Thursday, November 22, 2012

The Structure of a Scientific Revolution

A few days ago, Peter Coles posted an interesting comment about skepticism on his blog. In it, he showed the first graphs with data showing evidence for the acceleration of the expansion of the Universe from observations of distant supernovae. His point was that though the plot isn't much to look at, the statistical evidence for cosmic acceleration from supernovae data was quickly established and very soon became very widely believed.

Coles goes on to make some points about global warming skepticism, and most of the long discussion in the comments that follow is concerned with this. Which is unfortunate, as none of that discussion provides an exception to the general rule that arguments about global warming are a complete waste of time, because people have already decided what they want to believe before they start, and are subsequently impervious to any evidence, logic or persuasion. So although you may want to read the discussion there, let's not talk about the climate here.

Instead, I want to stick with the cosmology and pick up on a question that is more interesting. Let's take a quick look at the picture of the supernovae data from the High-Z Supernova Search Team and the Supernova Cosmology Project:
Evidence for dark energy from the Hubble diagram of supernovae. The top panel shows the distance modulus of the supernovae as a function of redshift, with three different theoretical model curves. The bottom panel shows the residual distance modulus relative to that in the model with the dotted curve (a Milne universe).
As Coles points out, most people who are not cosmologists (and some who are) look at these data and find them deeply unconvincing. The error bars are large. The points are widely scattered, and at least both the top two curves seem to give reasonably good fits. On top of that, there appear to be two distinct groups of supernovae: one group rather close to us, and the other much further away at higher redshifts (and therefore observed as they were a long time ago). Any inferences we draw from relative calibrations of these two groups rest on the assumption that deep down they are the same kind of objects, and that the Universe they existed in remained the same kind of Universe.

So why exactly did this cause such a revolution in the field? How did so many physicists become convinced, almost overnight, of the existence of this mysterious dark energy, that constitutes most of the energy of the Universe, but that we didn't understand then and don't understand now?

Let's start at the beginning. I mentioned in a previous post that observers can use supernovae of a special type, Type Ia, as "standard candles". They do this by calibrating the light curves of these supernovae in order to determine how intrinsically bright the explosion was, and thus — based on how bright it appears to us — how far away it was. Along the way they have to make many complex corrections for the colour of the supernova, and for intervening dust which changes both the brightness and colour. The reason this works at all is that Type Ia supernovae are all rather similar sorts of objects. In fact there was theoretical reason for believing that they were all essentially identical objects, since they were believed to originate in a thermonuclear explosion when a white dwarf star acquired enough mass from a binary companion to exceed the Chandrashekhar limit.

To extract the distance modulus for a particular supernova from the data — in simple terms, to figure out how far away it is — requires the use of some light-curve fitting algorithm. There's more than one algorithm available on the market. In fact there are two main ones: the Multi-color Light Curve Shape (MLCS) fitter and the Spectral Adaptive Lightcurve Template (SALT). SALT itself comes in two varieties, the older SALT and the newer SALT II. MLCS has a modern version, called MLCS2k2, which is the one that is used nowadays.

This is where things start to get messy, and the supernova data look even less convincing than before. For a start, these light curve fitters do not completely agree with each other. When used to fit the same sample of observed supernovae, they give different results. No one is completely sure which, if any, is the correct fitting algorithm, though proponents of MLCS often argue strongly that SALT is clearly at fault and vice versa.

It gets worse. The MLCS fitter needs some further inputs before it can produce a distance modulus; in particular it requires a model for how the dust of the host galaxy reddens the light of the supernova that we see. Now we know the properties of the dust in our own galaxy pretty well, but we know rather less about the dust in distant galaxies. A reasonable assumption might be that our galaxy is typical. But when MLCS is given a model of dust reddening based on our galaxy, the results it produces are "wrong" (which is to say, the best-fit cosmological model no longer agrees very well with that from other data, and the supernova dataset itself shows some peculiar properties indicative of some error — see here for a technical discussion). So instead we must postulate that in fact our galaxy is unique, and all other galaxies that host supernovae have a different sort of dust.

The next problem is that Type Ia supernovae actually aren't standard candles at all. Lots of people still tell you that they are (including me a few short paragraphs ago), but they're not. In fact they vary quite a bit. Bob Kirshner — one of the fathers of supernova cosmology — describes this continued misconception as "wishful thinking". One reason why they are not standard candles is probably because the usual story about them being white dwarfs exploding exactly at the Chandrashekhar limit is wrong, as I wrote about here.

How do the supernova teams deal with this non-standard-candle nature? They artificially increase the error bars on the measurement beyond purely observational errors. But how do they know by how much to increase the error bars? Well, most papers I know of don't really say (this one, for instance), but clearly they make them large enough — a large fraction of the total error — that the "correct" model is a good fit to the data. In fact the error values provided in many public releases of supernovae data are specific to the "correct" model assumed. But how do they know which the "correct" model is, you may well ask?

This inflation of error bars sometimes gives noticeably odd results. For instance, when fitting the standard $\Lambda$CDM cosmological model to data from the Union2 compilation, one gets a $\chi^2$ value of significantly less than one per degree of freedom. I was taught many years ago that $\chi^2<1$ was a sure sign the error bars were too large. It also means that models other than the "correct" model still provide a pretty good fit to the data — you can see an example in the figure above.

All of these add up to — I think — rather a lot of reasons to treat any inferences made on the basis of supernovae alone with quite a lot of caution. Especially since dark energy is such a preposterous notion. If this is the case now, when we have hundreds of supernovae and at high redshifts too, it was even worse at the time the results were first published in 1997 and 1998, when the statistical errors were still large. (As an example, a paper from the Supernova Cosmology Project team in July 1997 concluded that there was no evidence for dark energy, before the addition of just one new data point by October of that year changed the conclusions to almost exactly the opposite!)

In the comments to his post on this topic, Coles says that if the supernovae data were the only evidence we had for dark energy, nobody would believe in it. This is possibly true; certainly many cosmologists I know would agree. The reason that it is very hard not to believe in dark energy today is because of the preponderance of evidence for it that comes from all sorts of other sources: the cosmic microwave background seen by WMAP, the clustering of galaxies, baryon acoustic oscillations, the integrated Sachs-Wolfe effect and so on. These different lines of evidence all tend to agree with each other and produce a coherent story, which is why the $\Lambda$CDM model is also known as the "concordance" model.

But none of this corroborating evidence was around when the first supernova results were published. Yet by all accounts, people did believe them at the time. (Technically speaking, clustering data available at the time suggested that $\Omega_M<1$, which would imply $\Lambda>0$ if you further assumed spatial flatness of the Universe. The same is true for the "age problem".) WMAP didn't publish any data until 2003, fully five years later. It is the supernovae observations, open to question as they were, which are credited with the discovery of dark energy. In fact the Physics Nobel Prize for 2011 was awarded to Reiss, Schmidt and Perlmutter for this work.

It seems that the acceptance of dark energy was a Kuhnian paradigm shift just waiting to happen. Discontent with the Einstein-de Sitter alternative had been slowly growing for some time, and very strong theoretical priors on the flatness and large-scale homogeneity of the Universe because of a belief in inflation meant that a non-zero $\Lambda$ was the obvious alternative. The supernova data, relatively unconvincing as they may seem to us today, just appeared at exactly the right time. This was simply the final straw on the camel's back, and the subsequent revolution progressed fast. The existence of dark energy very quickly became very widely accepted.

(Some notable exceptions existed — and indeed, sometimes still exist — among particle theorists, whose theoretical prior in favour of $\Lambda=0$ far outweighs their prior in favour of homogeneity and flatness.)

What is also interesting is that it seems that the stronger the corroborating effect of evidence for dark energy from different observations has become, the more relaxed the cosmology community has become about considering alternatives. I wasn't on the scene in the late 90s of course, but I'm told that until around 2005 it was almost impossible to be taken seriously as a theorist if you either questioned the data or considered any alternative interpretation of it that did not involve either a cosmological constant or quintessence.

Such orthodoxy is clearly not only antithetical to scientific ideals but also rather risky. In this instance cosmology as a discipline got lucky, because we can look back and say that although the data at the time perhaps did not entirely warrant a strong belief in some dark energy, the data we have now do. But if we don't remain alert to alternatives, the next time a paradigm shift is required we might make the wrong choice.


  1. Hey Sesh,

    We used to work together at the Clarendon lab in Andrea´s group. I´ve been following your blog for a while now and really like it.

    I think that this is a very interesting post and I think that it shows something very common in all areas of science. 1. people can over-sell their idea if they believe, even if the data is lacking. 2. If it is what people want to hear, they can very happily accept it regardless of the data quality.

    Whereas if the opposite occurs, and you have good data that goes against the 'new'/'interesting' idea, in both cases it is very difficult for it to become accepted. The data is either discarded or argued about!

    As you say at the beginning, it is hard to convince people that have already made up their mind! I think this is a problem in for peer review because people are rarely truly objective


    1. Hi Simon,

      I certainly remember you and the others in Andrea's group, though I don't remember much of the condensed matter physics any more!

      Both your points are sadly valid. There is definitely sometimes a bandwagon effect in science, which is not how we learn it is supposed to be done. In some cases we manage to muddle through to the right answer in the end, I suppose, but it can be very wasteful of research time and a problem for peer review.

      I was actually planning to post something in the future about Bayesian approaches to cosmological evidence and the connection between this and the problem of making up your mind in advance of the data. It will have to wait a while though.

      In the meantime I'm glad you enjoy the blog!

  2. In response to a question I was asked elsewhere, I thought I should add a statement to the effect that I am not saying that the supernovae cannot be used to obtain any information about the Universe at all. It's just that I don't think that at the time they really constituted the extraordinary evidence that is needed to back up extraordinary claims.

  3. Hmm, sounds reasonable. That doesn't seem to be any big difference to most of us because we can just substitute dark energy with dark matter. So the only difference comes from the dark energy researchers?

    1. I'm not sure exactly what you are asking: what do you mean by substituting dark energy with dark matter?

    2. The original question that you asked (on Facebook), i.e., "do you think that the supernovae give some information, but without enough accuracy to distinguish acceleration?" is an interesting one though.

      The answer to that is that with the supernovae data *alone* if you trust the published error values, and you restrict yourself to a certain class of theoretical models (those with an FRW metric), then within that class the supernovae favour accelerating models marginally more than others, and they relatively strongly disfavour one specific non-accelerating FRW model (the Einstein-de Sitter model).

      On the other hand, if you remove the restriction to consider only FRW models, all bets are off. In particular there is another special class of models (those with an LTB metric) which can exactly mimic accelerating models without actually having any acceleration. And although LTB models are a bit contrived, there are other ideas, such as backreaction, which can do the same thing. To distinguish between these alternatives you must have data from sources other than the supernovae.

      These alternatives exist even if you treat the supernovae data as perfect. Current CMB and BAO measurements can disfavour some of them (but more on that some other time).

    3. Interesting. Let's wait and see how the observation goes. Thanks for the explanation. :)

  4. Fascinating story Sesh -- I knew that there were a bunch of odd steps on the way to the distant supernova story, but having them laid out together is great fun.

    I'm going to take issue with one thing: you describe the acceptance of Dark Energy as a Kuhnian paradigm shift (and imply it further in your title.)

    Kuhn's model outlines two types of scientific progress: one is problem-solving change: people do theoretical work by using and extending well-established theories, and ask and answer questions that are considered meaningful by the current scientific norms. New theories evolve, by modification or extension of the old.

    Then there's revolutionary change. Here, the questions that the new wave are asking and answering are often near-nonsensical or at least "missing the point" by the standards of the old practices. The new theories are not modifications, but entirely new structures, and it is only in some very special circumstances (e.g., in "the classical limit") that we can recover the some of the old theoretical apparatus.

    Now clearly, there could be a grey area. Some problem-solving changes have revolutionary aspects. But I'd place the Dark Energy hypothesis firmly on the "problem-solving side". The theory's got some modifications, but GR and even the useful cosmological solutions of GR are being used before and after the shift, there's a new term in the equations but it's a very straightforward extension -- you've solved the observational anomaly with problem-solving methods.

    You describe in detail the ease of the transition to dark energy. Kuhn mentions that for true revolutionary change, the most effective way of changing the minds of the scientific establishment is the death of its older members and the rise of the young.

    So, who cares? Well, I'd suggest that the current hunt for a theoretical "source" of dark energy is still taking place in a pre-revolutionary subject, because the change you've described is a recognition of "anomalies" in the current cosmological theories not a crisis itself. And anomaly recognition is a relatively easy thing to go through: most theories have a good number of anomalies hanging about. But maybe understanding dark energy DOES require a proper revolution. In which case, the next stage is a whole bunch more exciting: in the Kuhnian model it's called "crisis", and it's ever, ever so much fun...

    1. Good points all. Sorry for playing a little fast and loose with the philosophy. My main aim was just to tell the story of the data in an interesting fashion, with a bit of social commentary.

      However, now that I think of it, there are some other things about the story that might be relevant. The first is that there was a body of research that was rendered nonsensical by the acceptance of DE. For instance, there were many efforts to try to explain how the galaxy clustering data from the APM survey could be made consistent with an Einstein-de Sitter universe. Similarly there were attempts to reinterpret data to resolve the age problem (that an EdS universe appeared to be younger than the oldest objects it contained).

      On the theoretical side, Andrei Linde and others tried to obtain a model of inflation which could leave you with an end universe with $\Omega_M<1$ as opposed to the normal $\Omega_M=1$. (Apparently he was much criticised by colleagues for this though, so it probably wasn't a mainstream view.)

      These sorts of things simply ceased to be problems after DE was accepted.

      You are right that simply adding a $\Lambda$ term to the usual GR equations was not really much of a big deal to "astrophysicist" cosmologists. In fact this is probably why it caught on so quickly with them. But it was a big deal for "particle theorist" cosmologists, who had spent years of effort trying to solve the cosmological constant problem by showing that $\Lambda=0$ exactly, and were now told that in fact they had to solve the coincidence problem as well, by also obtaining some small but non-zero $\Lambda$. (The Preposterous Universe link above is a good explanation of the problem.) From this perspective I think you could describe it as a revolution.

    2. I think Kuhn's idea of the paradigm shift is hugely overrated. It practically never happens, if ever, in real science. Stuff like the heliocentric model becoming accepted doesn't count since mainly non-scientific forces determined what people were able to publicly support.

    3. Strange how you never meet anyone who respects Kuhn's work in their own field. Philosophers tend to think he does awful, sloppy philosophy (e.g., his concept of incommensurable theories), but that's OK, because he was trained as a physicist and his claims should be understood as historical.

      Historians of science seem to think he's an awful historian, but that's OK, because he was trained as a physicist, and he's really making a claim about the philosophy of science.

      Physicists seem to vary depending on their situation: if they're an iconoclast with an idea that isn't being accepted, they talk about him like a god. If they're in the mainstream, they tend to prefer Popper.

    4. A long time ago, during my undergraduate degree, I attended a weekly discussion session on the philosophy of science - which often means the philosophy of physics, because that seems to interest philosophers the most. The thing that struck me about all philosophers we read was that every time they made any statements about how they thought physics actually progressed it was so easy to come up with historical examples that did not, in fact, work like that. Each had some nuggets of insight but as soon as they made any sort of generalisations about process, I felt they invariably looked a bit stupid.

      I think physicists who have never really considered the philosophical side of science very much (and why should they, after all) might instinctively prefer Popper. But as soon as you stop to think about it, he appears hopelessly simplistic and naive.

  5. Unrelated: but good given the name of your blog, it turns out there is an odd blank on the map of the Earth. Welcome to Sandy Island.

    And here's the google maps link.,159.911499&spn=1.495445,2.705383&t=h&z=9

  6. I was on the scene in the late 1990s. It certainly didn't happen overnight that the current cosmological model became accepted by most cosmologists. It took about 10 years altogether.

    One word about climate change: the comparison between the two graphs isn't fair, as there is a huge number of other graphs which convincingly demonstrate global warming, not just the one Peter posted. (A good source of information is Tamino's blog "Open Mind" which IIRC is run by the brother of a cosmologist who also has a blog.) This isn't the case with the SNIa stuff where you and Peter showed the standard graphs.

    Also, let's be fair. Back when people believed in the Einstein-de Sitter universe, evidence for it was much worse than that for the "concordance model" today.

    Eddington and his Fundamental Theory is perhaps a good (bad?) example of why astronomers shouldn't do particle physics. However, I think that particle physicists shouldn't try to do cosmology by estimating lambda from vacuum energy and getting a hugely large number (not necessarily correct) then proclaiming the idea that obviously some cancellation happens as if that were the only possible explanation.

    Note that we would have arrived at the concordance model even if there were no SNIa data at all. Despite the problems you mention, two independent teams agree with each other within the errors and also with the concordance model as derived from other data. Some people hype the SNIa data because they are the only dataset which, alone, rules out lambda=0, but that is really a minor issue. Like Avogadro's number and the existence of atoms it is the convergence of several different methods on the same result which make the concordance model believable. (It is also not something which people wanted to have before the data were in; quite the opposite in fact.)

    I was at a conference in Prague in June where I had the impression that back-reaction is not a viable alternative explanation here.

    1. With some small reservations, I'll grant you that we would probably have arrived at concordance model without any SNIa.

      One of the reservations is a technical one: we actually need SNIa to measure $H_0$, and we need an input value of $H_0$ to extract a value of $\Lambda$ from WMAP. I will write more about this later. But let's assume we had a value of $H_0$ from nearby supernovae, but just didn't have any high redshift ones. Then yes, we would probably have got there.

      I'll also agree that there was no good evidence in favour of an EdS universe. And that it is possible to have too strong a prior in favour of $\Lambda=0$, given that there is obviously a major unsolved problem in QFT sitting there anyway.

      But I don't agree that SNIa data alone rule out $\Lambda=0$. It's possible to construct simple models with $\Lambda=0$ that are surprisingly hard to kill even when confronted with SNIa, the CMB, BAO, and even $H_0$ measurements. See my answer to Lingfei above. It is only when you add kinematic Sunyaev-Zel'dovich measurements in on top of everything else that they finally give up the ghost.

      There are lots of arguments about backreaction, and I think some people would still say it is not ruled out as a viable option. Perhaps more people would agree that backreaction could be important enough to spoil the concordance of the concordance model, even if some non-zero $\Lambda$ is still required.

    2. Well, there were papers by Ostriker and Steinhardt, and by Mike Turner, Lawrence Krauss etc back in the early 1990s which suggested that the concordance model was the best fit to the observations. Granted, this wasn't quite precision cosmology, but even then it was clear that this was a good fit. The more data came in, the better it looked, even without the SNIa stuff. Yes, it meant a Hubble constant too high for Sandage and non-zero lambda. As for actually pinning it down, yes, one needs WMAP and a good value for the Hubble constant.

      I think Sandage's chapters in The Deep Universe illustrate the prejudice at the time on the part of many people. Sandage was an observer who understood the theory of classical cosmology but, AFAIK, had no deeper knowledge of particle physics etc. He was completely convinced that inflation implied the EdS model. It is hard to believe that this did not influence his claim that the Hubble constant must be low (since he knew enough about astrophysics to know that the age arguments couldn't be brushed off).


    The latest post was visible in two browsers yesterday; today it is not. Even if it works for you, it probably doesn't for many others.

    1. Maybe it's not a change you made, but rather Blogger. I've seen some strange stuff at other Blogger blogs today which was not there yesterday, but not quite as bad.

    2. Thanks for the tip Philip. At the moment it works for me on three different browsers, so I'm not really sure what might have happened. Was the problem only that you could not see the most recent post (i.e. you could still see everything else)? Has it now resolved itself?

    3. It's working again now. At first I saw the page, then it went blank and I saw only the background. Also, it kept loading and loading without stopping, saying it was waiting for some Google aip or something similar.

      Now it works as before. Probably a change at Blogger which enough people noticed to get it corrected.

  8. Allow me to engage in some shameless self-promotion on the topic of this blog post, which I've also written up in a paper at arXiv:1505.02917 (accepted by MNRAS). Bottom line: If one drops the assumption that the universe is homogeneous on small scales (at least with regard to light propagation), but otherwise assumes the Friedmann-Lemaitre framework, then the m-z relation for type Ia supernova, considered alone, are not necessarily compatible with the concordance model. As a result, without additional assumptions, one can't get constraints on Omega and lambda which are competitive with other methods. (This didn't use to be true, but now is now that there are more data and higher-redshift data.) However, even with relaxing this assumption, the supernova data still indicate an accelerating universe.

    If one assumes that the universe is homogeneous (or at least that, for the purposes of light propagation, it can be treated as such, perhaps in some appropriate average sense) even on small scales (i.e. that of a supernova beam, which is exceedingly thin in a cosmological context), then the supernova data strongly indicate the concordance model (perhaps too strongly, which might indicate that the error bars on the distance modulus are too large). Since we are pretty certain that the concordance model is true, independently of supernova data, the most important information from the m-z relation for type Ia supernova might actually be that it indicates this (average) homogeneity, which tells us something about the distribution of (dark) matter at scales much smaller than can be probed by conventional observational cosmology or cosmological numerical simulations. (By the same token, until we have some independent measure of this small-scale matter distribution, we will have to take any conclusions about the equation of state w (exactly -1 for the traditional cosmological constant) and/or its evolution with a large grain of salt.)

    There is much more stuff in the paper.

  9. "(As an example, a paper from the Supernova Cosmology Project team in July 1997 concluded that there was no evidence for dark energy, before the addition of just one new data point by October of that year changed the conclusions to almost exactly the opposite!)"

    True, but not really surprising. They had few data points at the time, and it turned out that their first result, that there was no evidence for an accelerating universe, was influenced by what is now known to be an outlier. The error ellipses back then were huge. Of course, now there are more data, and higher-redshift data, and two main teams, and analyses by other people, so I think that, within the framework in which it is presented, that the cosmology claims based on supernova data are quite sound.