or any of the complicated relativistic extensions of MOND. Instead, consider

a minimalist definition: MOND is an algorithm (and a very simple

algorithm) which allows one to calculate the distribution of force in an

astronomical object from the observed distribution of baryonic matter.

And, as evidenced by rotation curves, it works! It works extremely well,

even explaining details in rotation curves which are clearly related to

corresponding details in the light or gas distribution. This fact is remarkable,

and it constitutes a severe challenge to CDM or to any dark matter that

clusters on the scale of galaxies. How can one image that dark matter

can reproduce this remarkable success of MOND? To think that

it could presupposes properties of dark matter that is totally at odds

with its perceived nature as a non-interacting (except for gravity),

non-dissipational fluid. The dark matter fluid is very different from

the baryonic fluid; the dm is immune from

influences that affect baryons: the baryonic fluid can dissipate — loose energy –,

it can be shocked, it can be removed by supernovae or stellar winds,

it can be swept out in collisions (e.g. the famous Bullet). Why then should

these two fluids be so intimately connected and similarly distributed

as to subsume the existence of the MOND algorithm? In fact, the success of

the MOND algorithm on the scale of galaxies is a falsification of CDM

or any dark matter that clusters on the scale of galaxies. To blandly

state that dark matter exists and accounts for the observations of

galaxy kinematics is to turn a blind eye to a vast range of phenomena;

to imagine that dark matter will someday, when we have more understanding

of the complicated baryonic physics, reproduce the correspondence

of rotation curves to the distribution of baryonic matter is a

leap of faith that is more akin to religion than to science. This goes as

well for the near perfect Tully-Fisher relation as pointed out by Stacy —

so perfect that the TF by itself implies a connection with physical

law rather than the messy details of galaxy formation. And how

will dark matter explain the ubiquitous emergence of a0 —

as the acceleration below which the discrepancy appears in galaxies,

as the normalization of the Tully-Fisher and Faber-Jackson relations,

as the internal acceleration of near isothermal systems ranging

from globular clusters to clusters of galaxies, and, when expressed

as surface brightness, as the characteristic (Freeman) surface brightness

of galaxies. If the putative dark matter particles are ever found

(and I doubt that they will be), then we have a lot of work ahead of us

to understand how these regularities, so neatly encapsulated by MOND,

emerge in the context of a non-interacting, dissipationless, dark matter fluid. ]]>

I agree with most of what you say. Effectively MOND “*kills DM+GR at Galactic Scales*” and effectively this means that “*GR needs modification*“.

I did not say that MOND works very well beyond Galactic scales. I said just the contrary and even explained why one must wait discrepancies: “*MOND is being applied outside its range of empirical validity*“.

I also wrote in this blog how, thanks to a new theory, **we do not need DM (neither DE) to explain observations beyond the Galactic scale anymore**.

FQXi Essays are limited in size by Contest rules, therefore I could not write about all the advantages beyond GR (my first draft Essay was over the size limit and I was forced to eliminate many interesting stuff! For instance, I gave some additional technical details, on how the new canonical theory goes beyond M-theory and the rest of quantum gravity approaches, in Dr. Tejinder Pal Singh Essay).

In despite of size limitations, details and further info are given in the cited literature and in the technical notes in my Essay. In the technical note in page 9, I explain the **assumptions and approximations over the which GR is based** and how we derive GR from a more fundamental theory. I explain how well-known problems of GR as “*the lack of gravitational energy-momentum-stress tensor*“, “*spacetime singularities*“, “*the problem of the systems of reference*“, “*violation of the usual conservation laws*“, and “*the impossibility to obtain a consistent quantization of such [geo]metric theory*” are absent in the new theory.

Moreover, I have commented in Dr. Corda Essay how we can already go beyond MOND, PCG, TeVeS… explaining data that those theories cannot explain, and also commented I have not still studied Pioneer anomaly enough to say.

]]>No MOND does not work very well beyond Galactic scales so we cannot conclude that at all. It is certainly possible, but we cannot determine that from the data alone. But that is not important MOND working at Galactic Scales kills DM+GR at Galactic Scales. This means GR needs modification. We don’t know what the correct theory is going to be. I am not a physicist or a mathematics. I am just a software developer, with an interest in the MOND problem. I can only conclude if a model is good based on its applications and what it predicts. Unfortunately I did not see much effort at resolving different problems of GR in the quoted essay. Particularly MOND and Pioneer Anomaly. ]]>

There is a third solution:

**1′) DM does not exist at all.**

“The fact that MOND does not work as well at cluster or higher scales…” This is only partially true

http://arxiv.org/abs/0704.0381

and, of course, discrepancies with MOND do not imply existence of DM, (ΛCDM has also difficulties http://adsabs.harvard.edu/abs/2010ApJ…718…60L), but that MOND is being applied outside its range of empirical validity and that a more general theory beyond MOND is needed.

As commented above (#101), MOND (and generalizations of it) can be derived from a truly general gravitational theory. You are right on that “the encompassing physical theory” was “discovered from a totally unexpected direction”!

Our goal was to correct other known deficiencies of GR (see the FQXi Essays cited above) and, as a bonus, we discovered that MOND and its acceleration scale were natural outcomes from the new theory.

If you look to my FQXi Essay, you will discover that the recent theory is much more general than Verlinde’s theory, which is based in a number of approximations and controversial assumptions.

]]>My problem is that the MOND fits the data without needing DM.

Since this simple equation works very well at the galactic scale everywhere. The fits actually keep on improving with more data. There can only be two solutions.

1) DM does not exist at Galactic scale.

2) DM position in space is defined by BMs position in space. This is simply untenable if we believe DM to be separate particles. Also BM is not supposed to interact with DM except by gravitational force. This is totally non-sensible

So the real solution is that DM does not exist at the galactic scale.

I would have had no problem with DM, if MOND did not work so well at galactic scale.

The fact that MOND does not work as well at cluster or higher scales makes no difference. It is probably an indication that some form of DM exists on those scales. I don’t even think that MOND can be enhanced to form a theory. TeVeS is just a toy theory that shows how to build one, but I am pretty sure the encompassing physical theory will be discovered from a totally unexpected direction. The recent Verlinde’s theory of Entropic gravity looks interesting.

I liken MOND to an Empirical law. Any quantum theory of gravity needs to bring out MOND or it is not physical. Since GR in its present form does not predict MOND, it is not physical.

It is as simple as that. Empirical laws must be explained by all physical theories. If Newtons gravitational theory did not explain Kepler’s laws, it would be as useless (at the solar system scale) as GR is presently (at the galactic scale).

]]>*Extended rotation curves of spiral galaxies – Dark haloes and modified dynamics. Mon. Not. R. astr. Soc. 1991: 249, 523-537. Begeman, K. G.; Broeils, A. H.; Sanders, R. H.*

Authors compare **three-parameter** dark-matter fits (M/L for the visible disk, plus two parameters for the dark matter halo: the core radius and the asymptotic circular velocity of the halo) with **one-parameter** MOND fits (M/L for the visible disk).

They find that **MOND works well and “in some cases better than multi-parameter dark-halo fits.”**

I am sorry to say this to dark-matter enthusiasts, but MOND rocks…

]]>MOND has **zero** parameters. It is the dark matter model which uses “free parameters that can be chosen to improve any fit” (as Question Mark says).

I invite you to read again the section 5.2 of Gentile et al.

http://arxiv.org/abs/1004.3421

**Two parameters for Burkert dark matter model** (central density and core radius).

**One/two parameters for the ΛCDM model** of Navarro, Frenk & White (concentration and virial mass). Gentile et al. use cosmological simulations to correlate both (see eq. 3), but due to bad fit to the data they repeated the fit leaving both parameters free (read section 6) and still obtained a bad fit and related difficulties.

**Zero parameters for MOND** (see equation 6).

Regarding http://arxiv.org/abs/1005.5456, the authors use M/L as a free parameter to correlate velocity with light distribution, **not** because M/L was a free parameter in MOND. MOND are equations 1 and 2 in that preprint and they have **zero** parameters.

If you were to repeat their analysis using dark matter models you would use one or two parameters (of the dark halo) **plus** the M/L ratio of the correlation to light.

I.e. using the Burkert dark matter model you have **three times more freedom** (rho_0, r_{core}, and M/L) and still cannot match MOND predictions.

Precisely, the fact that MOND has **zero** parameters is the reason which is so sensitive to uncertainties in distances, whereas the dark matter models can absorb distance uncertainties into the halo parameters.