Testing MiHsC in Dwarf Galaxies

The best test of MiHsC is to find circumstances where it is likely to appear - that is, in systems in the deep of space with very low accelerations. I've recently been looking into some ideal candidates: Milky Way dwarf spheroidal galaxies. The Milky Way has lots of these tiny systems orbiting around it and some of them are so wispy that they should show up MiHsC, and they do. The plot below shows the five wispiest cases I could find that also have observations of their stars' orbital velocity. In the figure the x-axis shows the visible mass of the system (in Solar masses) and the y-axis (black squares) shows the velocity (km/s), for the dwarfs Segue-1, Triangulum-II, Bootes, Coma Berenices and Ursa Major 2. The error bars (uncertainties) are also shown.

The first thing that can be done is to calculate the maximum orbital speed that Newton would allow without the systems becoming gravitational unbound given their visible mass (general relativity predicts similarly). These maximum Newtonian velocities are shown with crosses and are much smaller than the stars' observed speed which implies that the dwarfs should explode centrifugally (inertially) because of the inability of their visible mass to bind them gravitationally. However, they look bound. Dark matter enthusiasts will no doubt say "Just add dark matter", but in the case of Segue and Triangulum-II you have to add 2600 and 3600 times as much dark matter as the visible matter, which makes the dark matter hypothesis look ridiculous.

Another possibility is to use MoND, Milgrom's empirical formula that modifies gravity or inertia, and the results of that are shown in the Figure by the triangles. MoND uses an adjustable parameter a0 of 1.8x10^-10 m/s^2 and also predicts too low a maximum velocity: outside the uncertainties in the observed velocities in all but one case: Coma Berenices, but it is much better than Newton, or 'naked' GR.

Finally, the predicted maximum velocity of MiHsC is shown by the diamonds (using the same method I used for full scale galaxies in the reference below). MiHsC is the closest to the observations and agrees, given the error bars, with all but one of the observations (Triangulum 2). It certainly performs the best, which is impressive given that, unlike dark matter and MoND it has no adjustability. My goal now is to emulate Gandalf and collect a few more dwarfs, the lighter the better.

References

McCulloch, M.E., 2012. Testing quantised inertia on galactic scales. A&SS, 342, 2, 575-578.  Preprint

Comparison of GR, MoND, MiHsC

One of the great advantages MiHsC has, and that doesn't seem to be appreciated, is that it fits a lot of data without needing adjustment, so here is a table to emphasize that. In the left hand column I've listed eleven anomalies and in the other columns I've used a colour code to show how the theories listed at the top (General Relativity, MoND and MiHsC) fit the data. If the theory can't fit the data because it would need ridiculous amounts of adjustment then I've coloured the square red. If the theory can fit with an adjustment that needs more than one arbitrary number to define it (eg: the addition of dark matter) I have coloured the square orange. If the theory needs adjustment with only one arbitrary number the box is green, and if it needs no adjustment at all the box is blue.

It is inevitably a vague comparison, but general relativity produces a lot of orange (it fits, but with a lot of adjustment) because of its flexibility, aided by huge numbers of scientists with computers, arbitrarily adding dark matter and energy. MoND, which is simpler and has only one adjustable parameter shows more green, but also some red, because it has less flexibility and, for example, it cannot cope with galaxy clusters, nor the new data coming from labs, like the Tajmar effect and Shawyer's emdrive. 

MiHsC performs well without needing adjustment at all (lots of blue). This is because I have designed it from the ground up with some of these anomalies in mind from the start. This is how science should be done: working from the data to a theory, not, as is done with general relativity, by fudging a revered theory to fit the data. The details of this table are open to debate, but MiHsC obviously performs best on this measure, and more generally: scientists should try to propose theories that produce a conclusive red or blue, not orange.