Alberto

Which work have you read? The book? Would you kindly mention what do you mean by a0 and general potentials? If a0 is a kind of MOND constant, it cannot have the exact value there, because it is a theory and not a fitting sample. I'm also a bit doubtful about the impossibility of geometrization. Could you write a couple of words about it? It could throw a new light.

"Different authors" and "many theories" don't tell me too much. Aside from AQUAL, PCG, TeVeS, one can also peep into 'Alternative theories of gravitation' in Wikipedia and find others. Discussing WHO PREFERS WHAT - either change in inertia or change in gravitational interaction - is also not very fruitful, because science is neither a question of personal taste nor a question settled by a Parliament majority (though, unfortunately, the current mainstream resembles this ruling party very much ). If one just chooses, say, a law of gravitation to be SUCH&SUCH, it doesn't mean that we have got a theory, even if it describes the observations. This is NOT first principles. Those extra fields that one can find in most of the alternatives (including the covariantized MOND) are hardly better than dark matter. Actually, it is just it that those fields describe. The first principles could be the principle of relativity or the principle of equivalence, then they could lead to the geometrization... But since the way it was done in GRT caused the descrepancies on the galactic scale, and, consequently, the introduction of huge dark matter with the property of non-observability, it means that there is a need for another set of principles. By the way, the anisotropic geometrodynamics which I mentioned before uses equivalence first and relativity only afterwords and only as a limit case. That is, it starts with the world full of gravitating masses and only then looks what would be if there is no masses. And not vice versa as it is usually done. It seems logical and attractive, especially when I find no DM in the end. The law of gravitation has also changed there, but not because the author decided that it should be 'like that' or used the observations. It just TURNED OUT that it SHOULD be slightly different in a specific manner, if we follow the line of speculations stemming from the chosen first principles. The cH coincidence is explained there too.

OK, as you like. But I would only appreciate, if you mention those first principles. I mean, not the statement that the Newton law should be changed (because of the observations), but the reasons why it should be changed for exactly the form it obtains in MOND. I'm also interested in "several theories" deriving MOND, and it would be really geat if you mention two or three of them. Though if you mean the Beckenstein approach, one can say that it possesses the same drawback as other alternatives to the GRT. As to the constant, Milgrom does mention that it is rather close to the cH product, but no reason for that is suggested and no role of c and H in MOND is explained.

The observations show that the spiral galaxies' axis are strangely alined for the galaxies belonging to a wall. It doesn't seem that the Universe possesses a spin axis of its own, though the existence of such a feature as the Axis of Evil is really curious. At the same time, the rotational or better say tangential motions in the Universe are definitely underestimated (see, for example, the Anisotropic Geometrodynamics theory).

The problem with MOND is that it is a phenomenological theory that uses arbitrary functions and some new constant to fit observations. That is why in some cases it goes wrong. This is not so with, say, Anisotropic Geometrodynamics which provides the same results starting from the first principles and using already known constants. And no dark matter is needed there as well.