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.
Similar content being viewed by others
Notes
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.
Sklar uses the term ‘transient underdetermination’ to describe the scenario where available evidence underdetermines theory.
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).
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).
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).
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.
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.
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.
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.
For a list of predictions where \({a}_{0}\) appears, cf. Famaey & McGaugh (2012: 30).
A slightly dated review of how existing relativistic MOND theories fare for cosmological observations can be found in Famaey & McGaugh (2012: Section 9).
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.
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.
References
Acuna, P., & Dieks, D. (2014). Another look at empirical equivalence and underdetermination of theory choice. European Journal of Philosophy of Science, 4(2), 153–180.
Adán, S. (2014). Dark matter, the equivalence principle and modified gravity. Studies in History and Philosophy of Modern Physics, 45, 66–71.
Aguirre, A. (2004). Alternatives to Dark Matter (?). IAU Synposium 220: Dark Matter in Galaxies, (pp. 1–11).
Bekenstein, J. D. (2004). Relativistic gravitation theory for the modified Newtonian dynamics paradigm. Physical Review D, 70(8), 1–28.
Belot, G. (2015). Down to earth underdetermination. Philosophy and Phenomenological Research, 91(2), 456–464.
Bertone, G., & Tait, T. M. (2018). A new era in the search for dark matter. Nature, 562, 51–56.
Blair, A. (1990). Tycho Brahe’s critique of Copernicus and the Copernican System. Journal of the History of Ideas, 51(3), 355–377.
Boran, S., Desai, S., Kahya, E., & Woodard, R. (2018). GW170817 falsifies dark matter emulators. Physical Review D, 97(4), 041501.
Bournaud, F., Duc, P. A., & Brinks, E. (2007). Missing mass in collisional debris from galaxies. Science, 316(5828), 1166–1169.
Clowe, D., Gonzalez, A., & Markevitch, M. (2004). Weak-lensing mass reconstruction of the interacting cluster 1E 0657–558: Direct evidence for the existence of dark matter. The Astrophysical Journal, 604, 596–603.
De Baerdemaekerr, S., & Dawid, R. (2022). MOND and meta-empirical theory assessment. Synthese, 200, 344.
de Blok, W., & McGaugh, S. S. (1998). Testing modified Newtonian dynamics with low surface brightness galaxies: Rotation curve fits. The Astrophysical Journal, 508(1), 132–140.
Duhem, P. M. (1991 [1914]). The Aim and Structure of Physical Theory. (P. Wiener, Trans.) Princeton: Princeton University Press.
Earman, J. (1992). Bayes or Bust? A Critical Examination of Bayesian Confirmation Theory. The MIT Press.
Earman, J. (1993). Underdetermination, realism, and reason. Midwest Studies in Philosophy, 18, 19–38.
Famaey, B., & McGaugh, S. (2012). Modified newtonian dynamics (MOND): Observational phenomenology and relativistic extensions. Living Reviews in Relativity, 15(10). https://doi.org/10.12942/lrr-2012-10
Gentile, G., Famaey, B., Combes, F., Kroupa, P., Zhao, H. S., & Tiret, O. (2007). Tidal dwarf galaxies as a test of fundamental physics. Astronomy & Astrophysics, 472, L25–L28.
Goldberg, S. (1970). In defense of ether: The British response to Einstein’s Special Theory of Relativity, 1905–1911. Historical Studies in the Physical Sciences, 2, 89–125.
Haghi, H., Kroupa, P., Banik, I., Wu, X., Zonoozi, A. H., Javanmardi, B., ... Zhao, H. (2019). A new formulation of the external field effect in MOND and numerical simulations of ultra-diffuse dwarf galaxies – application to NGC 1052-DF2 and NGC 1052-DF4. Monthly Notices of the Royal Astronomical Society, 487(2), 2441–2454.
Islam, T., & Dutta, K. (2019). Modified gravity theories in light of the anomalous velocity dispersion of NGC1052-DF2. Physical Review D, 100(10), 104049.
Jerabkova, T., Boffin, H. M., Beccari, G., de Marchi, G., de Bruijne, J. H., & Prusti, T. (2021). The 800 pc long tidal tails of the Hyades star cluster. Astronomy & Astrophysics, 647, A137.
Kosso, P. (2013). Evidence of dark matter, and the interpretive role of General Relativity. Studies in History and Philosophy of Modern Physics, 44, 143–147.
Kroupa, P., Haghi, H., Javanmardi, B., Zonoozi, A. H., Müller, O., Banik, I., ... Dabringhausen, J. (2018). Does the galaxy NGC1052–DF2 falsify Milgromian dynamics? Nature, 561, E4–E5.
Kroupa, P., Jerabkova, T., Thies, I., Pflamm-Altenburg, J., Famaey, B., Boffin, H. M., ... Thomas, G. (2022). Asymmetrical tidal tails of open star clusters: stars crossing their cluster’s práh† challenge Newtonian gravitation. Monthly Notices of the Royal Astronomical Society, 517(3), 3613–3639.
Kukla, A. (1996). Does every theory have empirically equivalent rivals? Erkenntnis, 44(2), 137–166.
Laudan, L., & Leplin, J. (1991). Empirical equivalence and underdetermination. The Journal of Philosophy, 88(9), 449–472.
Massimi, M. (2018). Three problems about multi-scale modelling in cosmology. Studies in History and Philosophy of Modern Physics, 64, 26–38.
McGaugh, S. S. (2015). A tale of two paradigms: The mutual incommensurability of LCDM and MOND. Canadian Journal of Physics, 93(2), 250–259.
Merritt, D. (2017). Cosmology and convention. Studies in History and Philosophy of Modern Physics, 57, 41–52.
Milgrom, M. (1983a). A modification of the Newtonian dynamics as a possible alternative to the hidden mass hypothesis. Th Astrophysical Journal, 270, 365–370.
Milgrom, M. (1983b). A modification of the Newtonian dynamics - implications for galaxies. The Astrophysical Journal, 270, 371–384.
Milgrom, M. (1983c). A modification of the Newtonian dynamics - implications for galaxy clusters. The Astrophysical Journal, 270, 385–389.
Milgrom, M. (2009). Bimetric MOND gravity. Physical Review D, 80(12), 1–15.
Milgrom, M. (2014). MOND laws of galactic dynamics. Monthly Notices of the Royal Astronomical Society, 437(3), 2531–2541.
Milgrom, M. (2015). MOND theory. Canadian Journal of Physics, 93(2), 107–118.
Norton, J. (1995). Eliminative induction as a method of discovery: How einstein discovered general relativity. In J. Leplin (Ed.), The creation of ideas in physics. The University of Western Ontario series in philosophy of science (Vol. 55). Springer. https://doi.org/10.1007/978-94-011-0037-3_3
Quine, W. V. (1975). On empirically equivalent systems of the world. Erkenntnis, 9(3), 313–328.
Sanders, R. H. (2003). Clusters of galaxies with modified Newtonian dynamics. Monthly Notice of the Royal Astronomical Society, 342(3), 901–908.
Sanders, R. H., & McGaugh, S. S. (2002). Modified Newtonian dynamics as an alternative to dark matter. Annual Review of Astronomy and Astrophysics, 40, 262–317.
Shen, Z., Danieli, S., van Dokkum, P., Abraham, R., Brodie, J. P., Conroy, C., ... Chowdhury, D. D. (2021). A Tip of the Red Giant Branch Distance of 22.1±1.2Mpc to the Dark Matter Deficient Galaxy NGC 1052–DF2 from 40 Orbits of Hubble Space Telescope Imaging. The Astrophysical Journal Letters, 914, L12.
Siebert, H. (2005). The early search for stellar parallax: Galileo, Castelli, and Ramponi. Journal for the History of Astronomy, 36(3), 251–271.
Sklar, L. (1975). Methodological conservatism. The Philosophical Review, 84(3), 374–400.
Skordis, C., & Złośnik, T. (2019). Gravitational alternatives to dark matter with tensor mode speed equaling the speed of light. Physical Review D, 100(10), 1–8.
Stanford, K. (2006). Exceeding Our Grasp: Science, History, and the Problem of Unconceived Alternatives. Oxford University Press.
van Dokkum, P., Danieli, S., Cohen, Y., Merritt, A., Romanowsky, A. J., Abraham, R., ... Zhang, J. (2018). A galaxy lacking dark matter. Nature, 555, 629–632.
Vanderburgh, W. L. (2003). The dark matter double bind: Astrophysical aspects of the evidential warrant for General Relativity. Philosophy of Science, 70(4), 812–832.
Vanderburgh, W. L. (2014). On the interpretive role of theories of gravity and ‘ugly’ solutions to the total evidence for dark matter. Studies in History and Philosophy of Modern Physics, 47, 62–67.
Verlinde, E. P. (2017). Emergent gravity and the dark universe. SciPost Physics, 2(3), 1–41.
Zwicky, F. (1937). On the masses of nebulae and of clusters of nebulae. The Astrophysical Journal, 86(3), 217–246.
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.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Ethical approval
N/A
Informed consent
N/A
Financial or non-financial interests
N/A
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
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
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s13194-023-00532-x