David Merritt recently published the article “Cosmology and convention” in Studies in History and Philosophy of Science. This article is remarkable in many respects. For starters, it is rare that a practicing scientist reads a paper on the philosophy of science, much less publishes one in a philosophy journal.

I was initially loathe to start reading this article, frankly for fear of boredom: me reading about cosmology and the philosophy of science is like coals to Newcastle. I could not have been more wrong. It is a genuine page turner that should be read by everyone interested in cosmology.

I have struggled for a long time with whether dark matter constitutes a falsifiable scientific hypothesis. It straddles the border: specific dark matter candidates (e.g., WIMPs) are confirmable – a laboratory detection is both possible and plausible – but the concept of dark matter can never be excluded. If we fail to find WIMPs in the range of mass-cross section parameters space where we expected them, we can change the prediction. This moving of the goal post has already happened repeatedly.

The cross-section vs. mass parameter space for WIMPs. The original, “natural” weak interaction cross-section (10-39) was excluded long ago, as were early attempts to map out the theoretically expected parameter space (upper pink region). Later predictions drifted to progressively lower cross-sections. These evaded experimental limits at the time, and confident predictions were made that the dark matter would be found.  More recent data show otherwise: the gray region is excluded by PandaX (2016). [This plot was generated with the help of DMTools hosted at Brown.]
I do not find it encouraging that the goal posts keep moving. This raises the question, how far can we go? Arbitrarily low cross-sections can be extracted from theory if we work at it hard enough. How hard should we work? That is, what criteria do we set whereby we decide the WIMP hypothesis is mistaken?

There has to be some criterion by which we would consider the WIMP hypothesis to be falsified. Without such a criterion, it does not satisfy the strictest definition of a scientific hypothesis. If at some point we fail to find WIMPs and are dissatisfied with the theoretical fine-tuning required to keep them hidden, we are free to invent some other dark matter candidate. No WIMPs? Must be axions. Not axions? Would you believe light dark matter? [Worst. Name. Ever.] And so on, ad infinitum. The concept of dark matter is not falsifiable, even if specific dark matter candidates are subject to being made to seem very unlikely (e.g., brown dwarfs).

Faced with this situation, we can consult the philosophy science. Merritt discusses how many of the essential tenets of modern cosmology follow from what Popper would term “conventionalist stratagems” – ways to dodge serious consideration that a treasured theory is threatened. I find this a compelling terminology, as it formalizes an attitude I have witnessed among scientists, especially cosmologists, many times. It was put more colloquially by J.K. Galbraith:

“Faced with the choice between changing one’s mind and proving that there is no need to do so, almost everybody gets busy on the proof.”

Boiled down (Keuth 2005), the conventionalist strategems Popper identifies are

  1. ad hoc hypotheses
  2. modification of ostensive definitions
  3. doubting the reliability of the experimenter
  4. doubting the acumen of the theorist

These are stratagems to be avoided according to Popper. At the least they are pitfalls to be aware of, but as Merritt discusses, modern cosmology has marched down exactly this path, doing each of these in turn.

The ad hoc hypotheses of ΛCDM are of course Λ and CDM. Faced with the observation of a metric that cannot be reconciled with the prior expectation of a decelerating expansion rate, we re-invoke Einstein’s greatest blunder, Λ. We even generalize the notion and give it a fancy new name, dark energy, which has the convenient property that it can fit any observed set of monotonic distance-redshift pairs. Faced with an excess of gravitational attraction over what can be explained by normal matter, we invoke non-baryonic dark matter: some novel form of mass that has no place in the standard model of particle physics, has yet to show any hint of itself in the laboratory, and cannot be decisively excluded by experiment.

We didn’t accept these ad hoc add-ons easily or overnight. Persuasive astronomical evidence drove us there, but all these data really show is that something dire is wrong: General Relativity plus known standard model particles cannot explain the universe. Λ and CDM are more a first guess than a final answer. They’ve been around long enough that they have become familiar, almost beyond doubt. Nevertheless, they remain unproven ad hoc hypotheses.

The sentiment that is often asserted is that cosmology works so well that dark matter and dark energy must exist. But a more conservative statement would be that our present understanding of cosmology is correct if and only if these dark entities exist. The onus is on us to detect dark matter particles in the laboratory.

That’s just the first conventionalist stratagem. I could given many examples of violations of the other three, just from my own experience. That would make for a very long post indeed.

Instead, you should go read Merritt’s paper. There are too many things there to discuss, at least in a single post. You’re best going to the source. Be prepared for some cognitive dissonance.


30 thoughts on “LCDM has met the enemy, and it is itself

  1. Stacy, I think the blame (for this figure etc) lies more with particle physicists. Somehow they have done such a large sales pitch for dark matter \equiv supersymmetry (and supersymmetry \equiv dark matter) and WIMP miracle \equiv first evidence for BSM physics, that I don’t think they will give it up. This is despite that the fact that there is not a single shred of evidence from any astrophysical observation (galactic rotation curves, bullet cluster, CMB etc) that dark matter has electroweak scale interactions. At the end of the day “WIMP miracle” is just a numerical coincidence. OTOH another numerical coincidence (which is usually ignored by everyone) is cube of the QCD scale is equal to Hubble scale and first pointed out by Zeldovich in 1967. But almost no one
    take this serious (some exceptions are BJ Bjorken, N.J. Poplawski etc). Bt you will never see this concidence discussed in any major particle physics (or cosmology conference)


  2. That’s all fine and dandy EXCEPT, QCD axions are both theoretically and experimentally motivated.

    Everything else is delusional crap. It would be nice if you could even admit that to yourself.


    1. Thomas, I disagree. Axion is just one of the solutions to the strong CP problem in QCD and the limits are already getting quite stringent.. Why is the rest “delusional crap”?


      1. I find it hard be believe that you believe the limits are stringent when the axion mass range attributed to QCD equation of state calculations has not even been investigated yet, not by haloscopes with the required resolution, nor even by microwave cavity detectors, in fact, by no instruments whatsoever.

        The fact that there are legitimate solutions to the QCD CP problem indicates it’s a viable route to dark matter. There is ZERO evidence that string theory is relevant at any scale less than the Planck scale.

        The entire domain of string theory is math, not physics. So by all means, mathturbate away.

        I’m sure that US taxpayers appreciate all of those expensive WIMP detector efforts.

        Just as I am sure that people working on them enjoy their paychecks.


  3. Thanks for this post. I read David Merritt’s paper with much interest. This period in cosmology reminds me of the mid 20th century scientific and philosophical debates on conventionalism described in the book by J.D. North, “The Measure of the universe: A History of Modern Cosmology”

    That book describes the many failed alternatives to Einstein’s General Relativity etc. as proposed prior to 1965. In terms of scientific theory, observations and data North’s discussion is now well out of date. However in terms of the philosophical debate (over the role of metaphysics and unobservables in science and how to distinguish science from wishful thinking or rote learned mythology) much less has changed.


  4. Not sure how relevant this comment is to this post, but do you have any comment on the recent claims that the most distant galaxies seem to be rotating more slowly than expected by LCDM, implying that there was less DM back then, or at least that it was distributed very differently? Does MoND make any sort of relevant prediction about the early universe?


    1. Actually I may have found the answer to my question. On rereading the article I was looking at I found a sentence that said disk galaxies at high red shift are more compact than more recent galaxies. This means (at least to me) that less of the galaxy would be in the MoND regime, and therefore its rotation would be dominated by Kepler’s laws instead of Milgrom’s.


  5. Indeed, these are massive, high surface brightness galaxies. Their rotation curves are not very extended. By eye, it doesn’t look like they reach the MOND regime. They look like the inner parts of normal rotation curves for such galaxies. I’d expect to see flattening if they could get further out; don’t see anything surprising in the data so far as they go. Perhaps this is worthy of its own post in my copious spare time.


  6. Ron Smith,

    I think your comment is made relevant by reading the press release at the University of Bath


    In the last paragraph is a quote from one of the authors of the recent studies…repeated below

    “We have to be very careful when comparing these early massive and gas-rich rotating galaxies to the ones in our local universe,” cautions Natascha Förster Schreiber, co-author for all four studies. “Present-day spirals, such as our Milky Way, require additional dark matter in various amounts. On the other hand, local passive galaxies – which are dominated by a spheroidal component and are the likely descendants of the galaxies in our study – show similarly low dark matter fractions on galactic scales.”

    It seems that one of the authors (at least) is saying that the early galaxies so far observed are not yet statistically representative of the universe we see today, assuming LCDM is true.

    The alternative empirically driven approach (while you wait for more data to roll in) would be to assume that massive high surface brightness galaxies are the norm in the early universe and see where that leads you.


  7. I find the quote “We have to be very careful when comparing these early massive and gas-rich rotating galaxies to the ones in our local universe” ironic since what they see looks to me to be perfectly normal for galaxies of this type in the local universe.


  8. I have just been watching one of Sean Carroll’s YouTube video’s

    Let’s forgive him for not mentioning the failed (so far) experimental search for Dark Matter (direct searches have failed, plus there has been no discovery of transverse missing momentum by the LHC which might indicate the presence of weakly interacting particles emerging from the high energy collisions.)

    The main observational evidence he gives for accepting the Dark Matter thesis is:
    a) power spectrum of large scale cosmological structure
    b) the height of the third peak of the CMB anisotropy spectrum, due to acoustic oscillations in the very early universe, cannot be predicted unless Dark Matter is included in the model.
    c) MOND fails to explain the dynamics of galaxy clusters most especially the bullet cluster.

    In terms of b) Sean says that the oscillations of the dark matter and baryons are in phase for the first and third peaks and out of phase for the second and fourth peaks.

    Without dark matter you would perhaps need a transitory phase change that later disappeared e.g. (wild conjecture warning as the time scales may be all wrong) unstable neutronic matter forming that allows a delayed release of energy when it decays??

    Any thoughts to explain b) without dark matter?


      1. Yes; we discussed it. It is true – the collision velocity of the bullet cluster is problematic conventionally. It makes a good test as to whether someone actually knows what they’re talking about: lots of people cite the bullet cluster as being fatal to MOND, but are blissfully unaware that it is also problematic for LCDM.

        Liked by 1 person

  9. Sean and I had a long debate on these things: http://astroweb.case.edu/ssm/mond/carrollcorrespondence.html. I would mostly agree with all of these points (a)-(c), but with the exception of (b) it is not obvious that dark matter is always the better interpretation. The usual logic seems to be “clusters are a problem for MOND” therefore dark matter wins. But clusters are also problematic for LCDM, including the bullet cluster (for which the improbably high collision velocity is naturally explained by MOND). Plus no one seems to have heard of Abell 520, which is a counter-example to the bullet cluster that makes no sense in LCDM. But those are details. The real issue is attitude. If we come to the problem Knowing the Answer, we leave knowing it, regardless of the evidence. You can see that attitude writ large in my correspondence with him.

    Returning to (b), I do consider the CMB to be the best evidence for CDM. There is a much longer story (see the CMB section on http://astroweb.case.edu/ssm/mond), and I don’t know how it will be resolved. The CMB and rotation curves tell starkly different stories. The mainstream cosmology argument is that the CMB is impossible to understand without CDM [and therefore we may ignore any other evidence]. I find it just as hard to explain rotation curves without MOND, but I am not willing to ignore contrary lines of evidence.

    Still, it all comes down to attitude. Sean is like many cosmologists: quite sure he is right, with no evidence shaking that confidence. I differ in that I am quite shaken by the evidence, to the point that I changed my mind: I was wrong to have been so sure CDM HAD to be the answer. I’d be happy to be proven wrong, but so far the criteria I’ve set for that haven’t been met (https://arxiv.org/abs/1404.7525), and I’ve seen a lot more predictions come true without CDM it than with – including for the CMB.

    Liked by 1 person

    1. “Sean is like many cosmologists: quite sure he is right, with no evidence shaking that confidence.”
      That’s worryingly similar to what, for want of a better term, I’ll call a “fundamentalist” or, even, “science denying” stance.


  10. By the way – the Merritt paper is very thought provoking. It took me a couple of hours to read it thoroughly (I’m neither a scientist nor a philosopher) but it was well worth the effort. Thanks for posting about it.


  11. Stacy,

    Having read the material you link to above, I do agree with you that the empirically motivated MOND approach and the LCDM approach are in many ways incommensurable. In spite of the difficulties I think your debates with Sean and others are essential to help keep the “intellectual space” open so that young physicists think about, research and debate these important unresolved issues freely for themselves in their formative years.

    I think that ultimately this debate will only be ultimately resolved by finding a new physical theory, perhaps even a whole new systematic way for thinking (new paradigm) to add to all our current modes of thought.

    Given the empirical constraints, paths to a new theory seem to classify into two basic approaches: the first approach is the one pioneered by Einstein, that is to say quantum physics somehow emerges (is emergent) from some basic underlying continuum physics that includes the force of gravity; in the second approach gravity and all other continuum physics emerge from a fundamentally quantised physical framework.
    In the first approach kinetic and potential energy, in terms of gravitational and inertial physics at least, appear to be distinct (perhaps fundamentally distinct), whereas in the quantum (field) approach all energy, perhaps even dark energy, reduces to various forms of quantised kinetic energy.

    The debate concerning the nature of the most fundamental physics to underlly reality: continuum physics or quantum physics, has some similarities to the LCDM vs MOND debate. The two approaches are definitely incommensurable, and have proved empirically successful in different domains and scales of physics. As with LCDM and MOND, one approach is now considered to be much more mainstream and orthodox than the other.

    Independently of the outcome of these debates what we need is more physicists like you who are both able to think deeply and productively across what currently seem like incommensurably different points of view.

    Liked by 1 person

  12. Thanks for your kind words. It is important to think through things from both sides, on their own terms. It is impossible to be objective if we are unable to do this. It may be impossible anyway, but the distinction you observe between mainstream and not is all too real – and being in the mainstream tends to preclude thinking otherwise.

    As well as the fundamental quantum vs continuum nature of space-time, another fundamental puzzle is the origin of inertial mass. Why is inertial mass equivalent to gravitational charge? This isn’t true for any other force, and may be part of of why gravity is so hard to reconcile with quantum theory. The equivalence of inertial mass and gravitational charge is built into General Relativity, but Mach’s Principle is not – despite Einstein’s efforts to include it. I mention this because it seems a fundamental issue that *might* help inform the theoretical path forward.

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  13. As to the origin of inertial mass one’s approach now depends whether or not you take MOND seriously. For example does MOND apply “all the way down”, not just to hydrogen molecules, but to elementary particles as well. The alternative to taking MOND seriously are to ignore it and cling to Dark Matter, or to alternatively try to somehow to prove MOND phenomena are emergent somehow over larger spatial conglomerations of matter.

    Perhaps some younger particle physicists need to consider the serious possibility that “elementary” particles may have non-elementary multi-parameter inertial properties, perhaps dependent on something akin to the absolute gravitational potential at a particular location, (attributable to all matter in the visible universe giving rise to an “internal field effect” with something like Mach’s Principle then applying at any particular location in space), but also dependent somehow on the local spatial derivative of this potential, (equivalent to an acceleration and possibly linking somehow to the MOND “external field effect” phenomenon).

    If the inertial properties of elementary particles when moving through external “classical” gravitational fields are more complex than we thought, then this may imply that the inertial interactions between elementary particles are more complex than we thought possible classically speaking.

    There is a paper by Einstein published at the back of the collection of original papers, by Einstein, Lorentz, Weyl and Minkowski, entitled “The Principle of Relativity”. It perhaps marks the end of the period when Einstein was listened to by other mainstream physicists, and started the period when he was mostly ignored. In modern terms the title of the paper seems crazy beyond belief.

    page 191 “Do Gravitational fields play an essential part in the structure of elementary particles of matter?”

    The modern answer to this question would be that gravitational fields mysteriously emanate from elementary particles, but otherwise play absolutely no role in their structure or their interaction with other elementary particles. If you think about this seemingly crazy possibility raised by Einstein for any length of time, you come to realise that the only possible way weak gravitational fields can play a role in the structure of elementary particles is by modifying the point to point spatial energy density, and thus strength, of other fields (e.g. classical electric and magnetic fields).

    If there is even a small chance that taking MOND seriously al all scales can lead to fresh paradigm shifting insights into the fundamental nature of inertia and elementary particle physics, as well as cosmology, then surely somebody somewhere should be funded to have a go at it.

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  14. Moving back to the subject of incommensurability and handling anomalies in theories. I found the recent paper in the archive, and it seems to me throw up some interesting data on 6 low mass galaxies viewed both from a dark matter perspective and from a MOND perspective, I apologise if you have reviewed this paper elsewhere and I have missed it.

    The 6 galaxy rotation curves can all be fitted perfectly if one adds the right dark matter halo, which is not unexpected and perhaps wrong if any of these galaxies are unstable dynamically. In terms of MOND two of the curves (NGC 3621, 5949) are an excellent fit. NGC 6503 not quite as good. The remaining three are not a good fit because they have rising rotation curves which perhaps indicates instability.

    Can MOND be used to identify the unstable galaxies as a percentage of the total in any particular region of the universe? Later giving snapshot measures of local evolutionary activity that can later be compared statistically with models.
    Can the existing MOND theory make (falsifiable?) claims about how the dynamics of certain types of unstable galaxies evolve in time?

    Any thoughts?

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  15. I believe one should listen to Einstein. If he seriously asks the question “Do gravitational fields play an essential part in the structure of elementary particles of matter?” then it is not for lesser mortals to dismiss it as “crazy beyond belief”. The modern idea that gravitational fields emanate from matter without getting anything in return seems a lot more crazy to me. Gravity does change the shape of spacetime on all scales, however small, and it surely isn’t good enough to just ignore this.


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