Gravity
Gravity words.
| a₀ | The acceleration below which gravity in galaxies stops behaving as Newton predicts: about 10−10 m/s², a hundred billion times weaker than gravity at the Earth's surface. In this model it equals cH₀/2π, the speed of light times the expansion rate of the Universe divided by 2π, and is not fitted. |
| MOND | Modified Newtonian Dynamics (Milgrom 1983): the rule that below a₀ the pull is stronger than Newton's, in a way that reproduces galaxy rotation without dark matter. This site's law is a variant of MOND. |
| Phantom, phantom halo, phantom disc | The extra pull, described as if it came from invisible mass. A local MOND law puts that mass in a thin disc; the measurements want a round halo; this model gives a halo. |
| Monopolar response | The extra pull depends only on the total mass enclosed within your radius, as if that mass were a point at the centre. It ignores the local shape of the matter around you. |
| Local law | Any rule where the extra pull at a point depends on the ordinary gravitational field at that same point. All such rules are excluded by the Milky Way's vertical potential. |
| External-field effect (EFE) | In MOND, a system's internal gravity depends on the field of its surroundings, which breaks the strong equivalence principle. Detected in galaxies (Chae et al. 2020); it is why a local MOND law predicts a tidal distortion of the outer Solar System that Cassini does not see. |
| Vertical potential | How strongly stars are pulled back toward the plane of the Milky Way as they bob above and below it, measured with Gaia. The decisive data set of this site. |
| Q₂, the Saturn quadrupole | A tidal distortion of the gravitational field around the Sun that a local MOND law predicts and that the tracking of the Cassini spacecraft bounds. This model predicts essentially zero. |
| Formation memory | The rule that a system born from a dense collapse (a star cluster, the Solar System) is Newtonian for good, while one born from diffuse gas (a galaxy) shows the extra pull. It sorts Pal 14 from a dwarf galaxy of the same size and mass. |
| The medium that collapsed with a star's natal cloud and stays fully engaged around the star, 0.05 to 0.4 parsec across. The reason the Solar System is Newtonian. Formerly called an occlusion on this site. | |
| Wide binaries | Pairs of stars orbiting each other at thousands to tens of thousands of astronomical units, where their mutual pull is below a₀. Gaia measures them. This model predicts Newton at every separation; a boost would kill it. |
| Strong and weak equivalence principle | Weak: everything falls the same way, kept here. Strong: the laws of physics inside a freely falling box do not depend on the outside field, broken here, as in MOND, and as observed. |
| AeST | Aether Scalar Tensor theory (Skordis & Złośnik 2021): a relativistic theory that contains general relativity, reproduces MOND in galaxies and the cosmic microwave background. This site borrows it as the relativistic completion of the model. |
Data
Data words.
| SPARC | A catalogue of 175 galaxies with precise rotation curves and infrared photometry (Lelli, McGaugh & Schombert 2016). The 147 used here give 2,675 measured points. |
| Radial acceleration relation (RAR) | In galaxies, the observed acceleration is a tight function of the acceleration the visible matter alone would give. Its scatter, 0.13–0.14 dex, is what any model must match. |
| dex | A factor of ten. 0.138 dex of scatter means the points spread by about 37% (100.138 = 1.37) around the curve. |
| χ² | A goodness-of-fit number: the sum of squared mismatches between model and data in units of the measurement errors. Lower is better; a factor of 10 to 40 between two models is decisive. |
| Gaia DR3, DR4 | Data releases of the European Gaia satellite, which measures positions and motions of a billion stars. DR4 is due in December 2026 and will decide the wide-binary test. |
| Cassini bound | The limit on any anomalous tidal field near Saturn from the radio tracking of the Cassini spacecraft (Park et al. 2026): Q₂ below 3×10−27 s−2. |
| Pal 14, Segue 1, Crater II | Pal 14 is a distant, diffuse star cluster that behaves as Newton predicts. Segue 1 is an ultra-faint dwarf galaxy of similar size and mass that moves far too fast for its visible matter, a failure of every MOND-type law including this one. Crater II is a large, diffuse dwarf galaxy whose motions MOND predicted before they were measured. |
| GWTC-3, GWTC-4.0, GW250114 | Catalogues of gravitational-wave events from LIGO, Virgo and KAGRA, and the loudest single event, used here to bound what the vacuum medium can and cannot be. |
| S2 | A star that orbits the black hole at the centre of the Milky Way every 16 years, reaching 8,000 km/s. Its Keplerian orbit bounds how much the medium can feel the black hole's horizon. |
The medium
Medium words.
| The medium, the vacuum lattice | The hypothetical material filling space whose deformation would be the extra pull. Made of elements with slack and hard cores, sitting in spacetime, not being it. |
| Slack, engaged | An element carries no force until the strain on it exceeds its slack; then it is engaged and pushes back like a spring. Few engaged: soft response, MOND. All engaged: Newton. |
| u and ν | u is the strain on an element, the gravitational field divided by a₀. ν(u) is the boost factor of the pull, near 1 at high field and large at low field. |
| Soft glass, jamming | A disordered solid whose elements yield at distributed thresholds. Jamming is the point where hard cores lock the structure so it cannot rearrange: the mechanism of the memory. |
| de Sitter temperature | The temperature that the expanding Universe's horizon gives the vacuum: 2.8×10−30 kelvin. In the model it sets the slack of the elements, hence a₀. |
| Unruh effect | An accelerating observer sees the vacuum as slightly warm. The model's deepest and least proven step is that the medium's elements respond to this warmth. |
| Smectic medium | A medium organised in smooth layers, like a liquid crystal, responding only to the field component normal to the layers. It is what makes the response monopolar and the memory obligatory. |
The early Universe
Early-Universe words.
| Redshift z | How much the Universe has expanded since light left an object. z = 10 is about 470 million years after the Big Bang, z = 20 about 180 million. |
| Population III | The first generation of stars, made of hydrogen and helium only. None has been observed directly; their masses are inferred from the chemistry of the oldest stars and from He II emission at high redshift. |
| Pair-instability supernova (PISN) | The explosion that ends a star of 140–260 solar masses, leaving no remnant and a distinctive chemical fingerprint. No star carrying that fingerprint has been confirmed. |
| Jeans mass | The smallest lump of gas that gravity can make collapse against its own pressure. Stronger effective gravity lowers it, so clouds fragment into smaller stars. |
| Heavy seed, direct collapse | A black hole born at ten thousand to a hundred thousand solar masses from a gas cloud that collapsed without first forming ordinary stars. Needed to explain the oversized black holes JWST sees at z ≈ 10. |
| Eddington limit | The fastest a black hole can swallow gas before its own radiation blows the gas away: doubling its mass roughly every 45 million years. Unchanged in this model. |
| IMF, characteristic mass mch, slope x | The initial mass function is the distribution of masses at which stars are born; mch is its typical mass and x its slope at high mass (Salpeter's value is 2.35). |