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General Relativity, MOND, and the problem of unconceived alternatives

  • Paper in History and Philosophy of Science
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Abstract

Observational discrepancies in galactic rotation curves and cluster dispersion data have been interpreted to imply the existence of dark matter. Numerous efforts at its detection, however, have failed to turn up any positive result. As a dynamical theory is always operative on the assumed mass distribution to predict kinematic observations, some scientists see the discrepancy as telling against General Relativity. Among the many theories that seek to modify gravity, those that are built on Modified Newtonian Dynamics (MOND), or yield MOND behaviour at appropriate scales, achieve remarkable empirical success without assuming dark matter. The continued non-detection of dark matter and the empirical success of MOND supports the claim that the current evidential and theoretical context underdetermines General Relativity. In this article, I clarify the kind of underdetermination that can be said to threaten General Relativity. Specifically, I argue that the present evidential and theoretical context increase the possibility of an unconceived alternative to GR which would be just as well supported by the available evidence.

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Notes

  1. Discussion on underdetermination predate Quine’s articulation. Most notably, Duhem (1991[1914]) argues that unlike mathematics, physical sciences entertain the possibility of two contradictory theories being equally supported based on the predictions they make.

  2. Sklar uses the term ‘transient underdetermination’ to describe the scenario where available evidence underdetermines theory.

  3. He supports his conclusions by looking at the debate around inheritance in mid-nineteenth century England among biologists and naturalists and shows that scientists engaged in the debate failed to consider relevant alternatives to their views on inheritance that would later be accepted (2006: chapters 3, 4, 5).

  4. According to Stanford, eliminative inference is likely to be unreliable when we regularly fail to conceive alternatives to theories that attempt to describe constituents of nature that are “too small or too large or too amorphous for us to readily perceive; because the causal interactions between those entities are too fast or too slow or too rare or take place on too grand a scale for us to engage with in ordinary ways; these entities and interactions occur in times and places either far removed from our own or otherwise inconveniently located (e.g., at the dawn of life on Earth, in remote regions of the universe, at the center of the Sun), and so on” (Stanford, 2006:3).

  5. This point has been noted in the underdetermination literature by Andre Kukla, cf Kukla, 1996: Section 3.

  6. On the possibility that the stars are vastly distant from the earth than the planets, Ann Blair quotes Brahe: “It is necessary to preserve in these matters some decent proportion, lest things reach out to infinity and the just symmetry of creatures and visible things concerning size and distance be abandoned” (Blair, 1990: 364).

  7. The mass of a distant astronomical object can be calculated either by studying its luminosity or by studying its kinematics in conjunction with a theory of gravity. From the observed luminosity of a large astronomical object, its mass can be calculated by comparing the ‘mass-to-light ratios’ of analogous systems. The mass calculated by this method includes contributions from gas, dust, dim stars and other objects that emit too little light to be detectable over astronomical distances. The other method begins with finding the velocity at the edges of any rotating astronomical object, usually done by spectroscopic methods. The mass interior to a given radius can then be calculated from the observed radial velocities in conjunction with some theory of gravitational dynamics.

  8. A rotation curve is a plot of radial velocities against the distance from the centre of a galaxy. As GR yields Newtonian gravity at large distances from the galactic centre, the rotation curves of galaxies should be similar to the one observed for the solar system – it should rise to a peak that then falls asymptotically. Such a curve would be expected of a system which has its mass concentrated in its centre with mass density falling at the edges. The observations, however, show the curve becomes asymptotically flat instead of falling.

  9. The postulation of such particles as possible dark matter candidates is most often motivated by existing problems in particle physics. The most discussed WIMP models (neutralinos, gravitinos) arise from considerations of supersymmetry, a proposed extension to the Standard Model of particle physics that aims to solve other existing problems like the hierarchy problem.

  10. The point of McGaugh’s quote is to highlight a manoeuver that some see as non-scientific. McGaugh’s characterization of feedback as epicycles, however, need not be taken at face value. While the specifics of the process can be questioned, supernovae induced redistribution of mass does take place. Admittedly, such processes introduce a degree of freedom in the models which allow for agreement with the observations. However, having a parameter that can be tweaked across a range of scenario does not constitute a falsification.

  11. For a list of predictions where \({a}_{0}\) appears, cf. Famaey & McGaugh (2012: 30).

  12. Cf. Milgrom, 2014 for the derivation of MOND laws, and Famaey & McGaugh (2012, especially Section 5) for MOND phenomenology.

  13. A slightly dated review of how existing relativistic MOND theories fare for cosmological observations can be found in Famaey & McGaugh (2012: Section 9).

  14. The presence of dark baryons—ordinary matter that evades luminous detection—is required even in ΛCDM. Its use in MOND tells us that exponents of MOND are not averse to using dark matter-like explanations to rescue their hypothesis when such case arises.

  15. The significance of the bullet cluster for dark matter and modified gravity has also received attention from philosophers of science. Peter Kosso (2013) has argued that, because weak lensing requires only EEP and not the entire GR, it constitutes a novel proof for the existence of dark matter. Adán Sus (2014) rightly points out that it need not be the kind of nonbaryonic dark matter needed in ΛCDM as MOND theories like TeVeS can explain the observations without the need for such nonbaryonic dark matter. Finally, Vanderburgh (2014) asserts that the observations do not preclude the possibility that GR is incorrect and dark matter exists in the clusters.

  16. Milgrom (1983a) calls the dark matter hypothesis ‘ad hoc’; McGaugh (2015) likens it to ether, hence unfalsifiable; while Merritt (2017) terms the GR-based models ‘converntialist’.

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Acknowledgements

I would like to thank Prof. Vikram Sirola (IIT Bombay), Prof. Prasanta Bandyopadhyay (Montana State University) and Dr. Tarun Menon (Azim Premji University) for their valuable comments and suggestion. My special thanks to the two anonymous referees of this journal whose comments have greatly improved this essay.

Funding

I had presented versions of this article at the Philosophy of Dark Matter workshop at RWTH Aachen, and CLMPST 2019 at Prague. Both the organisers provided me with travel grants, for which I am extremely grateful.

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  1. Department of Humanities and Social Sciences, IIT Guwahati, Guwahati, 781 039, India

    Abhishek Kashyap

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Kashyap, A. General Relativity, MOND, and the problem of unconceived alternatives. Euro Jnl Phil Sci 13, 30 (2023). https://doi.org/10.1007/s13194-023-00532-x

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