The best way to do incisive science is to find an empirical case that can discriminate between hypotheses, in this case dark matter, MoND and QI.
Galaxy rotation is not ideal in that respect. To recap: galaxies spin far too fast at their edges to be stable. They should fly apart, but they appear to be gravitationally bound. So astro-physicists have proposed that there is invisible dark matter in them to hold them together. One of the properties of this dark matter has to be that it stays spread out, otherwise it would collapse to the centre of the galaxy and not predict the rotation correctly. The problem is that although QI can predict galaxy rotation, dark matter can be 'fudged' to predict it too, and even MoND is tweakable (a0).
Something un-fudge-able is needed and wide binaries are brilliant examples of unfudgeability. I have discussed them before. They are binary stars so far apart that their accelerations are as low as they are at the edges of galaxies. Hernandez et al. (2018) have shown in some brilliant papers, that wide binaries orbit each other far too fast, just as galaxies do. The data I have used here is from his latest paper which uses brand-new GAIA data. The data is shown by the crosses in the Figure below (prepared by my new post-doc Jesus Lucio). The x axis shows the separation of the stars in parsecs and the y axis shows their mutual speed in km/s. The grey area shows the uncertainty in the data, so it means that the orbital speed at each separation is somewhere in the grey area.
The dotted line shows the prediction of Newton or of general relativity (the same in this case). Just as in galaxies, although Newton/GR says the orbital speed should decrease with radius/separation (dotted line), the observed speeds stay much higher. Beyond a distance of 0.2 parsecs both Newton and general relativity are falsified. These theories disagree with the data and dark matter cannot be added to these wide binaries to save them, because to fit the larger galaxy it must stay diffuse. Unless they now come up with quantum dark matter that can be simultaneously spread out and clumpy!
The prediction of MoND is shown by the dashed line here with its fitting parameter set to a0 = 1.3x10^-10 m/s^2. It under-predicts the data at 1 parsec but if we set a0 = 2x10^-10 m/s^2 then it just about fits. However, the MoND prediction should probably be closer to the Newtonian/GR curve because it is subject to the External Field Effect (still under debate) which means that external accelerations bring it back towards Newtonian behaviour. These wide binaries are close to the Sun, and so accelerations due to the galaxy are still on the order of 8x10^-10 m/s^2. So, MoND is possibly also falsified by this data.
The prediction of quantised inertia is shown by the solid line, with the error shown by the two lighter solid lines above and below it. QI agrees with all the data (just). I submitted a paper on this to MNRAS a few weeks ago including a plot similar to this one, but in which QI did not quite agree. Well, a sincere thanks to my post-doc who recently spotted a factor of two error in my calculations which was making QI seem worse than it is, and he corrected it. So we will now resubmit with the new result.
In summary, QI predicts the orbits of these 83 pairs of wide binary stars better than other theories. Furthermore, QI does it without the need for any arbitrary fitting parameters (MoND needs one). QI needs just the observed mass, the observed speed of light and the observed cosmic scale. QI can only predict one outcome, and that turns out to agree with the data.
Hernandez, X., R.A.M. Cortes, C. Allen and R. Scarpa, 2018. Challenging a Newtonian prediction through Gaia wide binaries. https://arxiv.org/abs/1810.08696
McCulloch, M.E. and J.H. Lucio, 2019. Testing quantised inertia on wide binaries. Submitted to MNRAS.