is.

You can’t explain the third peak without a source for gravity that propagates independently of the baryons.

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Rainer, March 3:

MOND without non-baryonic DM is falsified by clusters, because you can’t fit them with the baryons implied by BBN regardless of what form they take.

Why is that? I just don’t get it, and am very open to be persuaded. 90% of all cosmic baryons are presently undetected, right? Only a fraction of the baryonic matter we see directly is in clusters (O(a few percent), let’s say 10%) So why can’t a small fraction, say O(2%), of all the cosmic dark baryons be in the form of e.g. jupiters in the central parts of clusters? They and stars would then dominate the cluster mass and be dissipationless —> no problem with the bullet cluster in MOND.

That’s admitted by most people, e.g. Sanders’ paper.

Where? In http://arxiv.org/abs/astro-ph/0703590 he states about cluster dark matter in MOND: “For example, there are more than enough undetected baryons to make up the missing dark component; they need only be present in some non-dissipative form which is difficult to observe.”

He also likes massive neutrinos, but not to the exclusion of baryonic dark matter.

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Stacy, March 4:

Hi Sean,

OK, now we are discussing science again.

I take your point about the CMB very seriously. It seems to me that you are putting a lot of weight on the third peak, which is not all THAT well constrained. WMAP really has to scrape to get there, so the result is dominated by the systematics of PSF modeling. I presume they’ve done that right, but there are double exponential corrections involved in subtracting the foreground and then getting back to the cosmic signal, so they don’t have to go far wrong to make a bad mistake with the third peak. Presumably PLANCK will clarify this soon, though a glance at their first release images does not provide a lot of confidence about the foreground MW masks that WMAP used. I also wonder, given the visceral reaction you and others have at any suggestion that LCDM might be questionsed, if the PLANCK team would let themselves admit a low third peak even if the saw it.

For now, we have an apparently clear detection of a high third peak in WMAP, and we need to explain the data we have rather than the data we hope soon to have. And honestly, I expect the most likely outcome to be a confirmation of WMAP, with only minor tweaks. So we have to understand the third peak along with clusters and rotation curves and dwarf spheroidals and everything else.

I freely admit that I don’t know how to make the third peak high. I also don’t know that a high-ish thrid peak can’t be obtained in a more general theory. I agree with your point that pure baryons shouldn’t do that – the vector is wrong, as you say. I’m not even convinced TeVeS can do it. But lots of theories (not just MOND-inspired ones) invoke scalar fields, so I can’t exclude the possibility.

I also agree that this is contrived. But we are WAY into contrivance with LCDM, a point I believe you’ve made yourself on occassion. We’ve just gotten familiar with the contrived parts so that they no longer bother us. That doesn’t make them any less contrived.

You make the point that the scalar field solution in TeVeS is just a contrived form of non-baryonic dark matter. But even in pure GR we could use some form of non-baryonic dark matter that gives us the MOND phenomenology. Why not consider an effect due to the physical nature of the particles? Until we detect WIMPs, surely you at least agree that we don’t really know what the dark matter is?

I know everybody invokes feedback to “fix” galaxies, but those models are just as contrived. Actually, they are considerably more contrived, as they inevitably require many more parameters, and those parameters are simply tuned to match observations. Any competent theorist can tune any model to fit a given set of data.

I must have said this to you before, but I will say it again. The MOND formula provides an apparently correct description of the effective force law in galaxies. How does the dark matter “know” to arrange itself just so as to look like MOND? If it manages this trick in galaxies, why not in the solar system? How would we know that the solar system isn’t really run by an inverse-cube force law, but there is dark matter arranged just so as to make it look like an inverse-square law?

Could anything be more contrived?

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Sean, March 6:

Hi Stacy–

I’m not sure what you are saying about the third peak in the CMB. We agree that “pure baryons shouldn’t do that.” I can only think of three possibilities.

(1) There is some sort of source for gravity other than baryons.
(2) There is a modification of gravity that doesn’t include new sources, but also doesn’t respond directly to where the sources actually are.
(3) The data aren’t good enough to say that the odd-numbered peaks are boosted relative to what we would expect from damped oscillations of baryons alone.

If it’s (1), then that’s non-baryonic dark matter and we should just admit it. I think that (2) is physically implausible, and as far as I know nobody has suggested otherwise. And I think that the time is past when anyone could credibly hang on to (3). Here’s a relatively recent figure (2 years ago) from Ned Wright’s web site.

Am I missing a possibility, or would you buy one of these three?

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Stacy, March 7:

Hi Sean,

I basically agree with the 3 possibilities you list. Indeed, I thought that was pretty much what I said.

You imply that it is hanging on to vain hope to explain the third peak of the CMB by anything other than a new source. I am saying that it is a vain hope to imagine that turning the crank on any number of CDM numerical simulations is ever going to spit out the observed MONDian phenomenology. Just because LCDM works for the CMB does not automatically guarantee that it’ll work in galaxies, any more than MOND’s success in galaxies means it must inevitably succeed as a the basis of a cosmological theory.

There is a very simple empirical result in the data for galaxies that cosmologists have, by and large, simply ignored. The stated excuse is usually something like “well, galaxies are complicated, non-linear structures” and so we should be excused from explaining them. Indeed, in LCDM galaxies probably should be complicated. But they’re not. They’re simple. So simple, the obey a single effective force law. Fitting that with dark matter is like fitting epicylces to planetary orbits. Of course you can do it – you have an infinite number of free parameters. But it don’t make no sense.

I have said for years now that they conclusion you come to depends on how you weigh the evidence. The CMB is an important piece of that evidence. So are rotation curves. It is not obvious to me that the third peak should count 100% and galaxies zero. Yet that is in effect the weighting that lots of people appear to be using.

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Sean, March 8:

Hi Stacy–

I think we’ve reached the end of what needs to be said. You agree with my three possibilities, and you agree (I think) that the CMB data are good enough to draw some conclusions. It comes down to whether you are willing to entertain the possibility that there is a mysterious new force that does not involve any new sources, yet also does not respond directly to where the actual sources are. (And in the process reproduces exactly what we would see if there were CDM.) You may think that is plausible — I, and most people in the field, do not. Therefore, we believe that there is non-baryonic DM, and the question is how it behaves.

You seem to think I am defending LCDM, when I have never mentioned it. I am defending the claim that “non-baryonic dark matter exists.” As I said in the original post, we certainly have to explain the phenomenology of galaxies and clusters, and the right explanation may very well involve a modification of gravity or interesting new physics in the dark sector — both of which I’ve written papers about. Nobody is suggesting that we ignore data from galaxies and clusters. But none of that data straightforwardly implies “non-baryonic dark matter does not exist.” It’s a complicated dynamical problem. The CMB — an enormously simpler system, where everything is in the linear regime — does straightforwardly imply “non-baryonic dark matter exists.” Admitting that will improve our chances for future progress.

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Stacy, March 8:

Yes, we’ve said what we’re going to say. But you still don’t seem to get it. The CMB is simple. It is not enormously simpler. Galaxies are also simple. One must invoke absurdly complex mechanisms to make that happen. The argument against dark matter doing this boils down to fine tuning. I don’t like fine tuning problems, especially when a theory is not otherwise falsifiable (e.g., epicycles). Note that as you claim not to be specifically defending LCDM, I am not specifically defending MOND. There is an empirical phenomenology that constitutes a fine tuning problem for ANY dark matter picture (that does not some how build it in).

Since we can’t explicitly falsify the existence of dark matter, what could be worse than this mother of all fine-tuning problems? I understand the implausibility of what you are saying in the CMB, but you seem to miss the same kind of point in galaxies. I worry that we won’t find WIMPs and keep pursuing other DM candidates indefinitely – how do we know when to stop? How would this be different from another millenium of dark epicycles?

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Rainer, March 18:

Dear disputants,

Thanks for this really informative and nearly polemic free (Stacy please stop blaming your colleagues to construct epicycles ) debate!

To me (and it seems also to Stacy) Sean’s concentration on his main argument, makes his case for some kind of “dark non-baryonic field that enters the stress-energy tensor in GR” quite convincing. It then stands to reason (but is not absolutely necessary) to identify it with a quantum field for some new massive particle.

If I may make Stacy’s main point in my own words: galaxies are observed to be simpler than they would be expected to be: at least a large fraction of them obeys a strange simple MOND rule, which is without a simple plausible motivation in known physics. In addition there are indications that galaxies sometimes behave in ways that they should not in LCDM (tidal dwarves should not contain dark matter but they seem to do).

This reminds one of atoms in classical physics, which were expected to show a very complex behaviour but obeyed strange simple rules, sometimes in contradiction to the known physical laws at the time. The old quantum condition comes to mind as somewhat analogous to MOND’s law of motion. Initially it was attempted to explain these rules within the known concepts, and that was all right and necessary.

But, as quantum mechanics showed, there is _also_ the possibility that strange simple rules for basic objects of the theory are first clues for really new concepts.

Sean, don’t you have at least a little bit of sympathy for this possibility?

I close with following proposal: CDM or MOND? is not a good question. A better question is: are the successes of the MOND rule _perhaps_ a first clue to new concepts which will modify our understanding of the “dark non-baryonic field that enters the stress-energy tensor in GR” in the sense that it is not only a new quantum field within standard QFT?

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Sean, March 18:

Hi Rainer–

Sure, I’m happy to agree with that. In fact, you will find exactly those sentiments way back in my original blog post on the topic. I just think we’re past the point where we can conclude that non-baryonic dark matter exists — what form it takes, how it interacts, and what additional things might be going on, are all crucially important questions. Of course DM faces important challenges from the phenomenology of complex structures, and that should be taken seriously; but no-DM alternatives are ruled out by the data, which should also be taken seriously.

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Stacy, March 19:

Science is dead.

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Which is why I devoted my opening statement at “The Great Debate” a few weeks ago to presenting the positive case for naturalism, rather than just arguing against the idea of God. And I tried to do so in terms that would be comprehensible to people who disagreed with me — at least that was the goal, you can judge for yourself whether I actually succeeded.

So here I’ve excerpted that opening ten-minute statement from the two-hour debate I had with Michael Shermer, Dinesh D’Souza, and Ian Hutchinson. I figure there must be people out there who might possibly be willing to watch a ten-minute video (or watch for one minute before changing the channel) but who wouldn’t even press “play” on the full version. This is the best I can do in ten minutes to sum up the progress in human understanding that has led us to reject the supernatural and accept that the natural world is all there is. And I did manage to work in Princess Elisabeth of Bohemia.

I am curious as to how the pitch goes over (given the constraints of time and the medium), so constructive criticism is appreciated.

In case you can’t get enough, Clark Gregg has collected all his favorite Agent Coulson moments. (Just ask the professional screenwriters: “I’m sure avengers is great, but the only marvel movie i’d truly kill or die to see is “AGENT COULSON – THE MOTION PICTURE.”)

As you remember, I did a bit of consulting on Thor, and my Caltech colleague Mark Wise helped out with Iron Man II. (Let’s just say Tony Stark’s basement particle accelerator could have looked even a lot less realistic.) I was asked to consult on The Avengers, but the production was so frantic that I don’t think I had a noticeable impact — basically I read the script and emailed some suggestions, but I don’t think any of them affected the final product. I did, however, manage not to give away any spoilers, despite impassioned pleas from people who heard I had read the thing.

Kevin Feige, president of Marvel Studios, has always liked to bring scientists in on the planning for their movies, in part precisely because of event films like The Avengers. It’s one thing to make a bunch of superhero films, but another to take seriously the idea of a shared universe. There have to be some laws of nature, even if they’re not the one’s we are used to, and you can’t just reboot them from movie to movie. (Just wait for my favorite upcoming project, Doctor Strange: Master of the Mystic Arts.) You have a guy in a flying metal suit teaming up with a Norse demigod, and that has to work, or at least seem to. Thus, the conceit that the Asgardians from Thor are really technologically-advanced aliens that seemed godlike to our ancestors.

These aren’t movies about science, by any stretch. But they are stories, and stories need to make sense and follow rules, otherwise there is no drama. Science is just the search for the underlying architecture of reality, whatever kind of reality we may be talking about. io9 agrees.

Penn’s School of Arts and Sciences has been posting about our involvement on its facebook page, where you can see my colleague Gary Bernstein delivering a lecture on planets at Astronomy Night

and attendees observing planets in Perelman Quadrangle.

A week or so ago, I spent a couple of days back at Syracuse University, where I was a faculty member for quite a few years. I was there primarily to participate in a special event that preceded the East Coast Gravity Meeting being held there on the following weekend. The event was a celebration – GoldbergFest – of the career of Josh Goldberg, a good personal friend, and an eminent relativist at Syracuse, who has been an emeritus professor there for many years now.

Josh began as a graduate student at Syracuse in the early 1950′s, working on conservation laws in General Relativity (GR) and on canonical quantization. At the time Syracuse had one of the few well-known relativity groups in the world, led by Peter Bergmann, and an impressive group of young people were trained under him, and later under Josh, as students and postdocs; people like Ted Newman, Ray Sachs, Art Komar, Roger Penrose, and many others. I’m certainly no expert on the precise history of the Syracuse group, but fortunately, as part of a special issue of General Relativity and Gravitation dedicated to Josh, to which I was honored to also contribute, Ted Newman describes it wonderfully. The Fest was a lovely event. I enjoyed the other speakers’ talks – John Stachel, Rafael Sorkin and Peter Saulson, and Ted Newman’s hilarious and touching after dinner speech, and the reminiscences of the other people at the dinner made for what I hope Josh thought was a wonderful day.

Over the next two days quite a few of our students and postdocs from Penn gave talks at the East Coast Gravity Meeting, and I was delighted to hear that our very own Godfrey Miller won the award for the best student presentation.

Returning To Penn, I just about had enough time to finish putting together the take-home final exam for my graduate General Relativity course, before heading off to NYU on Wednesday with our whole group for our semesterly joint meeting. We were joined, as usual, by a nice crowd from Columbia and Case Western for a day of talks and discussion. I always find these meetings to be incredibly useful scientifically, because the group is so interactive, boisterous and interested in the material, while being such warm and friendly hosts. It makes for an enjoyable day every time. Beyond the obvious exchange of ideas, these meetings also provide an opportunity for our students to get used to giving talks on their work. This time my student – Garrett Goon – and one of my colleague Justin Khoury’s students – Austin Joyce – gave our student talks, leading to some healthy discussion Wess-Zumino terms in new field theories and conformal cosmology, respectively. Both did a terrific job, although they’re becoming old pros at this point, rather than beginning students in need of practice.

To close out last week, Greg Gabadadze from NYU came down on Friday so that we could try to finish up some details in a project that is close to completion, before we start dispersing for various summer conferences. I’ll discuss these soon, I expect.

Today my final exam will be turned in and grading starts, an old friend is delivering a seminar in our group, and Sean’s student Kim Boddy arrives for a week so that the three of us can try to finish up a paper. The end of the semester always seems to go this way. While all these things are fun, life becomes excessively hectic for two weeks, and then travel begins.

First Lawrence Krauss came out with a new book, A Universe From Nothing: Why There Is Something Rather Than Nothing (based in part on a popular YouTube lecture), which addresses this question from the point of view of a modern cosmologist. Then David Albert, speaking as a modern philosopher of science, came out with quite a negative review of the book in the New York Times. And discussion has gone back and forth since then: here’s Jerry Coyne (mostly siding with Albert), the Rutgers Philosophy of Cosmology blog (with interesting voices in the comments), a long interview with Krauss in the Atlantic, comments by Massimo Pigliucci, and another response by Krauss on the Scientific American site.

I’ve been meaning to chime in, for personal as well as scientific reasons. I do work on the origin of the universe, after all, and both Lawrence and David are friends of the blog (and of me): Lawrence was our first guest-blogger, and David and I did Bloggingheads dialogues here and here.

Executive summary

This is going to be kind of long, so here’s the upshot. Very roughly, there are two different kinds of questions lurking around the issue of “Why is there something rather than nothing?” One question is, within some framework of physical laws that is flexible enough to allow for the possible existence of either “stuff” or “no stuff” (where “stuff” might include space and time itself), why does the actual manifestation of reality seem to feature all this stuff? The other is, why do we have this particular framework of physical law, or even something called “physical law” at all? Lawrence (again, roughly) addresses the first question, and David cares about the second, and both sides expend a lot of energy insisting that their question is the “right” one rather than just admitting they are different questions. Nothing about modern physics explains why we have these laws rather than some totally different laws, although physicists sometimes talk that way — a mistake they might be able to avoid if they took philosophers more seriously. Then the discussion quickly degrades into name-calling and point-missing, which is unfortunate because these are smart people who agree about 95% of the interesting issues, and the chance for productive engagement diminishes considerably with each installment.

How the universe works

Let’s talk about the actual way physics works, as we understand it. Ever since Newton, the paradigm for fundamental physics has been the same, and includes three pieces. First, there is the “space of states”: basically, a list of all the possible configurations the universe could conceivably be in. Second, there is some particular state representing the universe at some time, typically taken to be the present. Third, there is some rule for saying how the universe evolves with time. You give me the universe now, the laws of physics say what it will become in the future. This way of thinking is just as true for quantum mechanics or general relativity or quantum field theory as it was for Newtonian mechanics or Maxwell’s electrodynamics.

Quantum mechanics, in particular, is a specific yet very versatile implementation of this scheme. (And quantum field theory is just a particular example of quantum mechanics, not an entirely new way of thinking.) The states are “wave functions,” and the collection of every possible wave function for some given system is “Hilbert space.” The nice thing about Hilbert space is that it’s a very restrictive set of possibilities (because it’s a vector space, for you experts); once you tell me how big it is (how many dimensions), you’ve specified your Hilbert space completely. This is in stark contrast with classical mechanics, where the space of states can get extraordinarily complicated. And then there is a little machine — “the Hamiltonian” — that tells you how to evolve from one state to another as time passes. Again, there aren’t really that many kinds of Hamiltonians you can have; once you write down a certain list of numbers (the energy eigenvalues, for you pesky experts) you are completely done.

We should be open-minded about what form the ultimate laws of physics will take, but almost all modern attempts to get at them take quantum mechanics for granted. That’s true for string theory and other approaches to quantum gravity — they might take very different views of what constitutes “spacetime” or “matter,” but very rarely do they muck about with the essentials of quantum mechanics. It’s certainly the case for all of the scenarios Lawrence considers in his book. Within this framework, specifying “the laws of physics” is just a matter of picking a Hilbert space (which is just a matter of specifying how big it is) and picking a Hamiltonian. One of the great things about quantum mechanics is how extremely restrictive it is; we don’t have a lot of room for creativity in choosing what kinds of laws of physics might exist. It seems like there’s a lot of creativity, because Hilbert space can be extremely big and the underlying simplicity of the Hamiltonian can be obscured by our (as subsets of the universe) complicated interactions with the rest of the world, but it’s always the same basic recipe.

So within that framework, what does it mean to talk about “a universe from nothing”? We still have to distinguish between two possibilities, but at least this two-element list exhausts all of them.

Possibility one: time is fundamental

The first possibility is that the quantum state of the universe really does evolve in time — i.e. that the Hamiltonian is not zero, it truly does push the state forward in time. This seems like the generic case (there are more ways to be not-zero than to be zero), and it’s certainly the one that we spend time considering in introductory courses when we foist quantum mechanics on fearful undergraduates for the first time. A wonderful and under-appreciated consequence of quantum mechanics is that, if this possibility is right (the universe truly evolves), time cannot truly begin or end — it goes on forever. Very unlike classical mechanics, where the universe’s trajectory through the space of states can bring it smack up against a singularity, at which point time presumably ceases. In QM, every state is just as good as every other state, and the evolution will go happily marching along.

So what does this have to do with something vs. nothing? Well, as the quantum state of the universe evolves, it can pass through phases where it looks an awful lot like “nothing,” conventionally understood — i.e. it could look like completely empty space, or like some peculiar non-geometric phase where we wouldn’t recognize it as “space” at all. And later, through the relentless influence of the Hamiltonian, it could evolve into something that looks very much like “something,” even very much like the universe we see around us today. So if your definition of “nothing” is “emptiness” or “lack of space itself,” the laws of quantum mechanics provide a nice way to understand how that nothing can evolve into the marvelous something we find ourselves inside. This is interesting, and important, and worth writing a book about, and it’s one of the possibilities Lawrence discusses.

Possibility two: time is emergent/approximate

The other possibility is that the universe doesn’t evolve at all — the Hamiltonian is zero, and there is some space of possible states, but we just sit there, without a fundamental “passage of time.” Now, you might suspect that this is a logical possibility but not a plausible one; after all, don’t we see things change around us all the time? But in fact this possibility is the one you immediately bump into if you simply take classical general relativity and try to “quantize” it (i.e., invent the quantum theory that would reduce to GR in the classical limit). We don’t know that this is the right thing to do — Tom Banks, for example, would argue that it’s not — but it’s a possibility that is on the table, so we should think about what it would mean if it turns out to be true.

We certainly think that we perceive time passing, but maybe time is just emergent rather than fundamental. (I don’t like using “illusory” in this context, but others are not so circumspect.) That is, perhaps there is an alternative description of that single, unmoving point in Hilbert space — a description that looks approximately like “a universe evolving through time,” at least for some period of duration. Think of a block of metal sitting on a hot surface, not evolving with time but with a temperature gradient from top to bottom. It might be possible to conceptually divide the block into slices of equal temperature, and then write down an equation for how the state of the block changes from slice to slice, and find that the resulting mathematical formalism looks just like “evolution through time.” In this case, unlike the previous one, time could end (or begin), because time was only a useful approximation to begin with, valid in a certain regime.

This kind of scenario is exactly what quantum cosmologists like James Hartle, Stephen Hawking, Alex Vilenkin, Andrei Linde and others have in mind when they are talking about the “creation of the universe from nothing.” In this kind of picture, there is literally a moment in the history of the universe prior to which there weren’t any other moments. There is a boundary of time (presumably at the Big Bang), prior to which there was … nothing. No stuff, not even a quantum wave function; there was no prior thing, because there is no sensible notion of “prior.” This is also interesting, and important, and worth writing a book about, and it’s another one of the possibilities Lawrence discusses.

Why is there a universe at all?

So modern physics has given us these two ideas, both of which are interesting, and both of which resonate with our informal notion of “coming into existence out of nothing” — one of which is time evolution from empty space (or not-even-space) into a universe bursting with stuff, and the other of which posits time as an approximate notion that comes to an end at some boundary in an abstract space of possibilities.

What, then, do we have to complain about? Well, a bit of contemplation should reveal that this kind of reasoning might, if we grant you a certain definition of “nothing,” explain how the universe could arise from nothing. But it doesn’t, and doesn’t even really try to, explain why there is something rather than nothing — why this particular evolution of the wave function, or why even the apparatus of “wave functions” and “Hamiltonians” is the right way to think about the universe at all. And maybe you don’t care about those questions, and nobody would question your right not to care; but if the subtitle of your book is “Why There Is Something Rather Than Nothing,” you pretty much forfeit the right to claim you don’t care.

Do advances in modern physics and cosmology help us address these underlying questions, of why there is something called the universe at all, and why there are things called “the laws of physics,” and why those laws seem to take the form of quantum mechanics, and why some particular wave function and Hamiltonian? In a word: no. I don’t see how they could.

Sometimes physicists pretend that they are addressing these questions, which is too bad, because they are just being lazy and not thinking carefully about the problem. You might hear, for example, claims to the effect that our laws of physics could turn out to be the only conceivable laws, or the simplest possible laws. But that seems manifestly false. Just within the framework of quantum mechanics, there are an infinite number of possible Hilbert spaces, and an infinite number of possibile Hamiltonians, each of which defines a perfectly legitimate set of physical laws. And only one of them can be right, so it’s absurd to claim that our laws might be the only possible ones.

Invocations of “simplicity” are likewise of no help here. The universe could be just a single point, not evolving in time. Or it could be a single oscillator, rocking back and forth in perpetuity. Those would be very simple. There might turn out to be some definition of “simplicity” under which our laws are the simplest, but there will always be others in which they are not. And in any case, we would then have the question of why the laws are supposed to be simple? Likewise, appeals of the form “maybe all possible laws are real somewhere” fail to address the question. Why are all possible laws real?

And sometimes, on the other hand, modern cosmologists talk about different laws of physics in the context of a multiverse, and suggest that we see one set of laws rather than some other set for fundamentally anthropic reasons. But again, that’s just being sloppy. We’re talking here about the low-energy manifestation of the underlying laws, but those underlying laws are exactly the same everywhere throughout the multiverse. We are still left with the question of there are those deep-down laws that create a multiverse in the first place.

The end of explanations

All of these are interesting questions to ask, and none of them is addressed by modern physics or cosmology. Or at least, they are interesting questions to “raise,” but my own view is that the best answer is to promptly un-ask them. (Note that by now we’ve reached a purely philosophical issue, not a scientific one.)

“Why” questions don’t exist in a vacuum; they only make sense within some explanatory context. If we ask “why did the chicken cross the road?”, we understand that there are things called roads with certain properties, and things called chickens with various goals and motivations, and things that might be on the other side of the road, or other beneficial aspects of crossing it. It’s only within that context that a sensible answer to a “why” question can be offered. But the universe, and the laws of physics, aren’t embedded in some bigger context. They are the biggest context that there is, as far as we know. It’s okay to admit that a chain of explanations might end somewhere, and that somewhere might be with the universe and the laws it obeys, and the only further explanation might be “that’s just the way it is.”

Or not, of course. We should be good empiricists and be open to the possibility that what we think of as the universe really does exist within some larger context. But then we could presumably re-define that as the universe, and be stuck with the same questions. As long as you admit that there is more than one conceivable way for the universe to be (and I don’t see how one could not), there will always be some end of the line for explanations. I could be wrong about that, but an insistence that “the universe must explain itself” or some such thing seems like a completely unsupportable a priori assumption. (Not that anyone in this particular brouhaha seems to be taking such a stance.)

Sounds and furies

That’s all I have to say about the (fun, interesting) substantive questions, but I am not strong enough to resist a couple of remarks on the (tedious but strangely irresistible) procedural questions.

First, I think that Lawrence’s book makes a lot more sense when viewed as part of the ongoing atheism vs. theism popular debate, rather than as a careful philosophical investigation into a longstanding problem. Note that the afterword was written by Richard Dawkins, and Lawrence had originally asked Christopher Hitchens, before he became too ill — both of whom, while very smart people, are neither cosmologists nor philosophers. If your real goal is to refute claims that a Creator is a necessary (or even useful) part of a complete cosmological scheme, then the above points about “creation from nothing” are really quite on point. And that point is that the physical universe can perfectly well be self-contained; it doesn’t need anything or anyone from outside to get it started, even if it had a “beginning.” That doesn’t come close to addressing Leibniz’s classic question, but there’s little doubt that it’s a remarkable feature of modern physics with interesting implications for fundamental cosmology.

Second, after David’s review came out, Lawrence took the regrettable tack of lashing out at “moronic philosophers” and the discipline as a whole, rather than taking the high road and sticking to a substantive discussion of the issues. In the Atlantic interview especially, he takes numerous potshots that are just kind of silly. Like most scientists, Lawrence doesn’t get a lot out of the philosophy of science. That’s okay; the point of philosophy is not to be “useful” to science, any more than the point of mycology is to be “useful” to fungi. Philosophers of science aren’t trying to do science, they are trying to understand how science works, and how it should work, and to tease out the logic and standards underlying scientific argumentation, and to situate scientific knowledge within a broader epistemological context, and a bunch of other things that can be perfectly interesting without pretending to be science itself. And if you’re not interested, that’s fine. But trying to undermine the legitimacy of the field through a series of wisecracks is kind of lame, and ultimately anti-intellectual — it represents exactly the kind of unwillingness to engage respectfully with careful scholarship in another discipline that we so rightly deplore when people feel that way about science. It’s a shame when smart people who agree about most important things can’t disagree about some other things without throwing around insults. We should strive to be better than that.

Sorry for the tiny writing, there are a lot of particles! Click to embiggen and get a legible version.

This will be a somewhat different book than From Eternity to Here. While both are aimed at a general audience, FETH was a rather lengthy tome that made a careful argument in a hopefully novel way. Anyone could read it, but to get the most out of it you have to really sit and think about certain ideas. Particle, on the other hand, aims to be a fun and narratively gripping page-turner — a book that makes you eager to move quickly to the next chapter, rather than taking a few minutes to let the last one sink into your head. A bodice-ripper, if you will. It will be full of stories and fun anecdotes about the human beings who made the LHC happen and have devoted their lives to searching for the Higgs and particles beyond the Standard Model. A book you would be happy to give to your Grandmom in order to convey some of the excitement of modern physics. (Unless your Grandmom is a particle physicist, in which case she might think it’s at too low a level.)

At the same time, of course, I’m going to try to illuminate the central ideas of the Standard Model in as clear a fashion as I can manage. It won’t just be a list of particles; I’ll cover field theory, gauge bosons, and spontaneous symmetry breaking. All in fine bodice-ripping style. (Maybe get Fabio for the cover?)

If you are a particle physicist yourself, I’m happy to take input. This could take the form of a favorite analogy you like to use to explain some subtle concept, or some physics idea or piece of history you think really doesn’t get the attention it deserves in the popular media. Even better if you have some personal involvement in a fun story — you lost your virginity in the LHC tunnel, or you discovered asymptotic freedom but didn’t get around to publishing it. I’m talking to as many physicists as I can, but I can’t talk to everyone. I’m looking for tales that will make the human side of physics come alive.

Also happy to take input if you’re not a particle physicist! What are the concepts that we don’t do a good job explaining? What are the buzzwords you’ve heard about the don’t make sense? The questions you really want answered?

I sincerely believe the search for the Higgs and whatever might lie beyond is a Big Deal in the history of science, and I hope to convey some of the importance and excitement of this question to as large an audience as possible. I’ll be flitting around the country giving talks when the book comes out, so let me know if you have a big lecture hall full of eager minds that want to hear the latest dispatches from the particle trenches. Should be a fun ride.

But one small complaint is I’m not sure if he’s quite exactly worked out his audience. Early in the book, I was starting to fear it would be a rehash of stuff I already knew. It’s not. But there were some elementary rehashes that, frankly, I think if someone went into the book not having that knowledge already, they aren’t going to be able to grok the rest. This is not a mathematically demanding book, but it is a conceptually demanding book, and I am not sure if someone who doesn’t have some limited grounding in the mathematics side will be able to make it through the conceptual side without missing a lot.

The diagnosis is completely accurate. On the one hand, I do spend time going over the basics of relativity, quantum mechanics, and logarithms, in ways that hopefully make these ideas accessible to people who haven’t ever tried to understand them before. On the other hand, the meaty middle section of the book is conceptually very challenging for almost everybody, even if you are a regular consumer of popular physics books. We are simply not used to thinking in ways that don’t presume the arrow of time from the start, and some of the issues that arise are highly non-intuitive. I tried to keep things fun and engaging, but there’s no question that certain pages of the book require careful thinking and brain work.

What to do? I’m not sure that, given the material I wanted to cover in this book, there is much else one could do. Probably I could have had less about the basics of relativity, and moved what there is until later in the book. But although the central ideas are conceptually very challenging, I don’t think they’re actually inaccessible to anyone who is willing to put some thought into them, regardless of mathematical background. So I don’t regret that I didn’t write a leaner and more challenging book aimed only at the aficionados, although I appreciate that something along those lines might have been more focused. I think that the aficionados just have to get used to reading introductions to GR and QM from a wide variety of different books — at least until those topics become part of the standard high-school curriculum.

The first bit of news, which has been the subject of the most internet buzz, is a new paper by Chilean astronomers C. Moni Bidin, G. Carraro, R. A. Mendez, and R. Smith, which claims that there’s no evidence for dark matter in the dynamics of stars near the Sun. If this were true, it would imply something funny going on with the distribution of nearby dark matter, which could have significant implications for direct searches here on Earth (see below). It wouldn’t really be much of a threat to the idea of dark matter itself, since there’s plenty of evidence for dark matter elsewhere. But it might mean that the distribution in the Milky Way was very different from the kinds of models we like to use, for example by being much lumpier.

We just heard a great physics colloquium here at Caltech by Katie Freese, who talked about this result very briefly. Her opinion matched those of the skeptics in Ron Cowen’s article linked above: this paper makes a lot of assumptions, some of the a bit dubious, and we would need to see something much more solid before we become convinced. The biggest issue is that they don’t actually measure the DM distribution near the Sun; they try to measure it in a region between 1500 and 4000 parsecs below the galactic plane (which is actually pretty far away), and then fit to a model and extrapolate to what we should have nearby. This kind of procedure relies on our understanding of the vertical structure of the galactic disk, which isn’t all that great. So it’s definitely an intriguing result, one that should be taken seriously and followed up by other surveys, but nothing to lose sleep over just yet.

The second bit of news is another puzzling absence: a lack of neutrinos that were predicted to be produced by gamma-ray bursts. These bursts are among the most energetic events in the post-Big-Bang universe, and for a long time were a major mystery to astrophysicists. More recently, a consensus had grown up that GRB’s (as they are called) are associated with intense beams of particles created by newly-born supernovae. That’s a model that seems to fit most of the data, anyway, and it also makes a pretty good prediction for the production of associated neutrinos. But a new paper by the marvelous IceCube experiment has thrown a spanner into the works: they should have been able to see those neutrinos, and they don’t.

IceCube consists of a series of thousands of detectors arrayed within a cubic kilometer of Antarctic ice, and looks for flashes of light associated with high-energy particles passing through. Recently they have been keeping an eye out for signs of neutrinos that should be associated with GRB’s that have been detected by the Swift and Fermi satellites — but no luck. It’s a puzzle that will send GRB theorists back to the drawing board. One of the funny aspects of the story is that particles from GRB’s are a leading candidate to serve as the origin of high-energy cosmic rays, but that seems to be out the window now. It’s still possible that the cosmic rays come from active galactic nuclei, but there’s another group of theorists who have something new to chew on.

The final bit of news is even dicier, and hasn’t received any internet buzz at all yet — I only heard about it through Katie Freese’s talk. Maybe because there was no press release and the shocking claim is hidden within the guts of a technical paper with a boring title. The paper is by our friend Juan Collar and Nicole Fields. Recall that the DAMA dark matter experiment looks for an annual modulation due to the fact that the Earth moves through the dark-matter “wind” at different velocities during different times of the year. And they see a signal — very strongly — but many people have questioned whether what they are seeing is really due to dark matter. Juan has been leading another experiment, CoGeNT, which has been trying to check DAMA’s results — and has found a very tentative signal that seems to agree with them (which wasn’t what most people were expecting).

One of the reasons for the skepticism is that there are other experiments, which aren’t tuned specifically to look for annual modulations, but nevertheless should be sensitive to dark matter at the level implied by DAMA and CoGeNT — and they see nothing. More recently, some of these experiments have started looking for annual modulations — and they see nothing. Here for example is a recent paper by the CDMS experiment that says exactly that.

But the new paper by Collar and Fields claims that CDMS have analyzed their own data incorrectly. They argue that (1) CDMS isn’t really sensitive to the kind of annual modulation purportedly seen by CoGeNT, and (2) if you look carefully there is actually a statistically significant (more than 5 sigma!) bump at low energies, consistent with the kind of low-mass dark matter particle you would need to explain the annual modulations.

My impression is that the CDMS folks are unmoved by this argument. It’s certainly always very hard to analyze the data from somebody else’s experiment. This kind of controversy comes down to very particular aspects of data collection, analysis, and sources of systematic error. It’s way over my head, so I have no professional opinion about who is right. But at the very least it’s a reminder (as if we needed one) that the dark-matter-detection game is heating up, and big news might be creeping up on us. The universe loves puzzles.

Which is why it was so crushing to listen to this interview he did with Marilynne Robinson, a leader among the movement to reconcile science and religion. I didn’t agree with much of what Robinson said, but then again I didn’t really expect to. Nor did I expect Stewart to challenge her in any way; a “why just can’t we all get along” perspective is very consistent with his way of thinking. But I admit I was hoping he would not misrepresent modern science as thoroughly and lazily as he managed to do here. (It’s a 2010 interview, brought to my attention by Scott Derrickson’s Twitter feed; apologies if these complaints were hashed out elsewhere two years ago.)

If you skip ahead to 2:50, here’s what Stewart has to say:

I’ve always been fascinated that, the more you delve into science, the more it appears to rely on faith. You know, when they start to speak about the universe they say, well, actually, most of the universe is antimatter. Oh, really, where’s that? Well, you can’t see it. [Robinson: "Yes, exactly."] Well, where is it? It’s there. Can you measure it? We’re working on it. And it’s a very similar argument to someone who would say God created everything. Well where is he? He’s there. And I’m always struck by the similarity of the arguments at their core.

Obviously he means something like “dark matter,” not “antimatter,” but that’s a minor mixup of jargon. Much worse is that he clearly has absolutely no idea why we believe in dark matter — what the actual evidence for it is in real data. He betrays no understanding that we know how much dark matter there is, have ongoing strategies for detecting it, and spend a lot of time coming up with alternatives and testing them against the data. What kind of misguided “faith” would lead people to believe in dark matter, of all things? (The underlying problem with appeals to faith is that they cannot explain why we should have faith in one set of beliefs rather than some other set … but that’s an argument for a different day.)

In reality, the more you delve into science, the less it appears to rely on faith. When it comes to modern biology there are large parts I accept because of the testimony of experts; but when it comes to physics I actually understand the evidence behind it. There are certainly some good philosophical issues about what assumptions science must make to get off the ground: does it presume naturalism, can it address miracles, does it admit nomological facts, are there a priori truths about the physical world, can it deal with unobservable things? But Stewart isn’t engaging any of these issues; he’s just taking lazy swipes at parts of science he doesn’t understand, which he therefore feels justified in equating with faith. If believers in God spent a tiny fraction of the time that modern cosmologists spend trying to invent alternatives to their favorite ideas and testing them against evidence … well let’s just say the world would be a very different place.

For which I blame us, at least as much as I blame him. Stewart is obviously a smart guy who likes science and is interested in it, and frequently has scientists on his show. And yet, we have clearly completely failed to communicate the reasons why we scientists believe in apparently spooky-sounding things like dark matter.

“Science communication” is a many-faceted thing, and all of its facets are important. We need to do better getting K-12 students excited by science and grounded in the basics. We need to do better educating college students about how the world works, since they’re going to be running it soon. We need to do better in helping policymakers understand the science behind their decisions. We need to do better at encouraging and enabling a lifelong interest in science among the general public. And we clearly need to do a much better job at clearly conveying the foundations of our practice to interested non-specialists. There’s a strong temptation to emphasize the weird and bizarre things that we discover, because after all the natural world is full of surprises. But if we don’t at the same time do a good job at explaining why we believe the bizarre things, it will come back and bite us eventually.

In tomorrow’s New York Times, I’ve got a long story about a growing sense among scientists that science itself is getting dysfunctional. For them, the clearest sign of this dysfunction is the growing rate of retractions of scientific papers, either due to errors or due to misconduct. But retractions represent just the most obvious symptom of deep institutional problems with how science is done these days–how projects get funded, how scientists find jobs, and how they keep labs up and running.

However… essentially all the examples are from biologically-oriented fields. I’ll confess that Carl asked me if there is a similar feeling among physicists, and after some thought I decide that there really isn’t. There are certainly fumbles (faster-than-light neutrinos, anyone?) and scandals (Jan Hendrik Schön being the most obvious), but I don’t have any feeling that the problem is growing in a noticeable way. Biology and physics are fundamentally different, especially because of the tremendous pressure within medical sciences when it comes to any results that might turn out to be medically useful. Cosmologists certainly don’t have to worry about that.

But maybe this is a distorted view from within my personal bubble? Happy to hear informed opinion to the contrary. The relevant kind of informed opinion would actually involve a comparison of the situation today with the situation at some previous time, not just a litany of things you think are dysfunctional about the present day.

But that’s not what I want to talk about right now. Rather, our conversations nudged me into investigating some work that I have long known about but never really looked into: David Deutsch’s argument that probability in quantum mechanics doesn’t arise as part of a separate ad hoc assumption, but can be justified using decision theory. (Which led me to this weekend’s provocative quote.) Deutsch’s work (and subsequent refinements by another former guest blogger, David Wallace) is known to everyone who thinks about the foundations of quantum mechanics, but for some reason I had never sat down and read his paper. Now I have, and I think the basic idea is simple enough to put in a blog post — at least, a blog post aimed at people who are already familiar with the basics of quantum mechanics. (I don’t have the energy in me for a true popularization at the moment.) I’m going to try to get to the essence of the argument rather than being completely careful, so please see the original paper for the details.

The origin of probability in QM is obviously a crucial issue, but becomes even more pressing for those of us who are swayed by the Everett or Many-Worlds Interpretation. The MWI holds that we have a Hilbert space, and a wave function, and a rule (Schrödinger’s equation) for how the wave function evolves with time, and that’s it. No extra assumptions about “measurements” are allowed. Your measuring device is a quantum object that is described by the wave function, as are you, and all you ever do is obey the Schrödinger equation. If MWI is to have some chance of being right, we must be able to derive the Born Rule — the statement that the probability of obtaining a certain result from a quantum measurement is the square of the amplitude — from the underlying dynamics, not just postulate it.

Deutsch doesn’t actually spend time talking about decoherence or specific interpretations of QM. He takes for granted that when we have some observable X with some eigenstates |x_i>, and we have a system described by a state

then a measurement of X is going to return either x₁ or x₂. But we don’t know which, and at this stage of the game we certainly don’t know that the probability of x₁ is |a|² or the probability of x₂ is |b|²; that’s what we’d like to prove.

In fact let’s just focus on a simple special case, where

If we can prove that in this case, the probability of either outcome is 50%, we’ve done the hard part of the work — showing how probabilistic conclusions can arise at all from non-probabilistic assumptions. Then there’s a bit of mathematical lifting one must do to generalize to other possible amplitudes, but that part is conceptually straightforward. Deutsch refers to this crucial step as deriving “tends to from does,” in a mischievous parallel with attempts to derive ought from is. (Except I think in this case one has a chance of succeeding.)

The technique used will be decision theory, which is a way of formalizing how we make rational choices. In decision theory we think of everything we do as a “game,” and playing a game results in a “value” or “payoff” or “utility” — what we expect to gain by playing the game. If we have the choice between two different (mutually exclusive) actions, we always choose the one with higher value; if the values are equal, we are indifferent. We are also indifferent if we are given the choice between playing two games with values V₁ and V₂ or a single game with value V₃ = V₁ + V₂; that is, games can be broken into sub-games, and the values just add. Note that these properties make “value” something more subtle than “money.” To a non-wealthy person, the value of two million dollars is not equal to twice the value of one million dollars. The first million is more valuable, because the second million has a smaller marginal value than the first — the lifestyle change that it brings about is much less. But in the world of abstract “value points” this is taken into consideration, and our value is strictly linear; the value of an individual dollar will therefore depend on how many dollars we already have.

There are various axioms assumed by decision theory, but for the purposes of this blog post I’ll treat them as largely intuitive. Let’s imagine that the game we’re playing takes the form of a quantum measurement, and we have a quantum operator X whose eigenvalues are equal to the value we obtain by measuring them. That is, the value of an eigenstate |x> of X is given by

The tricky thing we would like to prove amounts to the statement that the value of a superposition is given by the Born Rule probabilities. That is, for our one simple case of interest, we want to show that

After that it would just be a matter of grinding. If we can prove this result, maximizing our value in the game of quantum mechanics is precisely the same as maximizing our expected value in a probabilistic world governed by the Born Rule.

To get there we need two simple propositions that can be justified within the framework of decision theory. The first is:

Given a game with a certain set of possible payoffs, the value of playing a game with precisely minus that set of payoffs is minus the value of the original game.

Note that payoffs need not be positive! This principle explains what it’s like to play a two-person zero-sum game. Whatever one person wins, the other loses. In that case, the value of the game to the two participants are equal in magnitude and opposite in sign. In our quantum-mechanics language, we have:

Keep that in mind. Here’s the other principle we need:

If we take a game and increase every possible payoff by a fixed amount k, the value is equivalent to playing the original game, then receiving value k.

If I want to change the value of a playing a game by k, it doesn’t matter whether I simply add k to each possible outcome, or just let you play the game and then give you k. I don’t think we can argue with that. In our quantum notation we would have

Okay, if we buy that, from now on it’s simple algebra. Let’s consider the specific choice

and plug this into (3). We get

You can probably see where this is going (if you’ve managed to make it this far). Use our other rule (2) to make this

which simplifies straightaway to

which is our sought-after result (1).

Now, notice this result by itself doesn’t contain the word “probability.” It’s simply a fairly formal manipulation, taking advantage of the additivity of values in decision theory and the linearity of quantum mechanics. But Deutsch argues — and on this I think he’s correct — that this result implies we should act as if the Born Rule is true if we are rational decision-makers. We’ve shown that the value of a game described by an equal quantum superposition of states |x₁> and |x₂> is equal to the value of a game where we have a 50% chance of gaining value x₁ and a 50% chance of gaining x₂. (In other words, if we acted as if the Born Rule were not true, someone else could make money off us by challenging us to such games, and that would be bad.) As someone who is sympathetic to pragmatism, I think that “we should always act as if A is true” is the same as “A is true.” So the Born Rule emerges from the MWI plus some seemingly-innocent axioms of decision theory.

While I certainly haven’t followed the considerable literature that has grown up around this proposal over the years, I’ll confess that it smells basically right to me. If anyone knows of any strong objections to the idea, I’d love to hear them. But reading about it has added a teensy bit to my confidence that the MWI is on the right track.

The idea of cosmological inflation is our best developed idea of how the physics of the early universe might lead to the observed universe today. This idea has been widely discussed in popular books and beyond, and in this context, many students have heard the loose description that inflation occurs when the universe is in an almost de Sitter state, and undergoes exponentially rapid expansion. There is nothing wrong with this explanation, but one consequence of accepting it before having a thorough grounding in GR is that it seems to imply that de Sitter space is a solution to GR that undergoes a rapid change over time. This leads to a few confused looks when I get to maximally symmetric spaces in my course.

You see, maximal symmetry means that you should be able to look at the space at different places and at different times and the metric should be just the same. So how are we to square that with the idea of an exponentially growing universe? Well, it all comes down to coordinate choices and the crucial existence of other matter in the universe.

Pure de Sitter space – the solution to the Einstein equations with a positive cosmological constant and no other matter sources – is, indeed, a maximally symmetric space. There exist a number of particularly useful coordinate choices for this space. In some cases, these consist of picking a useful time choice, and thus defining a family of spacelike surfaces (the spatial part of the spacetime at a constant value of this time choice). This is referred to as a slicing of the space, and it is, actually, possible to slice the space in three different ways that correspond to cosmologically expanding spaces with flat, positively-curved and negatively curved spatial parts, respectively. These are the ways of describing de Sitter space that are useful when considering inflation. However, there also exists a choice of coordinates in which the metric does not depend on time at all, and the mere existence of such a choice is enough to tell us that there is no fundamental sense in which this is an expanding cosmological spacetime. In fact, from what I just wrote, you might have a related question: even in the cosmological coordinates, what decides if the universe is flat, positively, or negatively curved?

In the case of pure de Sitter space there is no answer to these questions. All the coordinate choices are equally allowed of course, and so we might as well look at the static coordinates, and there is no cosmology here. However, importantly, in cosmology we are never interested in pure de Sitter space. We know that there is other matter in the universe. This may be either in the form of particles like us, or, in the case of inflation, the background field that causes inflation in the first place – the inflaton. These types of matter mean that the behavior of the metric is at best almost de Sitter – the difference from pure de Sitter being that, crucially, there are only certain coordinate systems in which the regular matter is homogeneous and isotropic, whereas for a cosmological constant this is true in all coordinate systems. Thus an almost de Sitter space has less symmetry than pure de Sitter. One is free to transform coordinates as much as one likes, but there will no longer be any choices in which the metric is static!

Of course, we find it most convenient to discuss cosmology in the (Friedmann, Robertson-Walker) coordinates that exploit the natural homogeneity and isotropy of the relevant matter sources. This picks out a slicing of the spacetime, and in this slicing, when the universe is almost de Sitter, the universe does expand almost exponentially rapidly – inflation! This also decides among the flat, positively and negatively curved options for the spatial part of the metric.

So it matters that inflation is “quasi-de Sitter”. It is this that gives sense to statements about inflation beginning, ending, and even operating in the way we usually describe. de Sitter space is beautiful symmetric and rich, but out real universe is somewhat messier, even at its earliest times.

“Despite the unrivaled empirical success of quantum theory, the very suggestion that it may be literally true as a description of nature is still greeted with cynicism, incomprehension, and even anger.”

Fang’s research area was quantum cosmology, but he was most well-known for his political activism, fighting against repression in China. Originally a member of the Communist Party, he was expelled for protesting some of the government’s policies. The NYT obituary relates an amusing/horrifying story, according to which Fang attracted the government’s censure by co-authoring a paper entitled “A Solution of the Cosmological Equations in Scalar-Tensor Theory, with Mass and Blackbody Radiation.” Seems pretty innocuous from where we are sitting, but in Communist China the Big Bang model was considered to be a challenge to Engels’s idea that that the universe was infinite, and therefore was deemed heresy. Googling around brought me to this 1988 article in Contemporary Chinese Thought, which shows what Fang was up against. The abstract quotes Lenin, and says in all seriousness “with every new advance in science the idealists distort and take advantage of the latest results of physics to “prove” with varying sleights of hand that the universe is finite, serving the reactionary rule of the moribund exploiting classes.”

In the late 1980′s Fang helped organize resistance to China’s authoritarian regime, in the lead-up to the Tiananmen Square protests. He was fired from his job as a professor, and sought refuge in the American embassy. He was finally permitted to leave the country and emigrate to America in 1990. He finally settled down at the University of Arizona, but continued his work campaigning for human rights.

When we apply GR to cosmology, we make use of the simplifying assumptions, backed up by observations, that there exists a definition of time such that at a fixed value of time, the universe is spatially homogeneous (looks the same wherever the observer is) and isotropic (looks the same in all directions around a point). We then specialize to the most general metric compatible with these assumptions, and write down the resulting Einstein equations with appropriate sources (regular matter, dark matter, radiation, a cosmological constant, etc.). The solutions to these equations are the famous Friedmann, Robertson-Walker spacetimes, describing the expansion (or contraction) of the universe.

It is important to take a moment to emphasize what we have done here. GR is indeed a beautiful geometric theory describing curved spacetime. But practically, we are solving differential equations, subject to (in this case) the condition that the universe look the way it does today. Differential equations describe the local behavior of a system and so, in GR, they describe the local geometry in the neighborhood of a spacetime point.

Because homogeneity and isotropy are quite restrictive assumptions, there are only three possible answers for the local geometry of space at any fixed point in time – it can be spatially positively curved (locally like a 3-dimensional sphere), flat (locally like a 3-dimensional version of a flat plane) or negatively spatially curved (locally like a 3-dimensional hyperboloid). A given cosmological solution to GR tells you one of these answers around a spacetime point, and homogeneity then tells you that this is the same answer around every spacetime point. This is what we mean when we say that GR tells us about geometry – the shape of the universe – as depicted in the NASA graphic below.

This raises a very different question that is often confused with the one above. If our solution tells us that the universe is locally a 3-sphere (or flat space, or a hyperboloid) around every point, then does that mean it is a 3-sphere, or an infinite flat 3-dimensional space, or an infinite hyperboloid. This is really a question of topology – how is it connected up – which also answers the question of whether the universe is finite or infinite. To illustrate the point, suppose we have solved the cosmological equations of GR, and discovered that at every spacetime point, the universe is locally a flat 3-dimensional space. This is, by the way, what observations actually indicate our universe is like. Then, just off the top of your head, you can think of many different spaces with precisely this same property. One example is, of course, that the universe is indeed a flat, infinite 3-dimensional space. Another is that the universe is a 3-torus, in which if you were to fix time and trace out a line away from any point along the x, y or z-axis, you traverse a circle and come right back to where you started. This is a finite volume space, that is connected up in a very specific way, but which is everywhere flat, just like the infinite example. In two dimensions, one might visualize it as

Of course, I could have only made one or two directions into circles (leaving it still infinite in some directions), or made the space into a finite one with more than one hole, or any number of other possibilities.

This is the beauty of topology, but it is not something that solving the equations of GR tells us. Rather it is an extra input into our solutions. It is, however, something we can test, most precisely through measurements of the Cosmic Microwave Background radiation, as I may discuss in a later post.

Completely independent of questions of topology, the geometry of a given cosmological solution raises another issue that is often mixed up with those of geometry and topology. Suppose that the universe contains only conventional matter sources (regular matter, dark matter and radiation, say), and suppose you know (you might question whether this is truly possible) that this is all it will ever contain. Then the equations easily predict that, in the case of positive spatial curvature, an expanding universe will ultimately reach a maximum size and recollapse in a big crunch, whereas flat or negatively curved universes will expand forever. These are predictions of the destiny of the universe, and often lead to the following connection

However, as I made clear, there are some assumptions that go into the connection between geometry and destiny, and although these may have seemed reasonable ones at one time, we know today that the accelerated expansion of the universe seems to point to the existence of some kind of dark energy (a cosmological constant, for example), that behaves in a way quite different from conventional mass-energy sources. In fact, we know that for sources like this, once acceleration begins, it is easily possible for a positively curved universe, for example, to expand forever. Indeed, in the case of a cosmological constant, this is precisely what happens.

So the universe may be positively or negatively curved, or flat, and our solutions to GR tell us this. They may be finite or infinite, and connected up in interesting ways, but GR does not tell us why this is the case. And the universe may expand forever or recollapse, but this depends on detailed properties of the cosmic energy budget, and not just on geometry. Cosmological spacetimes are some of the simplest solutions to GR that we know, and even they admit all kinds of potential complexities, beyond the most obvious possibilities. Wonderful, isn’t it?