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Feyerabend’s rule and dark matter

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Abstract

Paul Feyerabend argued that theories can be faced with experimental anomalies whose refuting character can only be recognized by developing alternatives to the theory. The alternate theory must explain the experimental results without contrivance and it must also be supported by independent evidence. I show that the situation described by Feyerabend arises again and again in experiments or observations that test the postulates in the standard cosmological model relating to dark matter. The alternate theory is Milgrom’s modified dynamics (MOND). I discuss three examples: the failure to detect dark-matter particles in laboratory experiments; the lack of evidence for dark-matter sub-haloes and the dwarf galaxies that are postulated to inhabit them; and the failure to confirm the predicted orbital decay of Milky Way satellite galaxies and other systems due to dynamical friction against the dark matter. In each case, Feyerabend’s criterion directs us to interpret the experimental or observational results as an indirect refutation of the standard cosmological model in favor of Milgrom’s theory.

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Notes

  1. Of course there are data which constitute anomalies for both theories. Two examples (both taken from Merritt, 2020): (i) the measured abundances of lithium-7 and deuterium imply, via the equations of big bang nucleosynthesis, very different numbers for the mean density of nuclei (‘baryons’) in the universe. This anomaly is independent of assumptions about dark matter and exists with equal force in both theories. (ii) The observed dynamics of galaxy clusters is difficult to explain under either theory. Under the standard model, dark matter is invoked to explain the cluster data, but only with limited success. Merritt (2020) also presents a list of anomalies that exist under the standard model but not under Milgrom’s theory (the ‘core-cusp’ problem, the ‘too big to fail’ problem, the ‘problem of the satellite planes’ etc.).

  2. Skordis & Złosnik were not the first to demonstrate empirical equivalence of this sort. At least two earlier versions of Milgrom’s theory (Angus 2009; Berezhiani & Khoury, 2015) successfully accounted for all large-scale cosmological data, but they did so by postulating forms of dark matter. Skordis & Złosnik were the first to achieve this without invoking any form of dark matter.

  3. Feyerabend does not state explicitly, in either of the cited articles, what he means by “second-order effects of motion”. I believe that “second-order” here means order V2/c2 where V is the speed of the observer relative to the Ether and c is the speed of light. The famous Michelson and Morley experiments were of second-order in this sense. Cei (2020, Chapter 7) remarks that “by 1895 the genuinely troubling results [from the standpoint of Lorentz’s theory] were only the ones of second order.”.

  4. Feyerabend (1987, p. 293). The misspelling of Worrall’s name is Feyerabend’s.

  5. Nevertheless there do exist relativistic versions of Milgrom’s theory that are, apparently, as successful as the standard model at explaining data from the cosmic microwave background, the matter power spectrum on cosmological scales etc. See Angus (2009) and Skordis and Złosnik (2020) for two examples.

  6. Even some normal matter is expected to be ‘dark’; for instance, the black hole and neutron star remnants that are believed to be produced during the late evolution of massive stars. Astrophysicists (both standard-model and Milgromian) typically try to account for the presence of these objects when computing the gravitational force from the normal matter.

  7. Indeed there is growing momentum, on the part of standard-model cosmologists, to define ‘galaxy,’ quite generally, as ‘a stellar system containing dark matter’; see Willman and Strader (2012).

  8. Standard-model cosmologists sometimes invoke, in this context, the so-called ‘WIMP miracle’: the fact that the self-annihilation cross-section needed to obtain the correct cosmological abundance of dark matter via thermal production in the early universe is similar to what is expected for a new particle (a ‘WIMP’) that interacts via the electroweak force. However there is an emerging consensus that this paradigm for dark matter has already been experimentally ruled out (e.g. Siegel, 2019). Karl van Bibber, in the Summary talk of the July 2016 Identification of Dark Matter (IDM2016) meeting in Sheffield, England, encouraged the experimenters in his audience not to be discouraged: “No hand-wringing over fraying of the ‘WIMP miracle’! … Often a deceptively too simple argument is just what’s required to get the ball rolling.”.

  9. Milgromian researchers prefer the name ‘dwarf over-prediction problem.’.

  10. This remarkable fact—established already in the 1970s (Kunkel & Demers, 1976; Lynden-Bell, 1976)—was all but ignored by standard-model cosmologists until quite recently, in spite of (or perhaps because of) the fact that it is so clearly at odds with the predicted distribution of dark sub-halos.

  11. The fact that the satellites lie spatially in a thin planar structure already implies a great deal of velocity correlation, unless one postulates that we are observing the structure at a special time.

  12. “Massive” means here that the mass of the body is much greater than the mass of a single dark-matter particle, i.e. M ≫ mχ.

  13. Dwarf galaxies are traditionally named after the constellation in which they sit. This naming scheme has become cumbersome as the number of identified dwarves has increased, e. g. Bootes I, Bootes II, Bootes III etc.

  14. For comprehensive reviews of the successes and failures of the two cosmological models, see Famaey and McGaugh (2012), Sanders (2019), Merritt (2020) and Skordis and Zlosnik (2020).

  15. E. g. Popper (1959, p. 108): “We choose the theory … which not only has hitherto stood up to the severest tests, but the one which is also testable in the most rigorous way.”.

  16. See, for instance, Laudan (1989, p. 316, note 33) or Worrall (1978, pp. 308–309 and 1991, pp. 343–344). Both authors note that Feyerabend’s rule directs us to choose the theory that has (in Laudan’s words) more “heuristic potential” in a Lakatosian sense; that is, greater potential for generating confirmed novel predictions.

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    David Merritt

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Merritt, D. Feyerabend’s rule and dark matter. Synthese 199, 8921–8942 (2021). https://doi.org/10.1007/s11229-021-03188-3

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