Possibly the best way to test Quantised Inertia (except in the lab and the lockdown has postponed that for now) is to look at far distant (ie: high redshift) galaxies whose light is reaching us from an epoch a long time ago. This is because QI's predictions of galaxy rotation are very different from those of the standard model and MoND at high redshift. For the older theories the relation between the orbital speed of stars at the edge of galaxies (v) is of the type
v^4 = KM
where M is the visible mass and K, crucially, is a constant. How quaint! In quantised inertia the K is no longer a constant, since the inertial mass depends on the width of the cosmic horizon, and the formula is
v^4 = (2Gc^2/Theta)M
where G is the gravitational constant, c is the speed of light and Theta is the width of the cosmos, which varies with time. In the mainstream way of looking at it, this variation is because the cosmos is physically expanding. I prefer to assume that the information that local matter has about the cosmos is expanding, rather than the cosmos itself (this was also claimed by Halton Arp). Therefore in the past the cosmos, and Theta, were smaller and so, according to QI, all inertial masses and centrifugal forces were lower. Therefore far-off, ancient galaxies could afford to spin faster at the same mass and still remain bound.
As luck would have it, astronomers are just starting to see such galaxies and I talked about six of them in the paper referenced below (McCulloch, 2017). It turns out that they do indeed spin faster. Another one has just been seen at Z=4.2 which is called, romantically, DLA0817g or The Wolfe Disk (see Neeleman, 2020) and this means I can now compare QI with seven data points. I have summarised the data here:
The plot shows the observed acceleration of stars at the edge of the galaxies (y axis) and you can see that it increases with redshift (black dots). See the black dots. Note that the value for the galaxy at redshift Z=2.242 is aberrant and it looks like an outlier. The plot also shows (blue dots) the predicted accelerations assuming, as quantised inertia does, that the galaxies cannot slow below the minimum acceleration of 2c^2/Theta where Theta is the cosmic scale at the epoch the galaxy is in. So, to recapitulate, the higher redshift galaxies were in a smaller cosmos, so according to QI all inertial masses were lower, so they could afford to spin faster and still remain stable. You can see that the predictions of quantised inertia track the observed increase in spin quite well. This is not yet conclusive though, since maybe other effects are present. The next step is to compare what Newton/GR predicts for the same plot, but for that I need to find the masses of these systems, which is not as easy as it sounds since some masses are derived from the dynamics so include the dark matter fudge. What is clear from this is that the more high redshift galaxies we observe in this way the better!
Neeleman, M., J.X. Prochaska, N. Kanekar, M. Rafelski, 2020. A cold massive, rotating disc 1.5 billion years after the big bang. Nature, Vol. 581. Link
McCulloch, M.E., 2017. Galaxy rotations from quantised inertia and visible matter only. Astrophysics and Space Science, 362,149. Link