MOND (split from New Study Claims Dark Matter Doesn’t Exist)

[martillo]

Why, in spite of modifying Newton's second law, not to modify the Gravity Law? Why not, just for instance, to just consider it having two terms one relevant at planetary systems (proportional to 1/r²) scale and the other at galactic scales (proportional to 1/r)? This could be if each term would have a factor making them neglihible at the other scales something not so difficult to imagine, I think. Afterall Newton didn't know about galaxies dynamics. Is that this cannot be compatible with Relativity Theory?

Edited February 19, 2021 by martillo

[Markus Hanke]

6 hours ago, martillo said:

Why, in spite of modifying Newton's second law, not to modify the Gravity Law? Why not, just for instance, to just consider it having two terms one relevant at planetary systems (proportional to 1/r²) scale and the other at galactic scales (proportional to 1/r)? This could be if each term would have a factor making them neglihible at the other scales something not so difficult to imagine, I think. Afterall Newton didn't know about galaxies dynamics. Is that this cannot be compatible with Relativity Theory?

Yes, it is possible to do this - both in the purely Newtonian domain, and as a relativistic theory. This is essentially what’s known as MOND (and relativistic MOND). 
The trouble is that the modification yields residual effects even on smaller scales, which can be experimentally tested for; the most well known of these effects would be that in most MOND models gravitational waves would propagate slower than the speed of light; but we know from observation that such waves do indeed seem to propagate at c, which eliminates a large number of MOND theories. The remaining MOND models then cannot fully explain the observed motions of galaxies and galaxy clusters, so they offer no real advantage over traditional Dark Matter.

[martillo]

15 hours ago, Markus Hanke said:

Yes, it is possible to do this - both in the purely Newtonian domain, and as a relativistic theory. This is essentially what’s known as MOND (and relativistic MOND). 
The trouble is that the modification yields residual effects even on smaller scales, which can be experimentally tested for; the most well known of these effects would be that in most MOND models gravitational waves would propagate slower than the speed of light; but we know from observation that such waves do indeed seem to propagate at c, which eliminates a large number of MOND theories. The remaining MOND models then cannot fully explain the observed motions of galaxies and galaxy clusters, so they offer no real advantage over traditional Dark Matter.

Seems you are confusing something. MOND theory (or theories) modifies Newton's Second Law F = ma by placing a factor µ = µ(a/a₀) in the equation: F = m.µ(a/a₀).a which, as it is said (https://en.wikipedia.org/wiki/Modified_Newtonian_dynamics),  introduces effects in systems with very slow accelerations. This would produce the effect of a centripetal force varying with 1/r in distance in spite of the classical 1/r² in the outer stars of the galaxies. 

What I'm talking about is to NOT modify Newton's Second Law F = ma but modify the Gravity Force Law: F = Gm₁m₂/r² which would have two terms: F = Gm₁m₂(f₁/r² + f₂/r) where f₁ would be a relevant factor at the "small" planetary scales and neglihible at the "big" galactic scales and inversely f₂ would be a relevant factor at galactic scales and neglihible at planetary scales. This could perfectly be done in Classical Physics but the question is if it cannot be done in Relativity Theory because seems this possibility isn't being considered. This would remove the necessity of the Dark Matter hypothesis...

Edited February 19, 2021 by martillo

[Markus Hanke]

10 hours ago, martillo said:

This could perfectly be done in Classical Physics but the question is if it cannot be done in Relativity Theory because seems this possibility isn't being considered.

I understood what you were trying to say, as this is an area I have been researching extensively myself.
Yes, it is possible to generalise MOND into the relativistic domain by introducing additional fields into the GR Lagrangian. Explicit examples are TeVeS (Tensor-Vector-Scalar gravity), GVT (gauge-vector-tensor gravity), STVG (scalar-tensor-vector gravity), various bigravity models, and quite a few others. So as you can see, this has indeed been considered, and a number of models have been developed. But as I pointed out before, all these models have problems of one kind or another - some make very good predictions in some areas, but fail in others; and some can be ruled out on observational grounds. None of these models has been successful enough to really replace the Dark Matter paradigm for now.