Is MOND necessarily nonlinear?
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915285386133504 |
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| author | Milgrom, Mordehai |
| author_facet | Milgrom, Mordehai |
| contents | The iconic, deep-MOND-limit (DML) relation between acceleration and mass, $a\sim (M\mathcal{A}_0)^{1/2}/r$, implies that, in MOND, accelerations cannot be linear in the mass distribution ($\mathcal{A}_0\equiv Ga_0$ is the DML constant, and $a_0$ the MOND acceleration). This leads to important idiosyncracies of MOND, such as a breakdown of the strong equivalence principle, and the resulting ``external-field effect''. I show that the DML axioms are, in themselves, consistent with a, possibly unique, nonrelativistic, action-based, linear formulation of the DML. This model suffers from important drawbacks, which may make it unacceptable as a basis for a full-fledged MOND theory. The model is unique among MOND theories propounded to date not only in being linear -- hence not exhibiting an external-field effect, for example -- but in constituting a modification of both Newtonian inertia and Newtonian gravity. This linear and time-local model inspires and begets several, one-parameter families of models. One family employs nonlinear, time-nonlocal kinetic terms, but still linear gravitational-field equations. Other families generalize the DMLs of AQUAL and QUMOND, modifying gravity as well as inertia. All families employ fractional time derivatives and possibly fractional Laplacians. At present, I cannot base some acceptable MOND theory on these models -- for example, I cannot offer a sensible umbrella theory that interpolates between these DML models and Newtonian dynamics. They are, however, quite useful in elucidating various matter-of-principle aspects of MOND; e.g., they help to understand which predictions follow from only the basic tenets of MOND -- so-called primary predictions -- and which are secondary, i.e., theory dependent. The models may also show the way to a wider class of MOND theories. (Abridged.) |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_07106 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Is MOND necessarily nonlinear? Milgrom, Mordehai General Relativity and Quantum Cosmology Cosmology and Nongalactic Astrophysics Astrophysics of Galaxies High Energy Physics - Phenomenology The iconic, deep-MOND-limit (DML) relation between acceleration and mass, $a\sim (M\mathcal{A}_0)^{1/2}/r$, implies that, in MOND, accelerations cannot be linear in the mass distribution ($\mathcal{A}_0\equiv Ga_0$ is the DML constant, and $a_0$ the MOND acceleration). This leads to important idiosyncracies of MOND, such as a breakdown of the strong equivalence principle, and the resulting ``external-field effect''. I show that the DML axioms are, in themselves, consistent with a, possibly unique, nonrelativistic, action-based, linear formulation of the DML. This model suffers from important drawbacks, which may make it unacceptable as a basis for a full-fledged MOND theory. The model is unique among MOND theories propounded to date not only in being linear -- hence not exhibiting an external-field effect, for example -- but in constituting a modification of both Newtonian inertia and Newtonian gravity. This linear and time-local model inspires and begets several, one-parameter families of models. One family employs nonlinear, time-nonlocal kinetic terms, but still linear gravitational-field equations. Other families generalize the DMLs of AQUAL and QUMOND, modifying gravity as well as inertia. All families employ fractional time derivatives and possibly fractional Laplacians. At present, I cannot base some acceptable MOND theory on these models -- for example, I cannot offer a sensible umbrella theory that interpolates between these DML models and Newtonian dynamics. They are, however, quite useful in elucidating various matter-of-principle aspects of MOND; e.g., they help to understand which predictions follow from only the basic tenets of MOND -- so-called primary predictions -- and which are secondary, i.e., theory dependent. The models may also show the way to a wider class of MOND theories. (Abridged.) |
| title | Is MOND necessarily nonlinear? |
| topic | General Relativity and Quantum Cosmology Cosmology and Nongalactic Astrophysics Astrophysics of Galaxies High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2503.07106 |