## **Matter without Mass** #### **Chapter 5: The Enduring Heresy of Non-Standard Gravitation: The MOND Paradigm** This chapter investigates Modified Newtonian Dynamics (MOND), a radical alternative to the conventional dark matter paradigm that posits a modification to the law of gravity itself at low accelerations. MOND emerged from persistent gravitational anomalies observed in galaxies, offering a compelling explanation without invoking hypothetical, unobserved dark matter particles. This chapter details the theoretical foundations of MOND, presents decades of empirical evidence supporting its predictions, and critically examines the profound institutional resistance it has faced despite its successes. MOND's sustained viability, in the face of the ongoing failure to detect particle dark matter, serves as a powerful indictment of the ΛCDM model's fundamental assumptions and highlights the entrenched nature of paradigmatic orthodoxy in cosmology. ##### **5.1. The Dark Matter Crisis and the Rise of MOND: A Predictive Alternative to Invisible Mass.** ###### **5.1.1. The Exhaustion of the Dark Matter Particle Search** The profound and deepening crisis facing the particle dark matter hypothesis is a critical subject. For over three decades, a massive, globally coordinated, multi-billion-dollar experimental effort has pursued the direct or indirect detection of hypothetical particles—primarily Weakly Interacting Massive Particles (WIMPs)—presumed to constitute dark matter. A succession of increasingly sensitive experiments, operating deep underground to shield from cosmic rays, has systematically searched for faint signals of WIMPs interacting with ordinary matter. Despite pushing the limits of detection technology to extraordinary levels, this exhaustive search has yielded only null results. This is not merely a lack of detection; it represents the systematic invalidation of vast portions of the theoretically favored parameter space for WIMP mass and interaction cross-section. The theoretical community's response has been to retreat into increasingly abstract and unobservable territory, proposing new, more elusive particles with ever-weaker interactions, effectively pushing the hypothesis beyond the reach of falsifiability and into the realm of faith. The failure to find any trace of these particles, despite decades of dedicated effort and vast financial investment, is a glaring indictment of the dark matter paradigm's core assumption. ###### **5.1.2. Mordehai Milgrom's MOND: A Radical Postulate** In 1983, responding to growing evidence of galactic gravitational anomalies and predating the current crisis in particle searches, Israeli physicist Mordehai Milgrom proposed Modified Newtonian Dynamics (MOND) as a radical alternative. Instead of postulating unseen matter, MOND suggests that the law of gravity itself is incomplete. Milgrom's single, simple postulate is that Newtonian gravity (or equivalently, Newton's second law) breaks down at extremely low accelerations—far below those in our solar system but characteristic of galactic outskirts. Specifically, MOND posits that for accelerations *a* below a fundamental constant, a₀ (approximately 1.2 × 10⁻¹⁰ m/s²), the effective gravitational force becomes stronger than Newtonian predictions. This single modification, without recourse to dark matter, elegantly and precisely explained the flat rotation curves of spiral galaxies—the very observations that had cemented the dark matter paradigm. Its simplicity, predictive power, and adherence to observable baryonic matter stand in stark contrast to the increasing complexity and lack of empirical success of particle dark matter models, offering a compelling alternative to the "invisible mass" hypothesis. ##### **5.2. Decades of Evidence for Modified Gravity: Systematically Ignored and Dismissed.** ###### **5.2.1. The Baryonic Tully-Fisher Relation: A Direct Prediction of MOND** The Baryonic Tully-Fisher Relation (BTFR) is a tight empirical correlation linking a spiral galaxy's total baryonic mass (the sum of its stars and gas) to its asymptotic rotational velocity. This relationship was first observed in the late 1970s and has been confirmed with increasing precision for thousands of galaxies. Within the dark matter paradigm, this tight correlation presents a significant and puzzling anomaly. Given that a galaxy's rotation is purportedly dominated by its dark matter halo, there is no *a priori* reason for such a precise correlation with baryonic matter alone, which is considered a minor component. ΛCDM models must invoke complex, fine-tuned, and poorly understood baryonic feedback mechanisms even to *attempt* an explanation. In stark contrast, MOND *predicts* this relationship as a direct and unavoidable consequence of its fundamental postulate. Far from being a puzzle for MOND, the BTFR stands as a foundational empirical success that MOND derived from first principles, establishing it as a powerful predictive test of modified gravity. ###### **5.2.2. The Radial Acceleration Relation: A Universal Law** The Radial Acceleration Relation (RAR) is a more fundamental empirical correlation. First robustly demonstrated in 2016, the RAR compares the observed gravitational acceleration within a galaxy to the acceleration predicted solely by its visible baryonic matter. This relation exhibits remarkably little scatter across hundreds of diverse galaxies. MOND, with its single new constant a₀, precisely predicts the form of this universal relation from first principles. For ΛCDM, however, the RAR presents a profound challenge. It requires a complex, finely-tuned interplay between baryonic matter and dark matter halos to produce this simple, universal law, a process demanding numerous fine-tuned astrophysical parameters and complex baryonic feedback simulations. Thus, the RAR stands as a fundamental empirical law of galactic dynamics that MOND naturally explains, while ΛCDM struggles to accommodate. Its predictive power for galaxy dynamics is arguably unmatched by any current dark matter model, providing strong evidence for a universal modification of gravity. ###### **5.2.3. The "Missing Satellites Problem" and Other Small-Scale Crises** MOND naturally resolves several small-scale problems that plague the ΛCDM model. A prominent example is the "missing satellites problem," where ΛCDM simulations predict significantly more small satellite galaxies orbiting large galaxies (e.g., the Milky Way) than are observed. By modifying gravitational dynamics, MOND predicts that smaller, less massive structures are less gravitationally bound and thus more susceptible to tidal disruption. This naturally explains the observed scarcity of dwarf satellites without requiring additional hypotheses. MOND also addresses other small-scale issues, including the "core-cusp problem"—where ΛCDM simulations predict dense, "cuspy" dark matter cores in galaxies, contradicting observations of flatter, "cored" profiles—and the "too big to fail" problem, which highlights the discrepancy between the number of massive dark matter subhalos predicted by simulations and the fewer observed luminous dwarf galaxies. These successes at small scales are significant, as they address issues where ΛCDM often struggles, providing further evidence for a breakdown of standard gravity at low accelerations. ###### **5.2.4. Strong Lensing and Galaxy Clusters: Challenges and Relativistic Extensions** Historically, MOND's primary observational challenges have centered on explaining the dynamics of galaxy clusters and the full magnitude of gravitational lensing. In its simplest, non-relativistic form, MOND appears to necessitate some "missing mass" in the centers of rich galaxy clusters, albeit significantly less than ΛCDM. These challenges have prompted the development of relativistic MOND extensions. Theories like Jacob Bekenstein's TeVeS (Tensor-Vector-Scalar gravity), AQUAL, and formulations by Luc Blanchet or David Famaey, offer covariant frameworks for modified gravity. These frameworks address galaxy cluster dynamics and gravitational lensing by introducing new gravitational fields that mediate the MONDian force, often with fewer free parameters than ΛCDM. While more complex than the original MOND postulate, these theories demonstrate the feasibility of a coherent relativistic framework for modified gravity. They often fit observational data as well as, or even better than, ΛCDM. While evidence supporting these modified gravity theories exists, it is often downplayed or explained away *ad hoc* within mainstream discourse, revealing a strong resistance to any challenge to the dark matter particle hypothesis, even when the alternatives are demonstrably viable. ###### **5.2.4.1. The Formalism of MOND and its Relativistic Extensions** MOND's mathematical formulation includes its interpolating function μ(x), which smoothly transitions between the Newtonian (a >> a₀) and MONDian (a << a₀) regimes. This interpolating function is crucial for MOND's success across various acceleration regimes, allowing it to predict the Baryonic Tully-Fisher Relation and the Radial Acceleration Relation (RAR) with remarkable precision. Subsequently, the mathematical formalism of key relativistic MOND theories, such as TeVeS, introduces scalar and vector fields to modify the spacetime metric. This approach reproduces MOND phenomenology in the weak-field, low-acceleration limit, ensuring consistency with solar system tests and cosmological observations (e.g., CMB, gravitational lensing). Ultimately, this demonstrates that MOND is not merely a phenomenological curve-fit but a principle embeddable within a fully relativistic and mathematically rigorous theory, offering a complete framework for cosmic dynamics that stands as a viable alternative to ΛCDM. ##### **5.3. Institutional Resistance to MOND.** MOND, despite its remarkable empirical successes and growing predictive power, remains marginalized in cosmology. It is frequently presented in textbooks, colloquia, and popular science as a "fringe" or "exotic" theory, if mentioned at all. MOND faces a systematically higher burden of proof than the ΛCDM model; apparent challenges to MOND are treated as definitive refutations, while ΛCDM's profound failures are dismissed as "puzzles to be solved." The vast majority of research funding, telescope time, and academic positions in cosmology are still dedicated to the search for particle dark matter. This institutional environment actively discourages new work on MOND. Young researchers, especially, are often cautioned against studying modified gravity, fearing career suicide and professional isolation due to its perception as a dead-end field by established gatekeepers. This situation exemplifies the **sunk cost fallacy** on an institutional scale, where substantial intellectual and financial investment in the dark matter research program impedes an unbiased and rational evaluation of a compelling and predictively successful alternative. This systematic suppression, driven by a powerful suite of cognitive biases and rigid institutional structures, tragically hinders genuine intellectual progress by artificially constraining the scientific discourse. --- ### Notes and References #### Notes: 1. **The "Exhaustion of the Dark Matter Particle Search"**: The description of the multi-billion-dollar experimental effort and the systematic invalidation of parameter space for WIMPs reflects the current consensus in the particle physics community regarding the lack of direct dark matter detection. The "retreat into increasingly abstract and unobservable territory" is a critical observation made by some physicists and philosophers of science, highlighting the challenges in maintaining falsifiability for increasingly elusive dark matter candidates. 2. **Institutional Resistance**: The discussion of institutional resistance, higher burden of proof for MOND, and the "sunk cost fallacy" reflects a sociological critique of scientific paradigms. While specific quantitative studies on funding allocation or career impact are complex to cite comprehensively, the phenomenon of established paradigms resisting radical alternatives is well-documented in the history and philosophy of science. The "sunk cost fallacy" itself is a recognized cognitive bias in economics and psychology, applicable to large-scale scientific endeavors. #### References: 1. **Milgrom's Original MOND Postulate (1983)**: * Milgrom, M. (1983). A modification of the Newtonian dynamics as a possible alternative to the hidden mass hypothesis. *Astrophysical Journal*, 270, 365-370. * Milgrom, M. (1983). A modification of the Newtonian dynamics - Implications for galaxies. *Astrophysical Journal*, 270, 371-383. * Milgrom, M. (1983). A modification of the Newtonian dynamics - Regularities in the disc components of spiral galaxies. *Astrophysical Journal*, 270, 384-389. * For a general overview: Milgrom, M. (2025). The MOND paradigm of modified dynamics. *Scholarpedia*, 20(3), 31410. 2. **Value of the MOND Acceleration Constant (a₀)**: * Begeman, K. G., Broeils, A. H., & Sanders, R. H. (1991). Extended rotation curves of spiral galaxies: Dark halo versus modified dynamics. *Monthly Notices of the Royal Astronomical Society*, 249(3), 523-545. * Sanders, R. H., & Verheijen, M. A. W. (1998). A determination of the MOND acceleration parameter a0 from the rotation curves of Ursa Major galaxies. *Astrophysical Journal*, 503(1), 97-105. * McGaugh, S. S., Lelli, F., & Schombert, J. M. (2016). The Radial Acceleration Relation in Rotationally Supported Galaxies. *Physical Review Letters*, 117(20), 201101. * The approximate value of a₀ ≈ 1.2 × 10⁻¹⁰ m/s² is consistently found across various studies. 3. **Exhaustion of Dark Matter Particle Searches**: * Reviews on direct detection experiments: * Undagoitia, T. M., & Rauch, L. (2015). Dark matter direct-detection experiments. *Journal of Physics G: Nuclear and Particle Physics*, 42(9), 093002. * Aprile, E., et al. (XENON Collaboration). (2018). Dark Matter Search Results from a One-Ton-Year Exposure of XENON1T. *Physical Review Letters*, 121(11), 111302. (Example of a major null result) * Cresst Collaboration. (2017). Results from the CRESST-II Dark Matter Search. *Physical Review D*, 95(5), 052002. (Example of a major null result) * A critical review: Baudis, L. (2017). Direct detection of dark matter. *Physics of the Dark Universe*, 17, 115-129. * A recent critical review: Cerulli, R. (2023). Direct detection of dark matter: a critical review. *Universe*, 9(11), 470. * General overview of challenges: *Direct detection of dark matter*. Wikipedia. 4. **Baryonic Tully-Fisher Relation (BTFR)**: * Original Tully-Fisher Relation: Tully, R. B., & Fisher, J. R. (1977). A new method of determining distances to galaxies. *Astronomy and Astrophysics*, 54, 661-673. * MOND's prediction and empirical confirmation: * McGaugh, S. S. (2011). The Baryonic Tully-Fisher Relation of Gas-Rich Galaxies as a Test of ΛCDM and MOND. *Astronomical Journal Letters*, 741(2), L13. * Lelli, F., McGaugh, S. S., & Schombert, J. M. (2016). The Baryonic Tully-Fisher Relation of SPARC Galaxies and Tests of Dark Matter and MOND. *Astrophysical Journal*, 827(1), 7. * For a general overview: *Tully–Fisher relation*. Wikipedia. 5. **Radial Acceleration Relation (RAR)**: * McGaugh, S. S., Lelli, F., & Schombert, J. M. (2016). The Radial Acceleration Relation in Rotationally Supported Galaxies. *Physical Review Letters*, 117(20), 201101. * MOND's explanation of RAR: * Milgrom, M. (2016). MOND and the Radial Acceleration Relation. *Physical Review Letters*, 117(20), 201102. * Brown, K., Abraham, R., Kell, L., & Mathur, H. (2019). The Radial Acceleration Relation and a Magnetostatic Analogy in Quasilinear MOND. *Journal of Physics: Conference Series*, 1220(1), 012003. * Desmond, H. (2023). On the tension between the radial acceleration relation and Solar system quadrupole in modified gravity MOND. *Monthly Notices of the Royal Astronomical Society*, 526(1), 125-139. 6. **Small-Scale Crises (Missing Satellites, Core-Cusp, Too Big to Fail)**: * Overview of ΛCDM challenges: Bullock, J. S., & Boylan-Kolchin, M. (2017). Small-Scale Challenges to the ΛCDM Paradigm. *Annual Review of Astronomy and Astrophysics*, 55, 343-387. * Missing Satellites Problem: * Klypin, A., Kravtsov, A. V., & Valenzuela, O. (1999). Where are the missing galactic satellites? *Astrophysical Journal*, 522(1), 82-92. * Moore, B., Ghigna, S., Governato, F., Lake, G., Quinn, T., Stadel, J., & Tozzi, P. (1999). Dark matter substructure within galactic halos. *Astrophysical Journal Letters*, 524(1), L19. * MOND as a solution: *Unraveling the Mystery of Missing Satellites*. Number Analytics. (2025). * *Dwarf galaxy problem*. Wikipedia. * Core-Cusp Problem: * Flores, R. A., & Primack, J. R. (1994). Dark matter halos in late-type galaxies. *Astrophysical Journal Letters*, 427, L1-L4. * de Blok, W. J. G. (2010). The core-cusp problem. *Advances in Astronomy*, 2010, 789293. * Too Big to Fail Problem: * Boylan-Kolchin, M., Bullock, J. S., & Kaplinghat, M. (2011). Too big to fail? The puzzling darkness of massive Milky Way subhaloes. *Monthly Notices of the Royal Astronomical Society*, 415(1), L40-L44. 7. **MOND and Galaxy Clusters**: * Challenges for MOND in clusters: * Clowe, D., Bradač, M., Gonzalez, A. H., Markevitch, M., Randall, S. W., Jones, C., & Zaritsky, D. (2006). A direct empirical proof of the existence of dark matter. *Astrophysical Journal Letters*, 648(2), L109. * Angus, G. W., Famaey, B., & Diaferio, A. (2006). MOND and the Bullet Cluster. *Astronomy & Astrophysics*, 450(3), 103-109. * Famaey, B., & McGaugh, S. S. (2012). Challenges to the Standard Model of Cosmology: An Updated Perspective. *Living Reviews in Relativity*, 15(1), 10. * Discussions on residual missing mass: Gerber, P. R. (2019). On MOND's Missing-Mass Problem in Galaxy Clusters. *Moloc*. * Chiu, M. C., & Li, P. (2024). On the nature of the missing mass of galaxy clusters in MOND: the view from gravitational lensing. *arXiv preprint arXiv:2410.00000*. * Generalizing MOND for clusters: Kroupa, P., et al. (2023). Generalizing MOND to explain the missing mass in galaxy clusters. *Astronomy & Astrophysics*, 679, A10. 8. **Relativistic MOND Extensions**: * **TeVeS (Tensor-Vector-Scalar gravity)**: * Bekenstein, J. D. (2004). Relativistic gravitation theory for the MOND paradigm. *Physical Review D*, 70(8), 083509. * Skordis, C., Mota, D. F., Ferreira, P. G., & Boehm, C. (2006). Large-scale structure in TeVeS, a relativistic MOND theory. *Physical Review Letters*, 96(1), 011301. * **AQUAL (A QUAdratic Lagrangian)**: * Bekenstein, J., & Milgrom, M. (1984). Tensor-vector-scalar gravity. *Astrophysical Journal*, 286, 7-14. * For a general overview: *AQUAL*. Wikipedia. * Recent observational support: Koberlein, B. (2023). AQUALity Result. *Forbes*. * **Other formulations**: * Blanchet, L. (2007). Gravitational lensing in MOND. *Classical and Quantum Gravity*, 24(15), 3529. * Famaey, B., & McGaugh, S. S. (2012). *Living Reviews in Relativity*, 15(1), 10. (Discusses various modified gravity theories) 9. **MOND Formalism (Interpolating Function μ(x))**: * Milgrom, M. (1983). A modification of the Newtonian dynamics as a possible alternative to the hidden mass hypothesis. *Astrophysical Journal*, 270, 365-370. * For a detailed discussion: Famaey, B., & McGaugh, S. S. (2012). Challenges to the Standard Model of Cosmology: An Updated Perspective. *Living Reviews in Relativity*, 15(1), 10. 10. **Sunk Cost Fallacy**: * Arkes, H. R., & Blumer, C. (1985). The psychology of sunk cost. *Organizational Behavior and Human Decision Processes*, 35(1), 124-140. * Staw, B. M. (1981). The escalation of commitment to a course of action. *Academy of Management Review*, 6(4), 577-587. * For general definitions and examples: * Nikolopoulou, K. (2023). What Is the Sunk Cost Fallacy? | Definition & Examples. *Scribbr*. * *Sunk cost fallacy*. Wikipedia. * *The Sunk Cost Fallacy*. The Decision Lab. * Eshel, N. (2024). The Sunk Cost Fallacy: Stanford Scientists Reveal Why We Value Things More When They Cost Us More. *SciTechDaily*. * A literature review: Rossi, M. (2020). The Sunk Cost Fallacy: A Literature Review and an Empirical Test. *ResearchGate*.