Dark matter as field instead of particle

Dark matter continues to be of uppermost concern for near and far reasons. The near reason is that most of the mass of galaxies seems to be missing because of the unexpected way they rotate, and far because standard cosmological theory doesn't work without it. This is about the near.

Virtually all searches for the identity of dark matter assume that it is some type of unfamiliar particle. After several decades the search continues. But what if dark matter exists but in an unexpected form? This was the subject of an earlier issue, * but it serves to illustrate the general utility of

m/r^2 = A/G, ....................................... (Newton)

where the left side is the mass to size ratio, which has been associated with the electron mass derivation and derived galactic supercluster acceleration (A ~ 6 x 10^-13 m/s^2) of late.

The rather popular Modified Newtonian Dynamics (MOND) assumes that classical (attractive) Newtonian gravity and general relativity are superfluous in such situations, and that dark matter does not exist in any form, and instead hypothesizes the fundamentally attractive

M/r^2 ≈ (a^2/a sub-0)/G?..................(MOND)

where?a sub-0 = (1.2 + or - 0.2) x 10^-10 m/s^2. "The basis of the modification is the assumption that in the limit of small acceleration a very low?a sub-0, the acceleration of a particle at distance?r?from a mass?M?satisfies approximately?a^2/a sub-0 ≈ MGr^-2, where?a sub-0?is a constant of the dimensions of an acceleration." **

Note the apparent similarity of relations (but dissimilarities in definitions) in general and of acceleration terms in particular,

(a^2/a sub-0) ~ > A

where the MOND term is three orders of magnitude larger than the mathematically unmodified (though repulsive) Newtonian. Recall, though, that the latter was derived at the galactic supercluster level with the standard mass and size ratio of the local supercluster, and the MOND is purely a mathematical fit to observed galaxy rotation patterns, and suitable primarily for the galaxy scale with the assumption that gravity is fundamentally attractive, patterned on "action at a distance" empirical Newtonian gravity, compiled at the Solar system scale. Thus MOND is an empiricism of an empiricism of the Solar system scale, and not a firm basis for the assumed absence of dark matter.?

In the Newtonian relation at the galaxy scale mass/energy should increase with the square of the radius toward proposed sources in large-scale space, while volume increases by the cube of the radius, so that galaxy density should decrease linearly with radius,?

ρ = (3/4Π)(A/G)?r^-1.

Fundamentally repulsive Newtonian gravity predicts dark matter as enhanced gravitational field to extend one order of magnitude beyond the visible matter of the Andromeda galaxy. While particulate matter might extend to twice galaxy radius, these differences could be settled by gravitational lens experiment of sufficient precision, in that the deflected light pattern in the former should be more laterally dispersed and smaller in peak magnitude.

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* Nov 30, 2021?An explanation of dark matter and dark energy from unmodified Newtonian gravity* | LinkedIn

** M. Milgrom, Astrophysical Journal. 270, 365 (1983a) https://ui.adsabs.harvard.edu/link_gateway/1983ApJ...270..365M/doi:10.1086/161130?

M. Milgrom, Scholarpedia, 9(6):31410?(2014)??https://dx.doi.org/10.4249/scholarpedia.31410